UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE BEHAVIOR …eml.ou.edu/paper/thesis/TZE-LIANG LEE.pdf · Figure 1-2: The original model pf the Rocker-Bogie suspension [courtesy by JPL]6 Figure

UNIVERSITY OF OKLAHOMA

GRADUATE COLLEGE

BEHAVIOR AND CONTROL OF A ROCKER-BOGIE SUSPENSION

UNDER RELATIVELY HIGH SPEED

A THESIS

SUBMITTED TO THE GRADUATE FACULTY

In partial fulfillment of the requirements for the

degree of

MASTER OF SCIENCE

By

TZE-LIANG LEE

Norman, Oklahoma

2002

BEHAVIOR AND CONTROL OF A ROCKER-BOGIE SUSPENSION UNDER RELATIVELY HIGH SPEED

A THESIS APPROVED FOR THE SCHOOL OF AEROSPACE AND

MECHANICAL ENGINEERING

BY _______________________________ DAVID P. MILLER – ADVISOR _______________________________ DONNA L. SHIRLEY _______________________________ KURT GRAMOLL

© Copyright by Tze-Liang Lee 2002 All Rights Reserved

iv

ACKNOWLEDGEMENTS

I would like to thank Professor David P. Miller for giving me the opportunity

to work on the research and for his guidance and technical assistance over the past

two years. Thanks to Dr. Kurt Gramoll and Dean Shirley for their advice and serving

in my committee. To the University of Oklahoma Aerospace and Mechanical

Machine shop, supervisor Mr. Billy Mayes, shop machinist Mr. Greg Williams and

part time students for their generous help and machining skills. I would have never

finished the construction and the experiment of the rocker-bogie test track without the

help from the AME shop staffs. Thanks to JPL for providing the rocker-bogie

drawings for this experiment.

I would like to thank my colleagues Mr. Justin Morgan, Mr. LiTan, Mr. Matt

Roman, and Mr. Tim Hunt for their considerable help in my research. Also, special

thanks to Mr. Carlos P. Borras for being a friend, mentor and for giving me for his

technical support and effort whenever I encountered problems. Thanks to all people

who read my thesis and transformed it into a proper English.

To my family, thanks for their support especially my mother Ms. Tay Chin-

Kan, father Mr. Lee Aik-Kien, Lee Tze-Wei(brother), Lee Tze-Lin(sister) for their

constant care and encouragement.

v

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ...................................................................................... iv

TABLE OF CONTENTS ........................................................................................... v

LIST OF FIGURES .................................................................................................. vii

LIST OF TABLES ................................................................................................... viii

ABSTRACT................................................................................................................ xi

Chapter 1 INTRODUCTION .................................................................................... 1

1.1 Background Reference ...................................................................................... 1 1.2 Description Of The Test.................................................................................... 3 1.3 Importance Of The Research ............................................................................ 4 1.4 Lessons We Hope To Learn From This Research ............................................ 4 1.5 Potential Capabilities ........................................................................................ 5

Chapter 2 DESCRIPTION OF FACILITY ............................................................. 7

2.1 Type of rocker bogie test track ......................................................................... 7 2.2 Experimental equipments................................................................................ 10

2.2.1 Obstacles ................................................................................................... 10 2.2.2 Strain Gauges ............................................................................................ 11 2.2.3 Power Plant ............................................................................................... 12 2.2.4 H-Bridge.................................................................................................... 12

2.3 Instrumentation ............................................................................................... 13 2.4 Development of LabVIEWTM Program.......................................................... 15

Chapter 3 MODEL DESIGN AND CONSTRUCTION........................................ 17

3.1 Model Design.................................................................................................. 17 3.2 Model Construction ........................................................................................ 19 3.3 Strain Gauges Preparation............................................................................... 21

3.3.1 Preparing the surface................................................................................. 21 3.3.2 The Wheatstone Bridge ............................................................................. 22 3.3.3 Mounting the Strain Gauges ..................................................................... 23

Chapter 4 TEST TRACK DATA ............................................................................ 25

vi

4.1 Force Calibration............................................................................................. 25 4.2 Mathematical Model Calibration.................................................................... 27

Chapter 5 RESULTS ................................................................................................ 30

5.1 Introduction..................................................................................................... 30 5.2 Horizontal Rocker-Bogie ................................................................................ 31

5.2.1 Front Wheel............................................................................................... 31 5.2.2 Middle Wheel............................................................................................ 45

5.3 Tilted Rocker-Bogie suspension..................................................................... 56 5.3.1 Tilted Rocker-Bogie Suspension Front Wheel ......................................... 57 5.3.2 Tilted Rocker-Bogie Suspension Middle Wheel ...................................... 66

5.4 Wheelie Maneuvers......................................................................................... 78 5.4.1 Comparison between non-wheelie and wheelie at speed of 1m/s............. 82 5.4.2 Further reduction of vertical shock ........................................................... 83

Chapter 6 CONCLUSIONS..................................................................................... 84

Chapter 7 RECOMMENDATIONS ....................................................................... 85

BIBLIOGRAPHY..................................................................................................... 87

Appendix A HORIZONTAL ROCKER-BOGIE FRONT WHEEL ................... 88

Appendix B HORIZONTAL ROCKER BOGIE MIDDLE WHEEL ............... 120

Appendix C TILTED ROCKER-BOGIE FRONT WHEEL.............................. 152

Appendix D TILT ROCKER-BOGIE MIDDLE WHEEL................................. 184

Appendix E Instrumentation ................................................................................. 217

Appendix F G-code for the wheel on CNC ........................................................... 222

Appendix G Interactive C programming Language for Handy-Board............. 224

vii

LIST OF FIGURES

Figure 1-1: The original model of FIDO rover [courtesy by JPL] ............................. 6 Figure 1-2: The original model pf the Rocker-Bogie suspension [courtesy by JPL] 6 Figure 2-1: Rocker Bogie Configuration.................................................................... 8 Figure 2-2: Isometric view: The rocker bogie is mounted on a slider shown above.

The sliders are then bolted on a test rig, which holds a conveyer belt. ..................... 8 Figure 2-3: Side View................................................................................................. 9 Figure 2-4: Front View ............................................................................................... 9 Figure 2-5: Rocker bogie climbs over an obstacle ................................................... 10 Figure 2-6: Wedge Obstacle ..................................................................................... 11 Figure 2-7: The Schematics of H-Bridge.................................................................. 12 Figure 2-8: SCB-68 Board Parts Locators Diagram [12] ......................................... 14 Figure 2-9: Impact.vi Front panel............................................................................. 15 Figure 2-10: The Block Diagram for the Impact.vi Front panel............................... 16 Figure 3-1: Wheatstone bridge configuration........................................................... 23 Figure 3-2: Installation of strain gauges ................................................................... 24 Figure 4-1: Relation between output excitation voltage and exerted force .............. 26 Figure 4-2: 2 lb weight for Force calibration............................................................ 26 Figure 4-3: Force calibration using 2 lb weight........................................................ 27 Figure 4-4: Graphical display of the mathematical calibration of the wheel............ 29 Figure 5-1: An output excitation voltage generated by the Front wheel at 0.5 m/s

while it goes over the 1- inch height wedge ............................................................. 31 Figure 5-2: Free body diagram of motor driven wheel............................................. 33 Figure 5-3: A graph of Impact force on Front wheel versus height of the wedge at

different speeds ........................................................................................................ 44 Figure 5-4: An output excitation voltage generated by the Middle wheel at 0.5 m/s

while it goes over the 1- inch height wedge ............................................................. 45 Figure 5-5: A graph of Impact force on Middle wheel versus height of the wedge at

different speeds* ...................................................................................................... 47 Figure 5-6: Tilted Rocker-Bogie suspension............................................................ 56 Figure 5-7: An output excitation voltage generated by the Tilted Rocker-bogie Front

wheel at 0.5 m/s while it goes over the 1- inch height wedge .................................. 57 Figure 5-8: A graph of Impact force on Front wheel versus height of the wedge at

different speeds for a Tilted suspension................................................................... 66 Figure 5-9: An output excitation voltage generated by the Tilted Rocker-Bogie

Middle wheel while it goes over the 1- inch height wedge ...................................... 67 Figure 5-10: A graph of Impact force on Middle wheel versus height of the wedge at

different speeds for a Tilted suspension................................................................... 68 Figure 5-11: The location of the two Infrared sensors for Wheelie.......................... 79 Figure 5-12: An Output excitation voltage generated on the Front vertical motor

mount as the Wheelie maneuver was performed ..................................................... 80 Figure 5-13: Output excitation voltage for Non-Wheelie......................................... 82 Figure 5-14: Output excitation voltage for Wheelie ................................................. 82

viii

LIST OF TABLES

Table 4-1: Results from the mathematical calibration of the wheel ......................... 28 Table 5-1: Behavior of the rocker bogie suspension when the Front Wheel hit a 1-

inch height wedge at speed 0.5 m/s ......................................................................... 36 Table 5-2: Behavior of the rocker bogie suspension when the Front Wheel hit a 1.5-

inch height wedge at speed 0.5 m/s ......................................................................... 36 Table 5-3: Behavior of the rocker bogie suspension when the Front Wheel hit a 2-











inch height wedge at speed 1 m/s............................................................................. 42 Table 5-14: Behavior of the rocker bogie suspension when the Front Wheel hit a 1.5-

inch height wedge at speed 1 m/s............................................................................. 42 Table 5-15: Behavior of the rocker bogie suspension when the Front Wheel hit a 2-

inch height wedge at speed 1 m/s............................................................................. 43 Table 5-16: Behavior of the rocker bogie suspension when the Front Wheel hit a 2.5-

inch height wedge at speed 1 m/s............................................................................. 43 Table 5-17 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1-

inch height wedge at speed 0.5 m/s ......................................................................... 48 Table 5-18 Behavior of the rocker bogie suspension when the Middle Wheel hit a

1.5-inch height wedge at speed 0.5 m/s ................................................................... 48 Table 5-19 Behavior of the rocker bogie suspension when the Middle Wheel hit a 2-

inch height wedge at speed 0.5 m/s ......................................................................... 49 Table 5-20 Behavior of the rocker bogie suspension when the Middle Wheel hit a

2.5-inch height wedge at speed 0.5 m/s ................................................................... 49 Table 5-21 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1-

inch height wedge at speed 0.7 m/s ......................................................................... 50

ix

Table 5-22 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1.5-inch height wedge at speed 0.7 m/s ................................................................... 50

Table 5-23 Behavior of the rocker bogie suspension when the Middle Wheel hit a 2-inch height wedge at speed 0.7 m/s ......................................................................... 51




Table 5-27 Behavior of the rocker bogie suspension when the Middle Wheel hit a 2-inch height wedge at speed 1 m/s............................................................................. 53



Table 5-30 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1.5-inch height wedge at speed 1 m/s ...................................................................... 54



Table 5-33: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 1- inch height wedge at speed 0.5 m/s .............................................................. 58

Table 5-34: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 1.5- inch height wedge at speed 0.5 m/s ........................................................... 58











x

Table 5-45: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 1- inch height wedge at speed 1 m/s ................................................................. 64

Table 5-46: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 1.5- inch height wedge at speed 1 m/s .............................................................. 64

Table 5-47: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 2- inch height wedge at speed 1 m/s ................................................................. 65

Table 5-48: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 2.5- inch height wedge at speed 1 m/s .............................................................. 65

















xi

ABSTRACT

The goal of the overall research program to which this thesis work will

contribute is to characterize the behavior of a rocker-bogie chassis as it encounters

obstacles at high speeds. Towards this end we will determine the 2-D kinematics and

dynamics performance of the rocker bogie chassis suspension when it crosses over

trapezium shape of wooden obstacles ranging from 1 inch height to 2 ½ inches height,

under variable speed capable of exceeding 0.1 m/s. Obstacles will clearly present a

difficult task to the rocker bogie, and it is important to develop an optimized set of

speed limits for the rover to be able to traverse in a stable condition. The scope of this

thesis is focused on the measuring of impact in longitudinal direction; and the

stability of the rocker bogie. In addition, the rocker bogie will perform an

unconventional maneuver called a “wheelie maneuver” in which the speeds among

the three wheels are varied so that they take advantage of the design to allow one of

the wheels to be forced into the air. The “wheelie maneuver” experiment will be

compared to the conventional maneuvers in terms of impact force. The experiment is

to determine the extent that the impacts can be reduced through the use of the wheelie

maneuvers.

1

Chapter 1 INTRODUCTION

1.1 Background Reference

In January of 1999, NASA conducted the first Astronaut-Rover (ASRO)

Interaction field experiment at Silver Lake in California’s Mojave Desert. In the

context of the human exploration of the Solar System, the interaction of the astronaut

and the rover as a complementary and interactive team is critical to assess. In this test,

a semi-autonomous rover, the NASA Ames Marshokhod was used to carry out

several tasks. There were four main science scenarios and detailed operational

procedures were tested during the ASRO test: First, the rover as a scout; Second, The

rover as a video coverage assistant; Third, The rover as a field science assistant;

Fourth, The Rover as a Field Technician Assistant.[1] In the last scenario, the rover

was used to carry tools and samples to the suited astronaut. These scenarios represent

four possible mission scenarios of astronaut-rover interaction in the field. The goal is

to evaluate the effectiveness, robustness and sequence of execution. In these scenarios

astronauts-rover interaction is a new, and important aspect that requires new and

better-adapted tools, as well as revolutionary exploration strategies.

A few issues were discovered which limit the utilization of the rover for the

astronaut. One of the operational problems that was immediately apparent during the

ASRO test, was that the rover was unable to keep pace with the astronaut causing the

astronaut to spend too much time either waiting or going to the rover to get tools or

soil samples [3,4]. Some tests with faster commercial robots show that these rovers

have difficulty following astronauts into areas of cluttered terrain; they will tip over

due to their high center of gravity.

2

The Field Integrated Design and Operations robot (FIDO) is an advanced

robot vehicle developed by the Jet Propulsion Laboratory (JPL) for future missions to

Mars. FIDO will conduct some experiments in 2001 and 2002 to assist the Mars

scientists and operations personnel by allowing them the opportunity to operate a

fully-instrumented rover within challenging geological terrains on Earth that are

similar to the planet Mars. The rocker-bogie design used by the FIDO has six

independent motors driving each of six wheels. These wheels are mounted to a

differential joint on two rocker arms. Each rocker has a rear wheel connected to one

end and a secondary rocker, called a bogie, connected to the other. At each end of the

bogie is a drive wheel, and the bogie is connected to the rocker with a free pivoting

joint (Bickler 1992)[7]. The dynamics and climbing capabilities of a high-speed

rocker-bogie system operating in natural terrain is yet to be known. A high-speed

rover is not intended due to the limitation of energy sources, computers, and the

payload. However, the problem faced by ASRO missions is significant, therefore the

need for the rocker-bogie system to operate at human walking speed (approximately

1m/s) is highly recommended. [2]

3

1.2 Description Of The Test

In order to test the behavior of the rocker-bogie suspension under high speed,

the AME Robotics Lab had constructed the rocker-bogie test track (Fig 2-2). This

consists of a non-powered conveyor belt and the left side of the rocker-bogie

suspension. As the wheels turn, they move against the belt that also turns. The

vertical motor-mounts that hold the wheels are installed with strain gauge force

sensors. These tests are to determine the capabilities of this suspension system at

human walking speed, and to apply some control strategies for the wheelie maneuver.

This mock-up runs ten times faster than the original. At the speed of 0.1 m/s,

as the front wheel is climbing over the obstacle the second and third wheel will try to

push from the back. This will increase the traction of the rover, because the second

and third wheels are still on the horizontal. We know the original rover can go over

obstacles, but what is the shock of doing so at ten times faster? Does dynamically

changing the middle wheel speed, and thus the wheel configuration at impact reduce

the shock?

The mock-up will be sitting on a non-powered conveyer belt. In order to get

higher torque output, a 15 V motor is mounted on each wheel, and the three wheels

are going to turn the conveyer belt. The purpose of the first stage of the experiment is

to test if the rover can safely traverse over wooden trapezoids ranging from 1 inch to

2.5 inches height with all wheels running at equal speed. The second stage of the

experiment will be running the motor number 2 at a higher speed, while varying the

speed of 1st and 3rd motors using PWM control. In the second stage, we would like to

characterize its climbing capability by pre-lifting the rocker (wheelie maneuver), as

4

mentioned earlier. The third stage of the experiment is to test a variable speed on each

wheel.

1.3 Importance Of The Research

Recently, there has been significant improvement in semi or fully autonomous

planetary rovers for exploration, but there remain challenges for scientists and

engineers to solve. The stability, the control and the behavior of the rover are the

main focus of the research. With the increase of autonomy and speed capability of the

rover, there is a higher possibility of the rover running into a stall and even damaging

the suspension. The fundamental motivation of this experiment work is to allow the

rover to traverse an obstacle at a higher speed then has been previously done, and to

be able to better characterize what the upper safe speed limit may be, which the

current existing rovers failed to reach. The potential application of this research

includes urban search and rescue & military surveillances [1] in which speed is

important.

The focus of the research is to predict the impact force on the mock up rover

when it runs over an obstacle. We are going to see if there is any risk on the rocker-

bogie suspension system traveling at high-speed situation. Due to the high speed of

the rover (1m/s), both static and dynamics forces are considered in calculating the

rover’s stability.

1.4 Lessons We Hope To Learn From This Research

The original FIDO has been successfully demonstrated; the design minimized

the pressure on the wheel, while maximizing the wheel traction and the ability for the

rover to go over an obstacle.

5

The challenge that lies ahead is to determine how much the impact force is

reduced or increased with the change of the speed. Furthermore, we need to

determine if the unconventional wheelie maneuver is an important control strategy.

1.5 Potential Capabilities

The rocker bogie has previously been shown to be able to traverse over an

obstacle at the slow speed of 0.1 m/s. There is a possibility for the rocker bogie

suspension to operate under higher speed, which will greatly expand its utility. A

rover fitted with a high-speed rocker bogie may assist an astronaut on the Moon or

Mars by running back and forth between a geological site and spacecraft under high

speed, without jeopardizing the rover.

6

Figure 1-1: The original model of FIDO rover [courtesy by JPL]

Figure 1-2: The original model pf the Rocker-Bogie suspension [courtesy by JPL]

7

Chapter 2 DESCRIPTION OF FACILITY

2.1 Type of rocker bogie test track

PRESENT RESEARCH

This project describes a mock up model for FIDO, which simulates only one

side of the six-wheeled passive suspension system, known as the rocker bogie

suspension. This suspension, patented by JPL in the mid-90’s, consists of 6 powered

wheels arranged in 2 sets of 3 wheels per side. The wheel has a diameter of 7.876

inches. A free pivot connects the bogie at point A (Figure 2-1), which holds the front

and middle wheel, to the rocker arm, which connects the rear wheel to the body. In

this mockup, the rocker joints of the suspension connect to and support the main

chassis of the rover through a shaft attached to two sliders. Originally, the sliders

were meant for office drawers. The sliders are mounted to the shaft at point B

together with two tall vertical members. The vertical members are used to hold the

rover over the conveyer belt.

8

Figure 2-1: Rocker Bogie Configuration

Figure 2-2: Isometric view: The rocker bogie is mounted on a slider shown above. The

sliders are then bolted on a test rig, which holds a conveyer belt.

9

Figure 2-3: Side View

Figure 2-4: Front View

10

Figure 2-5: Rocker bogie climbs over an obstacle

2.2 Experimental equipments

2.2.1 Obstacles

Rovers for planetary exploration in the future will need to travel several

kilometers over long periods. Simple analysis of the mobility of the rocker bogie

suspension must be developed and evaluated. It is important to predict if the rocker

bogie can successfully negotiate a given obstacle at high speed, without being tipped

over or stranded.

The obstacles used in the experiments are trapezoid wedges. The obstacles are

place on the conveyer belt, and the powered wheels drive the belt, which carries the

obstacle. There are 4 different heights (h) for the wedge obstacle, 1-inch, 1.5 inch, 2

inches and 2.5 inches. Each of them has 45o angle of inclination and 3.5 inches wide.

11

Figure 2-6: Wedge Obstacle

The front bogie is allowed to pivot ± 45o from the horizontal. The entire

structure of the mock up will be tested on its dynamics and rigidity using strain

gauges. FIDO needs to use the full potential of its mechanical system in a harsh and

unplanned environment. LabVIEW from National Instrument will serve as the data

acquisition equipment for this experiment.

2.2.2 Strain Gauges

As the rover traverses across the obstacle, the rover will slide upwards

depending on the sizes of the obstacles. At the same time, the strain on the rocker

bogie will be measured. When force is applied to the rocker bogie, it deforms. This

deformation is known as strain. Strictly speaking it means deformation per unit

length. The strain is measured with bonded resistance strain gauges [6]. The strain

gauges will only be mounted on the vertical member of the rocker bogie. Both

compressive (negative) and tensile (positive) strain will be measured.

12

2.2.3 Power Plant

Maxon Motor manufactured the motors that used by in the experiment. Each

motor has a power of 90W, nominal voltage of 15V capable of achieving an RPM of

7070 without load, a reduction of 86:1 planetary gear head, and a digital HP encoder.

The motor is not the original motor that is used by the existing FIDO rover.

A handy board (www.handyboard.com) is used for the speed control of the

motors, while external H-bridges are for the amplification of the power for the

motors. A digital video is used to measure the speed of the rover.

2.2.4 H-Bridge

Figure 2-7: The Schematics of H-Bridge

13

To reverse or change the speed a DC motor, one must be able to reverse or

control the magnitude of the current in the motor. The easiest way to do this is using

an H-bridge circuit. The basic operation of an H-bridge is very straightforward.

Current control is implemented as a switch strategy where the switching duty cycle is

varied according to the command given by the experiment. This switching strategy is

known as pulse width modulation (PWM). The handy board has built in library

routines to generate a PWM signal for any given duty cycle.

2.3 Instrumentation

The instrumentation used to measure the impact signal from the strain gages

consists of one data acquisition board, one signal amplifier, and one PCI card. The

data acquisition board is a National Instruments NI 6023E. The board utilizes a

twelve-bit analog to digital converter. It has a sixteen channel multiplexer to give it

the capability of scanning sixteen single ended inputs or eight differential inputs. It

has a scan rate of 200k samples per second. In order to achieve better common mode

rejection, the board was set in the differential operation mode. Shielded cables were

used and pair wires were twisted to reduce the effect of EMI (Electro-Magnetic

Interference). An instrumentation amplifier was used in order to provide the required

amount of excitation voltage and output amplification for the strain gauges. Four fine

insulated wires (0.01” diameter) were braided together and connected to the

Wheatstone Bridge. The signals were transmitted through the doubly shielded twisted

wires to the SCB-68 board.

14

Figure 2-8: SCB-68 Board Parts Locators Diagram [12]

15

2.4 Development of LabVIEWTM Program

The program LabVIEW was used as the interface between the experimenter

and the data acquisition board. LabVIEW was chosen for several reasons. Two of

these are the easy programming and its execution speed. LabVIEW is a graphical

programming environment that obtains its speed by compiling the graphical flow

diagram or “VI” (Virtual Instrument, development environment based on the G

programming language) for data acquisition and control, data analysis and data

presentation.

Figure 2-9: Impact.vi Front panel

Figure 2-9 shows the front panel for the Impact “VI” which was written to

provide a graphic display for the data acquisition system. There are three basic

16

functions in the Impact Front panel. First the program takes the measured impact

forces from the data acquisition board at a sample rate set by the experimenter.

Second, the program then display the impact forces with respect to time. Third, the

program will automatically save the data into a spreadsheet file, where the data can be

analyzed.

Figure 2-10: The Block Diagram for the Impact.vi Front panel

17

Chapter 3 MODEL DESIGN AND CONSTRUCTION

3.1 Model Design

A variable geometry model was built in order to circumvent the need to make

multiple models with different configurations. Basic geometric properties were varied

and the force analysis assessed through the conveyer belt test.

The model was constrained by two significant requirements. Each requirement

was examined and proper consideration was exercised to take into account the

influences of each sizing of the model.

The first constraint was that of the geometric design. The dimension of the

rocker-bogie design was based on the FIDO rover. The design was to ensure that the

dynamic similitude is enforced. Dynamic similitude is the condition when the test

suspension has the same initial condition at the same position as the FIDO rover. This

will ensure that the impact force on the vertical member will be very similar to that of

the FIDO rover. Then the impact analysis of the model can be reliably compared with

the real FIDO rover when it is traveling at the speed of one meter per second. The

dynamics similitude was achieved by making the distance between the wheels exactly

the same as the FIDO rover. The distance between the pivot and the wheels are also

exactly the same as the FIDO rover. The scale selection was driven by the

requirement that the model simulate the rocker-bogie, therefore a scale of 1:1 was

chosen.

The second requirement was there must be high traction generated between

the wheels and the conveyer belt during the motion. Therefore rubber material was

glued on the aluminum wheel to prevent any slippage between the wheels and the

18

conveyer belt, so that there is no loss in speed. This is to ensure there is enough

friction for the suspension to move the conveyor belt.

The actual FIDO model traverses at extremely slow speed, all previous

stability and performance calculations were performed at these low speed. In this

project the speeds were chosen to be 0.5 m/s, 0.7 m/s, 0.8 m/s and 1.0 m/s. The speed

was calculated using a digital video. The encoder mounted on the motor was used to

give the confirmation of accuracy for the digital video. Using this cruise condition,

the RPM of the motor was obtained from the digital video and the speed of the

suspension was then calculated. The display screen on the oscilloscope gives the

information of the RPM of the motor from the encoder.

The pivot point of the rocker-bogie in this project is located at approximate

35% of the suspension length, which is typical of current existing rocker-bogie rover

at this time period. There are two bearings at the pivot point. The JPL has optimized

the location of the pivot at this position for the speed of one mile per day and the size

of obstacle it will run into.

19

3.2 Model Construction

Model materials were chosen to meet the strength requirements and which

could be easily manufactured with the facilities available at the University of

Oklahoma, Aerospace and Mechanical Engineering machine shop. Except for the

wheels, rollers, and other parts that required tight tolerance and precision were

manufactured on the lathe and CNC (Computer Numeric Control) machine. Other

parts were made using press drill, hand drill, and band saw.

The whole body was made of aluminum. The construction process involved

five steps. The first step was to design each parts of the suspension model and

assemble it in Pro/Engineer®. The design and modification can be easily done in

Pro/Engineer. Manufacturing of the actual parts were printed and being constructed

in the AME shop. Second, the three motor mounts were made using the CNC

machine; the motor mounts are 9.5 inches in length, 2.625 inches wide, and 0.5 inch

thick. There is a ¼ inch deep-faced mill up to 1.6 inches from base of the motor

mount. This is to ensure all three wheels boss are able to fit onto the motor mounts.

The bosses are held by 4 countersunk screws to each wheel, and the motor shaft was

slid into the boss. A setscrew was introduced into the boss to ensure that the backlash

between the motor and the wheel were kept to a minimum.

In all parts, from the wheel to the motor mount, there has been a tremendous

amount of weight reduction. Six through holes were drilled on each of the 7.876

inches diameter aluminum wheels 60-degree angle apart, to reduce the load on the

motors, and increase the RPM simultaneously. Each hole measures 1.75 inches in

diameter and 2.4 inches away from the center point of the wheel. The weights of the

20

motor mount were reduced 50% by cutting through a rectangular hole across. This

will ensure there is enough flexibility at the vertical member when the bending stress

was applied as the wheel runs into an obstacle. The constructions of wheels were

based on a written G-code for the CNC machine.

The three wheels rover was sitting on the 84-inch long conveyor belt. The belt

is fastened onto two rollers on both ends of the test rig. The roller is manufactured out

of 3 inches diameter, 6 inches long cylinder. There are two huge rings (3-inches inner

diameter; 3 ½ inch outer diameter and half an inch wide) on each roller to keep the

conveyor belt to come off from the roller as it turns. The rings are press fit and set-

screwed onto the rollers. There are two ball bearings on both sides of the cylinders to

make sure the friction was kept to a minimum as the conveyor belt is running.

There are six supports for the conveyor belt; three of them consist of a single

1-inch diameter roller. The rest support the wheels and consist of two 1-inch diameter

rollers for each wheel.

The test track is to simulate the rocker-bogie suspension moving on the

ground. At the differential point where the body would normally be mounted, the

frame is mounted to two vertical bearings that are attached to the conveyor belt

frame. As the wheels turns, the conveyor belt also turns [2]. The purpose of the

vertical bearing is to make sure the suspension to cross over an obstacle; as it should

behave on a real model. Caution need to be taken as the experimenter need to make

sure that both of the vertical bearings need to slide up and down simultaneously.

Otherwise, the rocker-bogie suspension will be misaligned and causes it to lean at an

angle. Therefore, a wooden block (5 1/3” x 5 1/3” x 1 ½”) was installed between the

21

two vertical bearings. A horizontal 5 1/3” long ½ inch diameter aluminum rod was

added between the vertical bearings for extra reinforcement.

A sagging conveyor belt will cause slippage, as the wheels turn. This must be

eliminated. To make sure the conveyor belt is fully stretch, a tensional was made to

push on one of the conveyor belt roller in the direction where the rocker-bogie

suspension were traveled. The tensional are made up by two simple mechanical

systems. The front big roller is mounted on the frame on a pivot point. There are two-

¼ inch bolt mounted on the frame responsible to push the pivot, one on each side of

the frame. To further enhance the tension, the experimenter has added another 1-inch

diameter roller at the bottom of the conveyor belt, so that the belt runs over the roller.

This is the third point of support for the conveyor belt.

As the rocker-bogie travels at high speed (1 m/s), it will cause a left and right

vibration on the high frame that host the vertical bearings. The solution of eliminating

the vibration is to add three horizontal 1 ½ x 1 ½ inch square tubing at the bottom of

the test track. These three square tubing were riveted to the conveyor belt frame from

left to right.

3.3 Strain Gauges Preparation

3.3.1 Preparing the surface

Two motor mounts were fastened to both ends of the Front Rocker by ¼ inch

nuts and bolts. The entire experiment was focus on the Front Rocker. The motor

mounts which facing the direction of motion was faced machine and polished, for the

installation of strain gauges. For optimum performance, standard procedure provided

22

by the manufacturer was followed. Excess oil, grease and other contaminants had to

be removed using rags soaked in acetone.

3.3.2 The Wheatstone Bridge

To measure minute strains, the user must be able to measure minute resistance

changes. The Wheatstone Bridge configuration. Shown here in Figure 3-1, is capable

of measuring these small resistance changes. In addition, this configuration will help

to keep the measurement error to a minimum due to the change in temperature. Note

the signs associated with each gauge numbered 1 through 4.

The total strain is always the sum of the four strains. The total strain is

represented by a change in Vout. If each gauge had the same positive strain, the total

would be zero and Vout would remain unchanged. The actual arrangement of the

strain gauges will determine the type of strain you can measure and the output

change. For example, if a positive (tensile) strain is applied to gauges 1 and 3, and a

negative (compressive) strain to gages 2 and 4. [9] When this happens, the sensors

will act as the force sensor.

23

Figure 3-1: Wheatstone bridge configuration

3.3.3 Mounting the Strain Gauges

Four strain gauges are mounted on the forward and opposite sides of the

vertical motor mount. These four strain gauges served as force sensors for bending

effect on a cantilever beam.

24

Figure 3-2: Installation of strain gauges

25

Chapter 4 TEST TRACK DATA

4.1 Force Calibration

In order to develop a relationship between the output voltage excitation and

the impact force, a calibration method was generated. First, the rocker-bogie was

rotated 90o and clamped onto a vertical surface (Figure 4-3). A weight scale was used

to calibrate the force on the vertical motor mount, as the weight was hanging onto the

wheel pulling under the force of gravity. A force applied on a aluminum bar mounted

as a cantilever beam will produce a shear stresses and bending stresses on the bar.

These strain gauges are actually measuring the bending stresses of the beam, which

are proportional to the load. As the force was increased, by adding additional weights,

the output excitation voltage increased. The output excitation voltage was measured

using LabVIEW virtual instrument panel. A graph was generated between the output

excitation voltage and exerted force. This is a linear relationship; where the exerted

force is directly proportional to the output excitation voltage.

A useful law of conservation of momentum is assumed in this experiment.

This is an empirical observation, which appears to apply universally. In an impact the

total momentum of any number of impacting bodies always remains constant,

although the momentum of individual bodies within the system can vary and energy

losses can occur. Impact and momentum balances are used mainly in situations in

which the duration of the force is so short that no significant displacement occurs

before it is over. [11]

26

Figure 4-1: Relation between output excitation voltage and exerted force

Figure 4-2: 2 lb weight for Force calibration

27

Figure 4-3: Force calibration using 2 lb weight.

4.2 Mathematical Model Calibration

All four strain gauge have the same value, by symmetry, the voltage at B and

D must be the same, so Vout must be zero when balanced. The bridge is balanced, a

starting condition for the system, before every strain gauge is stretched. As the strain

gauges are stretched, the bridge became unbalanced and the value of Vout will change.

Vout is proportional to the change in gauge resistance. [10] By Ohm’s Law, the

current flows through branches ABC and ADC in Figure 3-1 are

1 2

inABC

VI

R R=

+

3 4

inADC

VI

R R=

+

28

Vin is the voltage supply to the Wheatstone bridge, The voltage drop across

R2, VB – VC is IABC times R2, the voltage drop across R3, VD – VC is IADC times R3,

then Vout is equal to VD – VB. Therefore,

3 2

3 4 1 2

in inout

R V R VV

R R R R= −

+ +

Generate common denominator,

3 1 2 4

3 4 1 2( )( )out in

R R R RV V

R R R R−

=+ +

To verify the results that had been taken from the LabVIEW, and to proof the

above equation, resistance of each of the strain gauges were taken from each force

calibrations. Given that the AC voltage supply Vin is 120V, the output excitation

voltage can be calculated. The results on Figure 4-4 are consistent with the LabVIEW

results in Figure 4-1.

2 lb 4 lb 6 lb 8 lb 10 lb Resistor no. R (Ohm) R (Ohm) R (Ohm) R (Ohm) R (Ohm)

1 54.1 51 51.8 50.6 502 54.1 51.2 51.1 50.5 49.63 54.4 51.2 50.9 51.2 50.14 54.3 50.8 51.3 50.9 50

V(out) 0.05519779 0.11787729 0.17332961 0.23564493 0.30090392

Table 4-1: Results from the mathematical calibration of the wheel

29

Figure 4-4: Graphical display of the mathematical calibration of the wheel

30

Chapter 5 RESULTS

5.1 Introduction

The results are separated into three major sections; first, results related to the

behavior of the front and middle wheel of the horizontal rocker-bogie configuration;

second results that related to the behavior of the front and middle wheel for 20 degree

tilted rocker-bogie configuration; and third results that related to the wheelie

maneuvers done by the both horizontal and tilted rocker-bogie configuration. For the

behavior and data analysis sections, all three results are examined.

Data that was obtained from the experiment are strain gauge voltage with

respect to number of samples at speed of 0.5 m/s, 0.7 m/s, 0.8 m/s and 1 m/s running

into 1”, 1.5”, 2”, and 2.5” height wedges, except the wheelie maneuver was

performed only at the speed of 1 m/s. All the data acquisition frequencies are set at

1000Hz.

31

5.2 Horizontal Rocker-Bogie

5.2.1 Front Wheel

This is a graph where data were collected from strain gauges mounted on the

Front wheel to read the impact force exerted by the wedge. Impulse and deceleration

of the front motor mount at speed 0.5 m/s over 1” height wedges can be calculated

from the output excitation voltage.

A B C D E F

Figure 5-1: An output excitation voltage generated by the Front wheel at 0.5 m/s while it goes over the 1-inch height wedge

Explanations

32

A - Signal where the suspension traveling at 0.5 m/s without running into a wedge

B – Signal where the Front wheel first hit the wedge

C – Signal where the Front wheel climbs over the wedge

D – Signal where the impact on the Second wheel transmitted back to the Front wheel

by the wedge

E –Signal where the Middle wheel climbs over the wedge transmitted back to the

Front wheel

F – Signal where the impact on the Rear wheel transmitted back to the Front wheel

The valuable information from the Output excitation voltage is the impulse and

momentum of the Rocker-bogie suspension. Impulse is defined as force multiply by

time, as applying on instantaneous velocity change to the mass so that,

2

1

t

tI Fdt= ∫

where I is impulse F is force and t is time. The units for Impulse are lbs (pound

second). Momentum is defined as mass multiplied by velocity, which has a same unit

as Impulse. Impulse and momentum can be related by Newton’s second Law of

motion.

dvF M

dt=

Fdt Mdv=

Integrating both sides,

2

1

t v

t uFdt Mdv=∫ ∫

Gives ( )I M v u= −

33

From the Output excitation voltage graph, the magnitude of force can be

calculated by referring to Figure 4-1, the Force and voltage relationship equation V =

0.03 F + 1 x 10-16. Impulse of the First wheel when it hits the wedge obstacle can be

determined by the area under the pulse. In Figure 5-1, notice that the signal where the

suspension traveling at 0.5 m/s without running into a wedge is in negative moment.

This can be explained by a free body diagram of a motor driven wheel below Figure

5-2.

Figure 5-2: Free body diagram of motor driven wheel

As the motor is driving the wheel, there is a frictional force and a moment

from the wheel acting on the conveyer belt. According to Newton’s Third Law of

motion, there is reaction force pushing on the wheel in the opposite direction. This

reaction force causes the negative moment on the Output excitation voltage.

34

The goal of the experiment is to find out the impact forces, the final velocity,

and the deceleration of the rocker-bogie when it hits the obstacle. From the Figure 5-

1, the area under the pulse at B can be calculated. The rapid change in the pulse at B

is due to the impact of the obstacle on the first wheel. Information of maximum

impact force, velocity at the maximum impulse, the deceleration of the suspension

can be found here.

Sample calculation:

Area 1: The magnitude of the voltage is

V = 0.054 + 0.051 = 0.105

The Force and voltage relation can determine the Force determined by V = 0.03 F

+ 1 x 10-16

0.105

3.50.03

F lb= =

F = 15.57 N

The time duration of the first spike can be determined by reading the number of

samples (1145 1068)

0.0771000

t s−

= =

The area under the spike is the impulse, 15.57 0.219I Ft x= =

I = -1.198 Ns

The velocity at maximum impact, I

v uM

= +

1.198

0.57.275

v = − +

v = 0.335 m/s

35

The deceleration can be obtain by v u

at− =

0.335 0.5

0.077a

− =

= - 2.143 m/s2

36

Average 1 inch height wedge v(initial) 0.5m/s time of impact 0.0734s Impact Force 14.94595N V(final) 0.350104m/s Deceleration -2.05443m/s2

xi xi-average (xi-average)2 16.013 1.067048 1.13859143

15.5687 0.622748 0.38781507 13.3446 -1.60135 2.56432823

14.53079 -0.41516 0.17235949 15.27215 0.326198 0.10640514

Sum 4.36949936 variance 0.87389987 Standard Deviation of impact Force 0.93482612N Table 5-1: Behavior of the rocker bogie suspension when the Front Wheel hit a 1-inch height wedge at speed 0.5 m/s

Average 1.5 inch height wedge v(initial) 0.5m/s time of impact 0.0546s Impact Force 16.33972N V(final) 0.377366m/s

Deceleration -2.24601m/s2

xi xi-average (xi-average)2 17.34798 1.008259 1.01658554 16.31007 -0.02965 0.0008792 15.86525 -0.47447 0.22512305 16.31007 -0.02965 0.0008792 15.86525 -0.47447 0.22512305

Sum 1.46859003 variance 0.29371801 Standard deviation of impact Force 0.54195757N Table 5-2: Behavior of the rocker bogie suspension when the Front Wheel hit a 1.5-inch height wedge at speed 0.5 m/s

37


xi xi-average (xi-average)2 15.86525 -1.09722 1.20389027 17.49625 0.533781 0.2849218 16.31007 -0.6524 0.42562489 18.08935 1.126881 1.26986004 17.05143 0.088961 0.007914

Sum 3.19221099 variance 0.6384422 Standard Deviation of impact Force 0.79902578N Table 5-3: Behavior of the rocker bogie suspension when the Front Wheel hit a 2-inch height wedge at speed 0.5 m/s



xi xi-average (xi-average)2 19.12726 0.711712 0.50653397 18.83071 0.415162 0.17235949 17.34798 -1.06757 1.13970143 18.08935 -0.3262 0.10640514 18.68244 0.266892 0.07123134


38


x i xi-average (xi-average)2 15.86525 -0.17792 0.0316572 15.27215 -0.77102 0.594479 16.01352 -0.02965 0.0008794 16.75489 0.711715 0.5065387 16.31007 0.266895 0.0712331

Sum 1.2047875 variance 0.2409575 Standard deviation of impact Force 0.4908742N Table 5-5: Behavior of the rocker bogie suspension when the Front Wheel hit a 1-inch height wedge at speed 0.7 m/s



x i xi-average (xi-average)2 17.34798 0.771021 0.5944739 16.75489 0.177931 0.0316596 16.16179 -0.41517 0.172365 16.31007 -0.26689 0.0712296 16.31007 -0.26689 0.0712296


39


x i xi-average (xi-average)2 17.94107 -0.11121 0.01236729 16.90316 -1.14912 1.32047294 17.49625 -0.55603 0.30916751 19.86863 1.816352 3.29913338




x i xi-average (xi-average)2 21.79618 1.927553 3.71546185 18.83071 -1.03792 1.07727101 19.27553 -0.5931 0.35176366 20.60999 0.741363 0.54961959 18.83071 -1.03792 1.07727101


40


x i xi-average (xi-average)2 16.60661 -0.97861 0.9576723 17.7928 0.207583 0.0430906

19.86863 2.283413 5.2139734 17.34798 -0.23724 0.0562816 16.31007 -1.27515 1.6260007




x i xi-average (xi-average)2 17.7928 -0.38551 0.1486185

17.94107 -0.23724 0.0562831 18.08935 -0.08896 0.007914 17.94107 -0.23724 0.0562831 19.12726 0.948949 0.9005048


41


x i xi-average (xi-average)2 19.57208 1.126877 1.26985252 18.08935 -0.35585 0.12663112 18.08935 -0.35585 0.12663112 18.08935 -0.35585 0.12663112 18.38589 -0.05931 0.00351799

Sum 1.65326388 variance 0.33065278 Standard 0.57502415N Table 5-11: Behavior of the rocker bogie suspension when the Front Wheel hit a 2-inch height wedge at speed 0.8 m/s



x i xi-average (xi-average)2 20.60999 -0.05931 0.00351799 20.16517 -0.50413 0.25414975 20.90654 0.237237 0.05628155 21.35136 0.682057 0.46520221 20.31345 -0.35585 0.12663112


42

Average 1 inch height wedge v(initial) 1m/s time of impact 0.09s Impact Force 18.03992N V(final) 0.781473m/s Deceleration -2.47971m/s2

x i xi-average (xi-average)2 18.83071 0.790788 0.62534531 18.23762 0.197698 0.03908441 17.05143 -0.98849 0.97711687

Sum 1.64154659 variance 0.5471822 Standard deviation of impact Force 0.73971765N Table 5-13: Behavior of the rocker bogie suspension when the Front Wheel hit a 1-inch height wedge at speed 1 m/s

Average 1.5 inch height wedge v(initial) 1m/s time of impact 0.0994s Impact Force 18.53417N V(final) 0.751692m/s Deceleration -2.54765m/s2

x i xi-average (xi-average)2 19.27553 0.741363 0.54961959 17.34798 -1.18619 1.40703881 18.38589 -0.14828 0.02198597 19.57208 1.037913 1.07726409 18.08935 -0.44482 0.19786187

Sum 3.25377032 variance 0.65075406 Standard deviation of impact Force 0.80669329N Table 5-14: Behavior of the rocker bogie suspension when the Front Wheel hit a 1.5-inch height wedge at speed 1 m/s

43


x i xi-average (xi-average)2 18.83071 -1.95721 3.8306762 20.60999 -0.17793 0.0316596 18.83071 -1.95721 3.8306762 19.86863 -0.91929 0.8450966 25.79956 5.011639 25.116522

Sum 33.654631 variance 6.7309261 Standard deviation of impact Force 2.5944028N Table 5-15: Behavior of the rocker bogie suspension when the Front Wheel hit a 2-inch height wedge at speed 1 m/s

Average 2.5 inch height wedge v(initial) 1m/s time of impact 0.0538s Impact Force 21.49963N V(final) 0.840077m/s


x i xi-average (xi-average)2 23.27891 1.779277 3.1658255 22.09273 0.593097 0.3517637 20.31345 -1.18618 1.4070309 22.53755 1.037917 1.077271 19.27553 -2.2241 4.9466356

Sum 10.948527 variance 2.1897053 Standard deviation of impact Force 1.4797653N Table 5-16: Behavior of the rocker bogie suspension when the Front Wheel hit a 2.5-inch height wedge at speed 1 m/s

44

Figure 5-3: A graph of Impact force on Front wheel versus height of the wedge at different speeds

Figure 5-3 showed a trend of the impact force exerted on the motor-mount,

which holds the first wheel. As speed increases the higher the impact force on the

vertical motor mount. The experimental result shows that the suspension will

encounter impact force of at least 14 Newtons and above in order to operate at or

above human walking speed. The existing rocker-bogie suspension configuration

cannot move at these higher speeds due to several issues, the frame is not strong

enough to withstand the impact force; there is also a risk of damaging the suspension

or flipping over if the rover ran into an obstacle at these speeds.

45

5.2.2 Middle Wheel

Data are collected from the Middle wheel. The strain gauges are mounted on

the Middle wheel to read the impact force exerted by the wedge. Impact force can be

calculated from the output excitation voltage of the middle motor mount at speed 0.5

m/s over 1” height wedges. Experiments on different speeds and different wedges,

which were previously done, were repeated here.

A B C D E F

Figure 5-4: An output excitation voltage generated by the Middle wheel at 0.5 m/s while it goes over the 1-inch height wedge

46

Explanations

A - Signal where the suspension before running into a wedge

B – Signal where the Front wheel first hit the wedge transmitted to the Middle wheel


D – Signal where the impact on the Middle wheel by the wedge

E – Signal where the Middle wheel climbs over the wedge

F – Signal where the impact on the Rear wheel transmitted back to the Middle wheel

The impact force on the Middle wheel is less severe than the First wheel, this

is because once the wedge hit and passed through the First wheel, the rover was not

traveling at 0.5m/s, it slowed down. The Middle wheel does not have enough time to

accelerate back to 0.5m/s before it hit the wedge.

47

Figure 5-5: A graph of Impact force on Middle wheel versus height of the wedge at different speeds*

*These are the speeds of the rover before its’ Front wheel hit the wedges

48

Average 1 inch height wedge time of impact 0.0614 S Impact Force 5.456459 N V(final) 0.455104 m/s Deceleration -0.75003 m/s2

xi (Forces) xi-average (xi-average)2 5.78266 0.326201 0.10640731

5.930933 0.474474 0.22512589 5.041293 -0.41517 0.17236253 6.22748 0.771021 0.5944739

4.299927 -1.15653 1.3375655 Sum 2.43593513 variance 0.48718703 Standard deviation of impact Force 0.69798784N Table 5-17 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1-inch height wedge at speed 0.5 m/s

Average 1.5 inches height wedge time of impact 0.091s Impact Force 7.33953N V(final) 0.409248m/s Deceleration -1.00887m/s2

xi (Forces) xi-average (xi-average)2 8.00676 0.66723 0.44519587 8.00676 0.66723 0.44519587

7.265393 -0.07414 0.00549629 6.079207 -1.26032 1.58841406

Sum 2.4843021 variance 0.62107553 Standard deviation of impact Force 0.78808345N Table 5-18 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1.5-inch height wedge at speed 0.5 m/s

49

Average 2 inch height wedge time of impact 0.0872s Impact Force 8.8370907N V(final) 0.3926114m/s Deceleration -1.2147204m/s2

xi (Forces) xi-average (xi-average)2 9.0446733 0.2075826 0.04309055 8.7481267 -0.088964 0.00791459 6.8205733 -2.0165174 4.06634229 10.23086 1.3937693 1.94259295 9.34122 0.5041293 0.25414638

Sum 6.31408677 Variance 1.26281735 Standard deviation of impact Force 1.12375146N Table 5-19 Behavior of the rocker bogie suspension when the Middle Wheel hit a 2-inch height wedge at speed 0.5 m/s

Average 2.5 inches height wedge time of impact 0.071s Impact Force 8.985364N V(final) 0.4128173m/s


xi (Forces) xi-average (xi-average)2 9.4894933 0.5041293 0.25414635 8.3033067 -0.6820573 0.46520216 9.0446733 0.0593093 0.00351759 8.3033067 -0.6820573 0.46520216

9.78604 0.800676 0.64108206 Sum 1.82915032 variance 0.36583006 Standard deviation of impact Force 0.60483887N Table 5-20 Behavior of the rocker bogie suspension when the Middle Wheel hit a 2.5-inch height wedge at speed 0.5 m/s

50

Average 1 inch height wedge time of impact 0.077s Impact Force 6.486958N V(final) 0.624707m/s


xi (Forces) xi-average (xi-average)2 5.78266 -0.7043 0.49603614 9.34122 2.854262 8.14680966 5.33784 -1.14912 1.32047294

5.486113 -1.00085 1.00169138 Sum 10.9650101 Variance 2.74125253 Standard deviation of impact Force 1.65567283N Table 5-21 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1-inch height wedge at speed 0.7 m/s

Average 1.5 inch height wedge time of impact 0.09675s Impact Force 10.305N V(final) 0.563482m/s Deceleration -1.41649m/s2

xi (Forces) xi-average (xi-average)2 9.78604 -0.51896 0.26931602

10.52741 0.222413 0.04946769 11.56532 1.260323 1.5884149 9.34122 -0.96378 0.92886546

Sum 2.83606408 Variance 0.70901602 Standard deviation of impact Force 0.84203089N Table 5-22 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1.5-inch height wedge at speed 0.7 m/s

51



11.56532 0.385511 0.14861847 11.1205 -0.05931 0.0035176

10.52741 -0.6524 0.42562489 11.56532 0.385511 0.14861847

Sum 0.72989703 variance 0.14597941 Standard deviation of impact Force 0.38207251N Table 5-23 Behavior of the rocker bogie suspension when the Middle Wheel hit a 2-inch height wedge at speed 0.7 m/s

Average 2.5 inch height wedge time of impact -0.0412s Impact Force 11.53567N V(final) 0.766166m/s Deceleration -1.58566m/s2

xi (Forces) xi-average (xi-average)2 10.37913 -1.15654 1.33757398 11.56532 0.029655 0.0008794 11.56532 0.029655 0.0008794 11.56532 0.029655 0.0008794 12.60323 1.067565 1.13969432


52




9.044673 -0.20758 0.0430907 9.34122 0.088964 0.00791459

9.489493 0.237237 0.05628139 9.044673 -0.20758 0.0430907



xi (Forces) xi-average (xi-average)2 10.82395 0.14827 0.02198399 10.52741 -0.14827 0.02198399 11.26877 0.59309 0.35175575 10.08259 -0.59309 0.35175575


53


xi (Forces) xi-average (xi-average)2 14.08597 2.164794 4.6863331 9.044673 -2.8765 8.2742695 12.30669 0.385514 0.148621 12.30669 0.385514 0.148621 11.86187 -0.05931 0.0035172

Sum 13.261362 variance 2.6522724 Standard deviation of impact Force 1.6285799N Table 5-27 Behavior of the rocker bogie suspension when the Middle Wheel hit a 2-inch height wedge at speed 1 m/s

Average 2.5 inch height wedge time of impact 0.1332s Impact Force 12.15841N V(final) 0.575159m/s


xi (Forces) xi-average (xi-average)2 12.30669 0.148277 0.021986 13.3446 1.186187 1.4070388

12.01014 -0.14827 0.021985 11.86187 -0.29654 0.0879379 11.26877 -0.88964 0.7914653


54


xi (Forces) xi-average (xi-average)2 11.56532 0.978604 0.95766579 10.52741 -0.05931 0.0035172 10.08259 -0.50413 0.25414302 10.97223 0.385514 0.14862104 9.78604 -0.80068 0.64108206




xi (Forces) xi-average (xi-average)2 8.748127 -2.40944 5.80540754 12.30669 1.149122 1.3204806 12.01014 0.852572 0.72687845 11.56532 0.407752 0.16626142

Sum 8.01902801 variance 2.004757 Standard deviation of impact Force 1.41589442N Table 5-30 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1.5-inch height wedge at speed 1 m/s

55


xi (Forces) xi-average (xi-average)2 12.75151 0.704302 0.49604084 13.04805 1.000842 1.00168404 10.82395 -1.22326 1.49636095 11.56532 -0.48189 0.23221637



xi (Forces) xi-average (xi-average)2 12.30669 0.059313 0.00351799 11.71359 -0.53379 0.28492892 12.30669 0.059313 0.00351799 12.60323 0.355853 0.12663112 12.30669 0.059313 0.00351799


56

5.3 Tilted Rocker-Bogie suspension

There is one possible way to reduce the impact force by simply increase the

moment arm of the vertical motor mount. In Figure 5-6, notice that the pivot has

increased 1 inch compared to the horizontal rocker-bogie suspension. Due to the

increase in moment arm, less impact force is expected, because the long arm acts as

an absorber.

Figure 5-6: Tilted Rocker-Bogie suspension

57

5.3.1 Tilted Rocker-Bogie Suspension Front Wheel

A B C D E F

Figure 5-7: An output excitation voltage generated by the Tilted Rocker-bogie Front wheel at 0.5 m/s while it goes over the 1-inch height wedge

Explanations

A - Signal where the suspension traveling at 0.5 m/s without running into a wedge

B – Signal where the Front wheel first hit the wedge


D – Signal where the impact on the Second wheel transmitted back to the Front wheel

by the wedge

E – Signal where the Middle wheel climbs over the wedge transmitted back to the

Front wheel

F – Signal where the impact on the Rear wheel transmitted back to the Front wheel

58

Average 1 inch height wedge v(initial) 0.5m/s time of impact 0.0402s Impact Force 12.72185N V(final) 0.430316m/s


xi (Forces) xi-average (xi-average)2 12.89978 0.177928 0.03165837 13.3446 0.622748 0.38781507 13.3446 0.622748 0.38781507

12.01014 -0.71171 0.50653397 12.01014 -0.71171 0.50653397

Sum 1.82035646 variance 0.36407129 Standard deviation of impact Force 0.6033832N Table 5-33: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 1-inch height wedge at speed 0.5 m/s




Sum 3.71985885 variance 0.74397177 Standard deviation of impact Force 0.86253798N Table 5-34: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 1.5-inch height wedge at speed 0.5 m/s

59



xi (Forces) xi-average (xi-average)2 14.23424 0.177928 0.03165837 14.23424 0.177928 0.03165837 13.78942 -0.266892 0.07123134 13.78942 -0.266892 0.07123134 14.23424 0.177928 0.03165837


Average 2.5 inch height wedge v(initial) 0.5m/s time of impact 0.0544s Impact Force 14.3232N V(final) 0.393818m/s Deceleration -1.953519m/s2

xi (Forces) xi-average (xi-average)2 12.89978 -1.423424 2.02613588 15.12388 0.800676 0.64108206 14.23424 -0.088964 0.00791459 14.23424 -0.088964 0.00791459 15.12388 0.800676 0.64108206


60



xi (Forces) xi-average (xi-average)2 12.89978 -0.08896 0.0079146 12.89978 -0.08896 0.0079146 13.3446 0.355856 0.1266335

12.89978 -0.08896 0.0079146 12.89978 -0.08896 0.0079146




xi (Forces) xi-average (xi-average)2 13.78942 0.177928 0.0316584 13.78942 0.177928 0.0316584 12.89978 -0.71171 0.506534 13.78942 0.177928 0.0316584 13.78942 0.177928 0.0316584


61



xi (Forces) xi-average (xi-average)2 13.78942 -0.80068 0.64108206 13.78942 -0.80068 0.64108206 15.12388 0.533784 0.28492536 15.12388 0.533784 0.28492536 15.12388 0.533784 0.28492536



xi (Forces) xi-average (xi-average)2 15.12388 0.266892 0.07123134 15.12388 0.266892 0.07123134 15.12388 0.266892 0.07123134 13.78942 -1.06757 1.13970143 15.12388 0.266892 0.07123134


62



xi (Forces) xi-average (xi-average)2 12.89978 -2.04617 4.18681985 12.89978 -2.04617 4.18681985 19.57208 4.626128 21.4010603 15.12388 0.177928 0.03165837 14.23424 -0.71171 0.50653397



xi (Forces) xi-average (xi-average)2 14.67906 -0.71171 0.50653397 15.12388 -0.26689 0.07123134 15.5687 0.177928 0.03165837 15.5687 0.177928 0.03165837

16.01352 0.622748 0.38781507 Sum 1.02889713 variance 0.20577943 Standard deviation of impact Force 0.45362917N Table 5-42: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 1.5-inch height wedge at speed 0.8 m/s

63



xi (Forces) xi-average (xi-average)2 16.90316 0.88964 0.791459 15.12388 -0.88964 0.791459 15.5687 -0.44482 0.197865

16.45834 0.44482 0.197865 16.01352 0 0




xi (Forces) xi-average (xi-average)2 16.45834 -0.80068 0.6410821 16.01352 -1.2455 1.5512603 17.34798 0.088964 0.0079146 18.23762 0.978604 0.9576658 18.23762 0.978604 0.9576658


64


xi (Forces) xi-average (xi-average)2 13.78942 -2.33531 5.45364944 12.89978 -3.22495 10.4002703 23.57546 7.450735 55.513452 15.12388 -1.00085 1.00169071 12.89978 -3.22495 10.4002703

Sum 82.7693327 variance 16.5538665 Standard deviation of impact Force 4.06864431N Table 5-45: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 1-inch height wedge at speed 1 m/s



xi (Forces) xi-average (xi-average)2 16.90316 0.622748 0.38781507 15.5687 -0.71171 0.50653397

16.01352 -0.26689 0.07123134 16.45834 0.177928 0.03165837 16.45834 0.177928 0.03165837

Sum 1.02889713 variance 0.20577943 Standard deviation of impact Force 0.45362917N Table 5-46: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 1.5-inch height wedge at speed 1 m/s

65

Average 2 inch height wedge v(initial) 1 m/s time of impact 0.047 s Impact Force 16.72523 N V(final) 0.893466 m/s Deceleration -2.27506 m/s2

xi (Forces) xi-average (xi-average)2 16.90316 0.177928 0.03165837 18.68244 1.957208 3.83066316 16.90316 0.177928 0.03165837 16.01352 -0.71171 0.50653397 15.12388 -1.60135 2.56432823

Sum 6.9648421 variance 1.39296842 Standard deviation of impact Force 1.18024083N Table 5-47: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 2-inch height wedge at speed 1 m/s




Sum 1.82035646 variance 0.36407129 Standard deviation of impact Force 0.6033832N Table 5-48: Behavior of the Tilted rocker bogie suspension when the Front Wheel hit a 2.5-inch height wedge at speed 1 m/s

66

Figure 5-8: A graph of Impact force on Front wheel versus height of the wedge at different speeds for a Tilted suspension

The result above shows that the Tilted suspension had less impact forces than

that of the original suspension. The Tilted suspension has an impact force of 12.72

Newton compared to 14.95 Newton for the original suspension under same speed and

same obstacle. However, the drawbacks of this design are obvious, the size of the

suspension is larger, which is not welcome in any space operations. Therefore, a

change in control strategy is preferred. Many of the impact forces and stresses

encountered by the frame may be reduced or eliminated by performing wheelie

maneuvers.

5.3.2 Tilted Rocker-Bogie Suspension Middle Wheel

Data are collected from the Middle wheel for the Tilted Rocker-bogie

suspension. The strain gauges are mounted on the Middle wheel to read the impact

force exerted by the wedge while traveling at different speeds. Impact force can be

67

calculated from the output excitation voltage of the middle motor mount at speed 0.5

m/s over 1” height wedges. Experiments on different speeds and different wedges,

which were previously done, were also repeated here.

A B C D E F

Figure 5-9: An output excitation voltage generated by the Tilted Rocker-Bogie Middle wheel while it goes over the 1-inch height wedge

68

Explanation

A - Signal where the Tilted suspension traveling at 0.5 m/s without running into a

wedge

B – Signal where the Front wheel first hit the wedge transmitted to the Middle wheel


D – Signal where the impact on the Middle wheel by the wedge

E – Signal where the Middle wheel climbs over the wedge

F – Signal where the impact on the Rear wheel transmitted back to the Middle wheel

Figure 5-10: A graph of Impact force on Middle wheel versus height of the wedge at different speeds for a Tilted suspension

Notice that (Figure 5-10) the Impact force on the Middle wheel Tilted

suspension are in the ballpark of 5 to 8 Netwons, slightly lower than that of the

69

Middle wheel Horizontal suspension (6 to 12 Newtons), even though they shared the

same dimensions.

70



xi (Forces) xi-average (xi-average)2 4.744747 -0.63016 0.3971033 8.303307 2.928399 8.5755188

4.4482 -0.92671 0.8587883 6.524027 1.149119 1.3204737 5.78266 0.407752 0.1662614



xi (Forces) xi-average (xi-average)2 5.041293 -0.50413 0.2541467 5.041293 -0.50413 0.2541467 5.33784 -0.20758 0.0430906

6.079207 0.533784 0.2849257 6.22748 0.682057 0.4652022


71




6.524027 -0.56344 0.3174628 7.265393 0.177928 0.0316583 6.820573 -0.26689 0.0712315 7.265393 0.177928 0.0316583




6.079207 -1.38388 1.9151352 9.044673 1.581582 2.5014013 8.748127 1.285036 1.6513172


72



xi (Forces) xi-average (xi-average)2 5.486113 -0.088964 0.00791465 5.78266 0.207583 0.04309056 5.78266 0.207583 0.04309056 5.78266 0.207583 0.04309056

5.041293 -0.533784 0.28492571 Sum 0.42211206 variance 0.08442241 Standard deviation of impact Force 0.29055535N Table 5-53 Behavior of the rocker bogie suspension when the Middle Wheel hit a 1-inch height wedge at speed 0.7 m/s



xi (Forces) xi-average (xi-average)2 6.968847 3.33E-07 1.1111E-13 6.524027 -0.44482 0.19786454 6.968847 3.33E-07 1.1111E-13 6.820573 -0.148274 0.02198508 7.56194 0.593093 0.3517597


73



xi (Forces) xi-average (xi-average)2 7.265393 -3.33333E-07 1.111E-13 7.56194 0.296546667 0.0879399

7.858487 0.593093667 0.3517601 7.265393 -3.33333E-07 1.111E-13 6.968847 -0.296546333 0.0879397



xi (Forces) xi-average (xi-average)2 8.599853 0.593093 0.3517593 8.303307 0.296547 0.0879401 7.265393 -0.741367 0.549625 6.820573 -1.186187 1.4070396 9.044673 1.037913 1.0772634


74



xi (Forces) xi-average (xi-average)2 6.079207 -0.44482 0.1978645 7.858487 1.33446 1.7807844 7.265393 0.741366 0.549624 6.079207 -0.44482 0.1978645 5.33784 -1.18619 1.4070388




xi (Forces) xi-average (xi-average)2 7.265393 -0.11121 0.0123666 7.56194 0.185342 0.0343515

7.858487 0.481889 0.2322167 6.820573 -0.55603 0.3091642 7.265393 -0.11121 0.0123666


75



xi (Forces) xi-average (xi-average)2 7.858487 0.355856 0.1266337 7.710213 0.207582 0.0430904 7.56194 0.059309 0.0035176

8.303307 0.800676 0.6410826 6.079207 -1.42342 2.0261349



xi (Forces) xi-average (xi-average)2 10.23086 2.520647 6.3536596 6.22748 -1.48273 2.1984981

10.08259 2.372377 5.628171 6.22748 -1.48273 2.1984981 5.78266 -1.92755 3.7154619

6.820573 -0.88964 0.7914599 Sum 20.885749 variance 3.4809581 Standard deviation of impact Force 1.8657326N Table 5-60 Behavior of the rocker bogie suspension when the Middle Wheel hit a 2.5-inch height wedge at speed 0.8 m/s

76



xi (Forces) xi-average (xi-average)2 7.56194 -0.3262 0.10640731 7.56194 -0.3262 0.10640731

8.303307 0.41517 0.17236253 8.00676 0.11862 0.01407039 8.00676 0.11862 0.01407039




6.968847 -0.26689 0.07123116 6.524027 -0.71171 0.5065335 8.00676 0.77102 0.5944739 8.45158 1.21584 1.47827015


77



xi (Forces) xi-average (xi-average)2 6.079207 -1.30481 1.70251609 6.375753 -1.00826 1.01658621 7.56194 0.177928 0.03165837

7.858487 0.474475 0.22512653 9.044673 1.660661 2.75779496



xi (Forces) xi-average (xi-average)2 10.52741 1.986866 3.9476365 7.858487 -0.68206 0.46520175 6.968847 -1.5717 2.47023146 8.748127 0.207583 0.0430907 8.599853 0.059309 0.00351756


78

5.4 Wheelie Maneuvers

The wheelie maneuver consists of varying the speeds among the three wheels

so that the wheels are able to manipulate the frame and the traction. As this happens,

one of the wheels is forced into the air. The speeds are controlled by a HandyBoard

and three H-bridges using PWM. An Interactive C language program was used to

change the speeds of all three wheels. The Interactive C program defines NORMAL

speed which is 25% of its’ maximum capability, and FAST speed which is 100%

capability.

In order to lift the Front wheel off the conveyer belt, the following control

needs to be done, as the obstacle approaches the Front wheel, speed up the Middle

wheel, run the Rear wheel 25% in opposite direction for 0.25 seconds. When the

obstacle is under the Front wheel, run all the wheels to NORMAL speed.

In order to lift the Middle wheel, as the obstacle approaches the Middle wheel,

slow the Front wheel, run the Rear wheel at maximum speed. When the obstacle is

under the Middle wheel, return all wheels to normal speed.

The test rack is capable of driving the vehicle at speeds equal to and

exceeding 1 m/s. The infrared sensors are used for detecting the in-coming obstacle.

The front wheelie is initiated as the obstacle gets within 10 inches of the Front wheel

(detected by infrared sensor number 1). At this moment, the rear wheel is given by

the PWM signal to rotate in the reverse direction (25% of maximum speed), and the

Middle wheel is signaled to increase its speed to maximum. As the obstacle is directly

under the Front wheel (detected by a infrared sensor number 2 located at Front

wheel), the Front wheel speeds return to NORMAL, so that the wheel can roll down

79

from the forward side of the obstacle. The Middle wheel wheelie is initiated 0.1s after

the obstacle pass under the Front wheel. At this moment, the Front wheel is

programmed to rotate in the 10% of the maximum speed in the opposite direction,

and the Rear wheel is programmed to rotate maximum speed in forward direction,

this action forced the Middle wheel into the air, avoiding the obstacle.

Figure 5-11: The location of the two Infrared sensors for Wheelie

Infrared sensor 1 Infrared sensor 2

80

A B C D E F G H

Figure 5-12: An Output excitation voltage generated on the Front vertical motor mount as the Wheelie maneuver was performed

The points of interest on the graph (Figure 5-12) are

A - Signal where the suspension traveling at 1 m/s without running into a wedge

B – Signal where the Front wheel was lifting into the air

C – Signal where the Front wheel was in the air

D – Signal where the Rocker hit the mechanical stop

E – Signal where the Front wheel landed on the conveyer belt

F – Signal where the Front wheel rotated in different direction

G – Signal where the Middle wheel was lifting into the air

H – Signal where the Middle wheel landed on the conveyer belt

81

Under wheelie maneuver, the force exerted on the vertical motor mount is

simply due to the gravity acting on the mass of the motor, wheel and the motor

mount. Three of these components have a total mass of 1.19 kg. The average force

exerted on the vertical motor mount is 12.08 Newton. As the mass of the rocker-bogie

increase, the force acting on the bogie also increased. The moment of inertial will

increase simultaneously as the mass increase. One of the suggestions to make the

wheelie maneuver efficient is to build a lighter rocker arm.

Average Force 2.716666667 lbf Force 12.08427667 N

Table 5.4.1 Force generated by Wheelie Maneuver by Horizontal Rocker-Bogie

Similar theory applied to the Middle wheelie, except with a lower moment of

inertia. The reason is the distance between the pivot point and the center of Middle

wheel is 7.24 inches compared with center of Front wheel, which are 11.43 inches.

82

5.4.1 Comparison between non-wheelie and wheelie at speed of 1m/s

Figure 5-13: Output excitation voltage for Non-Wheelie

Figure 5-14: Output excitation voltage for Wheelie

83

5.4.2 Further reduction of vertical shock

Installing dampers can solve the increase in impulse in vertical direction of the

rocker-bogie suspension due to the wheelie when the Front and Middle wheel landed

on the conveyor belt or ground. An example of a device that can provide a force that

depends on position and a force that depends on velocity is a strut that is commonly

used on aircraft landing gear as a combination spring and shock absorber. It consists

of a piston and cylinder mechanical system.

When the wheel landed, the piston is pushed up into a cylinder; the air at the

top of the cylinder is compressed. (The hydraulic oil is essentially incompressible.)

This air spring creates a force that depends on the vertical distance moved. As the

piston moves, it will create a force that will absorb the landing force depends on the

speed of the motion.

84

Chapter 6 CONCLUSIONS

The behavior of the Horizontal rocker-bogie suspension under high speed was

shown; the impact forces on the Front wheel and Middle wheel were presented. The

second result of the Tilted rocker-bogie configuration which have a lower impact

force under same condition with the Horizontal rocker-bogie were presented. These

results verify that our claims of a reduced impact force on the rocker-bogie

suspension by performing the wheelie maneuver are accurate.

The behavior of the Horizontal rocker-bogie indicates that the impact force is

between 14 and 22 Netwons traveling between 0.5m/s and 1 m/s. Note that a rocker-

bogie suspension will experience a much higher impact force, if the real rover is

heavier or carries a big payload. The impact forces on the Middle wheel of this

configuration is 1 time less than the Front wheel, because the Middle wheel is not fast

enough to speed up before collision.

The second result of the Tilted rocker-bogie suspension is a test to verify the

lower impact force by increasing the moment arm of the vertical motor mount.

Generally, the impact force is reduced by approximately 2 to 3 Newtons. The impact

force on the Middle wheel of this configuration is slightly less than the Horizontal

rocker-bogie Middle wheel configuration.

The claim of reducing impact force on a wheelie maneuver of the rocker-

bogie is accurate. Strictly speaking, there was no direct impact or collision between

the wheels (except the Rear wheel) and the wedges. The only forces acting on the

rocker are the weight and the impact onto the conveyor belt when it landed.

85

Chapter 7 RECOMMENDATIONS

The recommendations are divided into two areas. The first recommendations

presented relate only to the experimental procedure and process used in the quantities

obtained. The second recommendation are those which relating to any future high

speed Rocker-Bogie class rover experimental and theoretical work, needed to develop

a deeper understanding of the suspension.

First, in order to obtain more accurate data from the impact force, some

precautions must be taken. It is important to examine potential error sources prior to

taking data. Some strain gauges may be damaged during installation, therefore it is

important to check the resistance of the strain gauge every time prior to the

experiment. Electrical noise and interference may alter the readings. Shields and

insulation coatings may prevent this problem. As mentioned earlier, shielded cables

were used and pair wires were twisted to reduce the effect of EMI (Electro-Magnetic

Interference). Thermally induced voltages caused by thermocouple effect are one of

the factors that give inaccurate readings. Load cells and accelerometers are

recommended for the experiment.

Larger heat sinks for the MOSFET on the H-Bridge are strongly

recommended; this is because the H-Bridge draws tremendous of current (up to 20

amps without heatsinks, 40 amps with heat sinks). This will create a potential fire

hazard situation when 20 amps of current flows through the circuits. There are two

ways to reduce the hazard; to introduce cool air onto the MOSFET by a fan, and to

place some dry ice on top of the MOSFET.

86

Higher data acquisition frequency is required for any impact test. Careful

selection of the data acquisition board and LabVIEW programming would determine

the accuracy and precision of impact data between 0.001s.

Future work, both experimentally and theoretically, must be carried out to

give a full understanding of the Rocker-Bogie suspension. This work may provide the

designers of the six wheels Rocker-Bogie suspension operating under high speed to

make better design decisions and optimization. In order to carry out the Front

Wheelie maneuver, a powerful sensors needs to be installed on the Rocker-Bogie

rover capable of sensing a traversable obstacle 10 inches before collision. In addition,

for the Middle Wheelie, a correct position is needed for the second sensor. In order to

travel at higher speed, huge motors are needed, as well as a new motor-mount needs

to be designed. This work would provide information related to the impact force in

horizontal direction. Without such information, designing a high-speed Rocker-Bogie

suspension would be difficult.

87

BIBLIOGRAPHY

1. Nathalie A. Cabrol, http://www.seti-inst.edu/science/litu/natalie-c/Welcome.html Project Science Lead. SETI Institute, NASA Ames Research Center. 2. David P. Miller, Speed and Interface Issues for Robot-Astronaut Surface Teams

Department of Aerospace and Mechanical Engineering, University of Oklahoma.

3. Herve Hacot, Steven Dubowsky, Philippe Bidaud, Analysis And Simulation of A Rocker-Bogie Exploration Rover. Department of Mechanical Engineering Massachusetts Institute of Technology.

4. Herve Hacot, Analysis and traction control of a rocker-bogie planetary rover

Master thesis Department of Mechanical Engineering Massachusetts Institute of Technology, Cambridge, MA, May 1998.

5. Shih-Liang(Sid) Wang, Case Studies on NASA Mars Rover’s Mobility System.

2000 ASEE Southeast Section Conference. Department of Mechanical Engineering, North Carolina A&T State University.

6. Mars Pathfinder: http://mars.jpl.nasa.gov/MPF/sitemap/rover.html

7. Donna L. Shirley, Managing Martians Broadways Books. June 1998.

8. National Instruments Corp., SCB-68 68-Pin Shielded Connector Block

Installation guide, Part number 320745-01. February 1994

9. Omega Engineering, The Pressure Strain and Force HandbookTM. Omega Engineering, Inc. 2000.

10. Omega Engineering, TT300 Strain Gauge User Manual

11. Anthony J. Wheeler, Ahmad R. Ganji, Introduction to Engineering

Experimentation. Prentice-Hall 1996.

12. M.A. Macaulay, Introduction to Impact Engineering. Chapman and Hall 1987.

13. http://digital.ni.com/manuals.nsf/webAdvsearch/345FDA749430DFE68625665E00635A1A?OpenDocument

14. Assembling The Speed Controller

http://professionals.com/~cmcmanis/robotics/h-bridge/h-bridge.html

15. Omega Engineering DMD-465 Bridge-sensor User’s guide

88

Appendix A HORIZONTAL ROCKER-BOGIE FRONT WHEEL 0.5m/s 1 inch 2 inch data14 f1 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 925 0.054 Coordinate 1 857 0.068Coordinate 2 863 -0.054 Coordinate 2 800 -0.039Mass 7.275kg Mass 7.275kg time of impact 0.062s time of impact 0.057s Force 3.6lbf Force 3.566667lbf Force 16.01352N Force 15.86525N Impulse -0.99284Ns Impulse -0.90432Ns V(final) 0.363527m/s V(final) 0.375695m/s

Average Decel -2.20117m/s2 Average Decel -2.18079m/s2 data15 f2 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1145 0.051 Coordinate 1 641 0.076Coordinate 2 1068 -0.054 Coordinate 2 589 -0.042Mass 7.275kg Mass 7.275kg time of impact 0.077s time of impact 0.052s Force 3.5lbf Force 3.933333lbf Force 15.5687N Force 17.49625N Impulse -1.19879Ns Impulse -0.90981Ns V(final) 0.335218m/s V(final) 0.374941m/s

Average Decel -2.14003m/s2 Average Decel -2.40498m/s2 data16 f3 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1127 0.044 Coordinate 1 1167 0.059Coordinate 2 1043 -0.046 Coordinate 2 1107 -0.051Mass 7.275kg Mass 7.275kg time of impact 0.084s time of impact 0.06s Force 3lbf Force 3.666667lbf Force 13.3446N Force 16.31007N Impulse -1.12095Ns Impulse -0.9786Ns V(final) 0.345918m/s V(final) 0.365484m/s

Average Decel -1.83431m/s2 Average Decel -2.24193m/s2

89

data17 f4 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 2711 0.054 Coordinate 1 734 0.071Coordinate 2 2631 -0.044 Coordinate 2 635 -0.051Mass 7.275kg Mass 7.275kg time of impact 0.08s time of impact 0.099s Force 3.266667lbf Force 4.066667lbf Force 14.53079N Force 18.08935N Impulse -1.16246Ns Impulse -1.79085Ns V(final) 0.340211m/s V(final) 0.253836m/s

Average Decel -1.99736m/s2 Average Decel -2.48651m/s2 data18 f5 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1265 0.049 Coordinate 1 463 0.061Coordinate 2 1201 -0.054 Coordinate 2 401 -0.054Mass 7.275kg Mass 7.275kg time of impact 0.064s time of impact 0.062s Force 3.433333lbf Force 3.833333lbf Force 15.27215N Force 17.05143N Impulse -0.97742Ns Impulse -1.05719Ns V(final) 0.365647m/s V(final) 0.354682m/s

Average Decel -2.09927m/s2 Average Decel -2.34384m/s2 1 inch height wedge 2 inch height wedge v(initial) 0.5m/s v(initial) 0.5m/s time of impact 0.0734s time of impact 0.066s Impact Force 14.94595N Impact Force 16.96247N V(final) 0.350104m/s V(final) 0.344927m/s Deceleration -2.05443m/s2 Deceleration -2.33161m/s2

90

HORIZONTAL ROCKER-BOGIE FRONT WHEEL 0.5m/s 1.5 inch 2.5 inch dtm1 rr1 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 758 0.044 Coordinate 1 857 0.068Coordinate 2 703 -0.073 Coordinate 2 806 -0.061Mass 7.275kg Mass 7.275kg time of impact 0.055s time of impact 0.051s Force 3.9lbf Force 4.3lbf Force 17.34798N Force 19.12726N Impulse -0.95414Ns Impulse -0.97549Ns V(final) 0.368847m/s V(final) 0.365912m/s Average Decel -2.3846m/s2 Average Decel -2.62918m/s2 dtm2 rr2 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1462 0.073 Coordinate 1 532 0.073Coordinate 2 1408 -0.037 Coordinate 2 470 -0.054Mass 7.275kg Mass 7.275kg time of impact 0.054s time of impact 0.062s Force 3.666667lbf Force 4.233333lbf Force 16.31007N Force 18.83071N Impulse -0.88074Ns Impulse -1.1675Ns V(final) 0.378936m/s V(final) 0.339518m/s Average Decel -2.24193m/s2 Average Decel -2.58841m/s2 dtm3 rr3 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 379 0.073 Coordinate 1 741 0.066Coordinate 2 330 -0.034 Coordinate 2 679 -0.051Mass 7.275kg Mass 7.275kg time of impact 0.049s time of impact 0.062s Force 3.566667lbf Force 3.9lbf Force 15.86525N Force 17.34798N Impulse -0.7774Ns Impulse -1.07557Ns V(final) 0.393141m/s V(final) 0.352155m/s Average Decel -2.18079m/s2 Average Decel -2.3846m/s2

91

dtm4 rr4 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 774 0.073 Coordinate 1 834 0.068Coordinate 2 720 -0.037 Coordinate 2 783 -0.054Mass 7.275kg Mass 7.275kg time of impact 0.054s time of impact 0.051s Force 3.666667lbf Force 4.066667lbf Force 16.31007N Force 18.08935N Impulse -0.88074Ns Impulse -0.92256Ns V(final) 0.378936m/s V(final) 0.373188m/s

Average Decel -2.24193m/s2 Average Decel -2.48651m/s2 dtm5 rr5 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1311 0.056 Coordinate 1 789 0.063Coordinate 2 1250 -0.051 Coordinate 2 741 -0.063Mass 7.275kg Mass 7.275kg time of impact 0.061s time of impact 0.048s Force 3.566667lbf Force 4.2lbf Force 15.86525N Force 18.68244N Impulse -0.96778Ns Impulse -0.89676Ns V(final) 0.366972m/s V(final) 0.376734m/s

Average Decel -2.18079m/s2 Average Decel -2.56803m/s2 1.5 inch height wedge 2.5 inch height wedge v(initial) 0.5m/s v(initial) 0.5m/s time of impact 0.0546s time of impact 0.0548s Impact Force 16.33972N Impact Force 18.41555N V(final) 0.377366m/s V(final) 0.361501m/s Deceleration -2.24601m/s2 Deceleration -2.53135m/s2

92

Output excitation voltage of the front motor mount at speed 0.5 m/s over 1.0” height wedge

93


94

Output excitation voltage of the front motor mount at speed 0.5 m/s over 2” height wedge

95


96

HORIZONTAL ROCKER-BOGIE FRONT WHEEL 0.7m/s 1 inch 2 inch data1 cant1 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1192 0.061 Coordinate 1 782 0.079Coordinate 2 1146 -0.046 Coordinate 2 707 -0.042Mass 7.275kg Mass 7.275kg time of impact 0.046s time of impact 0.075s Force 3.566667lbf Force 4.033333lbf Force 15.86525N Force 17.94107N Impulse -0.7298Ns Impulse -1.34558Ns V(final) 0.599684m/s V(final) 0.51504m/s Average Decel -2.18079m/s2 Average Decel -2.46613m/s2 data2 cant2 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 707 0.061 Coordinate 1 888 0.068Coordinate 2 668 -0.042 Coordinate 2 826 -0.046Mass 7.275kg Mass 7.275kg time of impact 0.039s time of impact 0.062s Force 3.433333lbf Force 3.8lbf Force 15.27215N Force 16.90316N Impulse -0.59561Ns Impulse -1.048Ns V(final) 0.618129m/s V(final) 0.555946m/s Average Decel -2.09927m/s2 Average Decel -2.32346m/s2 data3 cant3 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 434 0.059 Coordinate 1 1076 0.081Coordinate 2 393 -0.049 Coordinate 2 1015 -0.037Mass 7.275kg Mass 7.275kg time of impact 0.041s time of impact 0.061s Force 3.6lbf Force 3.933333lbf Force 16.01352N Force 17.49625N Impulse -0.65655Ns Impulse -1.06727Ns V(final) 0.609752m/s V(final) 0.553296m/s Average Decel -2.20117m/s2 Average Decel -2.40498m/s2

97

data4 cant4 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 750 0.059 Coordinate 1 574 0.073Coordinate 2 700 -0.054 Coordinate 2 523 -0.061Mass 7.275kg Mass 7.275kg time of impact 0.05s time of impact 0.051s Force 3.766667lbf Force 4.466667lbf Force 16.75489N Force 19.86863N Impulse -0.83774Ns Impulse -1.0133Ns V(final) 0.584846m/s V(final) 0.560715m/s

Average Decel -2.30308m/s2 Average Decel -2.73108m/s2 data5 V(initial) 0.7m/s time voltage Coordinate 1 606 0.061 Coordinate 2 564 -0.049 Mass 7.275kg time of impact 0.042s Force 3.666667lbf Force 16.31007N Impulse -0.68502Ns V(final) 0.605839m/s

Average Decel -2.24193m/s2 1 inch height wedge 2 inch height wedge v(initial) 0.7m/s v(initial) 0.7m/s time of impact 0.0436s time of impact 0.06225s Impact Force 16.04317N Impact Force 18.05228N V(final) 0.60365m/s V(final) 0.546249m/s Deceleration -2.20525m/s2 Deceleration -2.48141m/s2

98

HORIZONTAL ROCKER-BOGIE FRONT WHEEL 0.7m/s 1.5 inch 2.5 inch test1 dd2 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1001 0.071 Coordinate 1 629 0.088Coordinate 2 933 -0.046 Coordinate 2 527 -0.059Mass 7.275kg Mass 7.275kg time of impact 0.068s time of impact 0.102s Force 3.9lbf Force 4.9lbf Force 17.34798N Force 21.79618N Impulse -1.17966Ns Impulse -2.22321Ns V(final) 0.537847m/s V(final) 0.394404m/s Average Decel -2.3846m/s2 Average Decel -2.99604m/s2 test2 dd3 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 824 0.071 Coordinate 1 349 0.088Coordinate 2 771 -0.042 Coordinate 2 285 -0.039Mass 7.275kg Mass 7.275kg time of impact 0.053s time of impact 0.064s Force 3.766667lbf Force 4.233333lbf Force 16.75489N Force 18.83071N Impulse -0.88801Ns Impulse -1.20517Ns V(final) 0.577937m/s V(final) 0.534341m/s Average Decel -2.30308m/s2 Average Decel -2.58841m/s2 test4 dd4 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 491 0.072 Coordinate 1 101 0.081Coordinate 2 438 -0.037 Coordinate 2 46 -0.049Mass 7.275kg Mass 7.275kg time of impact 0.053s time of impact 0.055s Force 3.633333lbf Force 4.333333lbf Force 16.16179N Force 19.27553N Impulse -0.85658Ns Impulse -1.06015Ns V(final) 0.582258m/s V(final) 0.554274m/s Average Decel -2.22155m/s2 Average Decel -2.64956m/s2

99

test5 dd8 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 916 0.073 Coordinate 1 398 0.071Coordinate 2 853 -0.037 Coordinate 2 335 -0.068Mass 7.275kg Mass 7.275kg time of impact 0.063s time of impact 0.063s Force 3.666667lbf Force 4.633333lbf Force 16.31007N Force 20.60999N Impulse -1.02753Ns Impulse -1.29843Ns V(final) 0.558758m/s V(final) 0.521522m/s

Average Decel -2.24193m/s2 Average Decel -2.83299m/s2 test6 dd9 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1129 0.073 Coordinate 1 779 0.068Coordinate 2 1066 -0.037 Coordinate 2 720 -0.059Mass 7.275kg Mass 7.275kg time of impact 0.063s time of impact 0.059s Force 3.666667lbf Force 4.233333lbf Force 16.31007N Force 18.83071N Impulse -1.02753Ns Impulse -1.11101Ns V(final) 0.558758m/s V(final) 0.547284m/s


100


101


102


103


104

HORIZONTAL ROCKER-BOGIE FRONT WHEEL 0.8m/s 1 inch 2 inch data111 ex1 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 450 0.112 Coordinate 1 586 0.125Coordinate 2 402 0 Coordinate 2 529 -0.007Mass 7.275kg Mass 7.275kg time of impact 0.048s time of impact 0.057s Force 3.733333lbf Force 4.4lbf Force 16.60661N Force 19.57208N Impulse -0.79712Ns Impulse -1.11561Ns V(final) 0.690431m/s V(final) 0.646652m/s Average Decel -2.2827m/s2 Average Decel -2.69032m/s2 data112 ex2 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 839 0.12 Coordinate 1 773 0.117Coordinate 2 794 0 Coordinate 2 718 -0.005Mass 7.275kg Mass 7.275kg time of impact 0.045s time of impact 0.055s Force 4lbf Force 4.066667lbf Force 17.7928N Force 18.08935N Impulse -0.80068Ns Impulse -0.99491Ns V(final) 0.689941m/s V(final) 0.663242m/s Average Decel -2.44575m/s2 Average Decel -2.48651m/s2 data113 ex3 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 529 0.078 Coordinate 1 394 0.122Coordinate 2 453 -0.056 Coordinate 2 337 0Mass 7.275kg Mass 7.275kg time of impact 0.076s time of impact 0.057s Force 4.466667lbf Force 4.066667lbf Force 19.86863N Force 18.08935N Impulse -1.51002Ns Impulse -1.03109Ns V(final) 0.592438m/s V(final) 0.658269m/s Average Decel -2.73108m/s2 Average Decel -2.48651m/s2

105

data115 ex5 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 283 0.117 Coordinate 1 656 0.117Coordinate 2 230 0 Coordinate 2 588 -0.005Mass 7.275kg Mass 7.275kg time of impact 0.053s time of impact 0.068s Force 3.9lbf Force 4.066667lbf Force 17.34798N Force 18.08935N Impulse -0.91944Ns Impulse -1.23008Ns V(final) 0.673616m/s V(final) 0.630917m/s

Average Decel -2.3846m/s2 Average Decel -2.48651m/s2 data116 ex6 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 354 0.11 Coordinate 1 514 0.119Coordinate 2 302 Coordinate 2 460 -0.005Mass 7.275kg Mass 7.275kg time of impact 0.052s time of impact 0.054s Force 3.666667lbf Force 4.133333lbf Force 16.31007N Force 18.38589N Impulse -0.84812Ns Impulse -0.99284Ns V(final) 0.683419m/s V(final) 0.663527m/s


106

HORIZONTAL ROCKER-BOGIE FRONT WHEEL 0.8m/s 1.5 inch 2.5 inch e1 sk2 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 336 0.118 Coordinate 1 831 0.09Coordinate 2 289 -0.002 Coordinate 2 775 -0.049Mass 7.275kg Mass 7.275kg time of impact 0.047s time of impact 0.056s Force 4lbf Force 4.633333lbf Force 17.7928N Force 20.60999N Impulse -0.83626Ns Impulse -1.15416Ns V(final) 0.68505m/s V(final) 0.641353m/s Average Decel -2.44575m/s2 Average Decel -2.83299m/s2 e3 sk3 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 564 0.123 Coordinate 1 792 0.09Coordinate 2 509 0.002 Coordinate 2 738 -0.046Mass 7.275kg Mass 7.275kg time of impact 0.055s time of impact 0.054s Force 4.033333lbf Force 4.533333lbf Force 17.94107N Force 20.16517N Impulse -0.98676Ns Impulse -1.08892Ns V(final) 0.664363m/s V(final) 0.65032m/s Average Decel -2.46613m/s2 Average Decel -2.77185m/s2 e4 sk4 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 611 0.122 Coordinate 1 619 0.09Coordinate 2 512 0 Coordinate 2 568 -0.051Mass 7.275kg Mass 7.275kg time of impact 0.099s time of impact 0.051s Force 4.066667lbf Force 4.7lbf Force 18.08935N Force 20.90654N Impulse -1.79085Ns Impulse -1.06623Ns V(final) 0.553836m/s V(final) 0.653439m/s Average Decel -2.48651m/s2 Average Decel -2.87375m/s2

107

e5 sk5 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 679 0.123 Coordinate 1 644 0.095Coordinate 2 625 0.002 Coordinate 2 597 -0.049Mass 7.275kg Mass 7.275kg time of impact 0.054s time of impact 0.047s Force 4.033333lbf Force 4.8lbf Force 17.94107N Force 21.35136N Impulse -0.96882Ns Impulse -1.00351Ns V(final) 0.666829m/s V(final) 0.66206m/s

Average Decel -2.46613m/s2 Average Decel -2.93489m/s2 e6 sk6 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 466 0.122 Coordinate 1 557 0.081Coordinate 2 410 -0.007 Coordinate 2 491 -0.056Mass 7.275kg Mass 7.275kg time of impact 0.056s time of impact 0.066s Force 4.3lbf Force 4.566667lbf Force 19.12726N Force 20.31345N Impulse -1.07113Ns Impulse -1.34069Ns V(final) 0.652766m/s V(final) 0.615713m/s


108


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112

HORIZONTAL ROCKER-BOGIE FRONT WHEEL 1m/s 1inch 2 inch q1 exp2 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 351 0.071 Coordinate 1 1000 0.132Coordinate 2 296 -0.056 Coordinate 2 946 0.005Mass 7.275kg Mass 7.275kg time of impact 0.055s time of impact 0.054s Force 4.233333lbf Force 4.233333lbf Force 18.83071N Force 18.83071N Impulse -1.03569Ns Impulse -1.01686Ns V(final) 0.857637m/s V(final) 0.860226m/s Average Decel -2.58841m/s2 Average Decel -2.58841m/s2 q2 exp3 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 611 0.079 Coordinate 1 373 0.1Coordinate 2 554 -0.044 Coordinate 2 309 -0.039Mass 7.275kg Mass 7.275kg time of impact 0.057s time of impact 0.064s Force 4.1lbf Force 4.633333lbf Force 18.23762N Force 20.60999N Impulse -1.03954Ns Impulse -1.31904Ns V(final) 0.857107m/s V(final) 0.818689m/s Average Decel -2.50689m/s2 Average Decel -2.83299m/s2 q3 exp4 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 550 0.076 Coordinate 1 596 0.095Coordinate 2 392 -0.039 Coordinate 2 544 -0.032Mass 7.275kg Mass 7.275kg time of impact 0.158s time of impact 0.052s Force 3.833333lbf Force 4.233333lbf Force 17.05143N Force 18.83071N Impulse -2.69413Ns Impulse -0.9792Ns V(final) 0.629673m/s V(final) 0.865402m/s Average Decel -2.34384m/s2 Average Decel -2.58841m/s2

113

exp5 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 Coordinate 1 399 0.095Coordinate 2 Coordinate 2 325 -0.039Mass 7.275kg Mass 7.275kg time of impact 0s time of impact 0.074s Force 0lbf Force 4.466667lbf Force 0N Force 19.86863N Impulse 0Ns Impulse -1.47028Ns V(final) 1m/s V(final) 0.7979m/s

Average Decel #DIV/0! m/s2 Average Decel -2.73108m/s2 exp6 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 Coordinate 1 672 0.132Coordinate 2 Coordinate 2 593 -0.042Mass 7.275kg Mass 7.275kg time of impact 0s time of impact 0.079s Force 0lbf Force 5.8lbf Force 0N Force 25.79956N Impulse 0Ns Impulse -2.03817Ns V(final) 1m/s V(final) 0.71984m/s

Average Decel #DIV/0! m/s2 Average Decel -3.54633m/s2 1 inch height wedge 2 inch height wedge v(initial) 1m/s v(initial) 1m/s time of impact 0.09s time of impact 0.0646s Impact Force 18.03992N Impact Force 20.78792N V(final) 0.781473m/s V(final) 0.812411m/s Deceleration -2.47971m/s2 Deceleration -2.85745m/s2

114

HORIZONTAL ROCKER-BOGIE FRONT WHEEL 1m/s 1.5 inch 2.5 inch qq1 yes1 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 418 0.088 Coordinate 1 779 0.12Coordinate 2 364 -0.042 Coordinate 2 721 -0.037Mass 7.275kg Mass 7.275kg time of impact 0.054s time of impact 0.058s Force 4.333333lbf Force 5.233333lbf Force 19.27553N Force 23.27891N Impulse -1.04088Ns Impulse -1.35018Ns V(final) 0.856924m/s V(final) 0.814409m/s Average Decel -2.64956m/s2 Average Decel -3.19985m/s2 qq2 yes2 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 585 0.085 Coordinate 1 573 0.117Coordinate 2 403 -0.032 Coordinate 2 519 -0.032Mass 7.275kg Mass 7.275kg time of impact 0.182s time of impact 0.054s Force 3.9lbf Force 4.966667lbf Force 17.34798N Force 22.09273N Impulse -3.15733Ns Impulse -1.19301Ns V(final) 0.566002m/s V(final) 0.836013m/s Average Decel -2.3846m/s2 Average Decel -3.0368m/s2 qq3 yes3 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 556 0.095 Coordinate 1 412 0.11Coordinate 2 501 -0.029 Coordinate 2 365 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.055s time of impact 0.047s Force 4.133333lbf Force 4.566667lbf Force 18.38589N Force 20.31345N Impulse -1.01122Ns Impulse -0.95473Ns V(final) 0.861m/s V(final) 0.868765m/s Average Decel -2.52727m/s2 Average Decel -2.79223m/s2

115

qq4 yes4 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 891 0.09 Coordinate 1 712 0.125Coordinate 2 826 -0.042 Coordinate 2 651 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.065s time of impact 0.061s Force 4.4lbf Force 5.066667lbf Force 19.57208N Force 22.53755N Impulse -1.27219Ns Impulse -1.37479Ns V(final) 0.825129m/s V(final) 0.811025m/s

Average Decel -2.69032m/s2 Average Decel -3.09794m/s2 qq5 yes5 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 425 0.098 Coordinate 1 649 0.103Coordinate 2 284 -0.024 Coordinate 2 600 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.141s time of impact 0.049s Force 4.066667lbf Force 4.333333lbf Force 18.08935N Force 19.27553N Impulse -2.5506Ns Impulse -0.9445Ns V(final) 0.649402m/s V(final) 0.870172m/s

Average Decel -2.48651m/s2 Average Decel -2.64956m/s2 1.5 inch height wedge 2.5 inch height wedge v(initial) 1m/s v(initial) 1m/s time of impact 0.0994s time of impact 0.0538s Impact Force 18.53417N Impact Force 21.49963N V(final) 0.751692m/s V(final) 0.840077m/s Deceleration -2.54765m/s2 Deceleration -2.95528m/s2

116

Output excitation voltage of the front motor mount at speed 1 m/s over 1.0” height wedge

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120

Appendix B HORIZONTAL ROCKER BOGIE MIDDLE WHEEL 0.5m/s

1 inch 2 inch scope1 he1 time voltage time voltage Coordinate 1 1721 0.007 Coordinate 1 1886 0.056Coordinate 2 1674 -0.032 Coordinate 2 1802 -0.005Mass 7.275kg Mass 7.275kg time 0.047s time 0.084s Force 1.3lbf Force 2.033333lbf Force 5.78266N Force 9.044673N Impulse -0.27179Ns Impulse -0.75975Ns Average Decel -0.79487m/s2 Average Decel -1.24325m/s2

scope2 he2 time voltage time voltage Coordinate 1 1467 0.02 Coordinate 1 2005 0.061Coordinate 2 1422 -0.02 Coordinate 2 1914 0.002Mass 7.275kg Mass 7.275kg time of impact 0.045s time of impact 0.091s Force 1.333333lbf Force 1.966667lbf Force 5.930933N Force 8.748127N Impulse -0.26689Ns Impulse -0.79608Ns Average Decel -0.81525m/s2 Average Decel -1.20249m/s2

scope3 he3 time voltage time voltage Coordinate 1 1601 0.017 Coordinate 1 1716 0.022Coordinate 2 1520 -0.017 Coordinate 2 1647 -0.024Mass 7.275kg Mass 7.275kg time of impact 0.081s time of impact 0.069s Force 1.133333lbf Force 1.533333lbf Force 5.041293N Force 6.820573N Impulse -0.40834Ns Impulse -0.47062Ns Average Decel -0.69296m/s2 Average Decel -0.93754m/s2

121



time of impact 0.0614s time of impact 0.0872s Impact Force 5.456459N Impact Force 8.837091N Deceleration -0.75003m/s2 Deceleration -1.21472m/s2

122

HORIZONTAL ROCKER BOGIE MIDDLE WHEEL 0.5m/s

1.5 inch 2.5 inch We1 she1 time voltage time voltage Coordinate 1 1558 0.039 Coordinate 1 2095 0.049Coordinate 2 1472 -0.015 Coordinate 2 2039 -0.015Mass 7.275kg Mass 7.275kg time of impact 0.086s time of impact 0.056s Force 1.8lbf Force 2.133333lbf Force 8.00676N Force 9.489493N Impulse -0.68858Ns Impulse -0.53141Ns

Average Decel -1.10059m/s2 Average Decel -1.3044m/s2 We3 she2 time voltage time voltage Coordinate 1 1706 0.039 Coordinate 1 2056 0.046Coordinate 2 1637 -0.015 Coordinate 2 1983 -0.01Mass 7.275kg Mass 7.275kg time of impact 0.069s time of impact 0.073s Force 1.8lbf Force 1.866667lbf Force 8.00676N Force 8.303307N Impulse -0.55247Ns Impulse -0.60614Ns

Average Decel -1.10059m/s2 Average Decel -1.14135m/s2 We4 she3 time voltage time voltage Coordinate 1 1950 0.039 Coordinate 1 1135 0.056Coordinate 2 1841 -0.01 Coordinate 2 1055 -0.005Mass 7.275kg Mass 7.275kg time of impact 0.109s time of impact 0.08s Force 1.633333lbf Force 2.033333lbf Force 7.265393N Force 9.044673N Impulse -0.79193Ns Impulse -0.72357Ns Average Decel -0.99868m/s2 Average Decel -1.24325m/s2 We5 she4 time voltage time voltage Coordinate 1 1914 0.034 Coordinate 1 2193 0.054Coordinate 2 1814 -0.007 Coordinate 2 2113 -0.002Mass 7.275kg Mass 7.275kg

123

time of impact 0.1s time of impact 0.08s Force 1.366667lbf Force 1.866667lbf Force 6.079207N Force 8.303307N Impulse -0.60792Ns Impulse -0.66426Ns

Average Decel -0.83563m/s2 Average Decel -1.14135m/s2 she5 time voltage Coordinate 1 2169 0.054 Coordinate 2 2103 -0.012 Mass 7.275kg time of impact 0.066s Force 2.2lbf Force 9.78604N Impulse -0.64588Ns Average Decel -1.34516m/s2 Average Average time of impact 0.091s time of impact 0.071s Impact Force 7.33953N Impact Force 8.985364N Deceleration -1.00887m/s2 Deceleration -1.2351m/s2

124

Output excitation voltage of the middle motor mount at speed 0.5 m/s over 1.0” height wedge

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128


1 inch 2 inch kiss1 good1 time Voltage time voltage Coordinate 1 1586 0.01 Coordinate 1 1419 0.051Coordinate 2 1528 -0.029 Coordinate 2 1326 -0.024Mass 7.275Kg Mass 7.275kg time of impact 0.058S time of impact 0.093s Force 1.3Lbf Force 2.5lbf Force 5.78266N Force 11.1205N Impulse -0.33539Ns Impulse -1.03421Ns

Average Decel -0.79487m/s2 Average Decel -1.52859m/s2 kiss2 good2 time Voltage time voltage Coordinate 1 1568 0.029 Coordinate 1 1589 0.054Coordinate 2 1440 -0.034 Coordinate 2 1497 -0.024Mass 7.275Kg Mass 7.275kg time of impact 0.128S time of impact 0.092s Force 2.1Lbf Force 2.6lbf Force 9.34122N Force 11.56532N Impulse -1.19568Ns Impulse -1.06401Ns

Average Decel -1.28402m/s2 Average Decel -1.58973m/s2 kiss3 good3 time Voltage time voltage Coordinate 1 1553 0.002 Coordinate 1 1657 0.046Coordinate 2 1490 -0.034 Coordinate 2 1568 -0.029Mass 7.275Kg Mass 7.275kg time of impact 0.063S time of impact 0.089s Force 1.2Lbf Force 2.5lbf Force 5.33784N Force 11.1205N Impulse -0.33628Ns Impulse -0.98972Ns Average Decel -0.73372m/s2 Average Decel -1.52859m/s2 kiss4 good4 time Voltage time Voltage Coordinate 1 1478 0 Coordinate 1 1684 0.039Coordinate 2 1419 -0.037 Coordinate 2 1593 -0.032Mass 7.275Kg Mass 7.275Kg

129

time of impact 0.059s time of impact 0.091s Force 1.233333Lbf Force 2.366667Lbf Force 5.486113N Force 10.52741N Impulse -0.32368Ns Impulse -0.95799Ns

Average Decel -0.7541m/s2 Average Decel -1.44707m/s2 good5 time Voltage Coordinate 1 2044 0.044 Coordinate 2 1934 -0.034 Mass 7.275Kg time of impact 0.11S Force 2.6Lbf Force 11.56532N Impulse -1.27219Ns Average Decel -1.58973m/s2 Average Average time of impact 0.077S time of impact 0.095s Impact Force 6.486958N Impact Force 11.17981N Deceleration -0.89168m/s2 Deceleration -1.53674m/s2

130


1.5 inch 2.5 inch kipr1 stg1 time Voltage time voltage Coordinate 1 1561 0.037 Coordinate 1 1958 0.05Coordinate 2 1501 -0.029 Coordinate 2 1850 -0.02Mass 7.275Kg Mass 7.275kg time of impact 0.06S time of impact 0.108s Force 2.2lbf Force 2.333333lbf Force 9.78604N Force 10.37913N Impulse -0.58716Ns Impulse -1.12095Ns

Average Decel -1.34516M/s2 Average Decel -1.42668m/s2 kipr2 stg2 time Voltage time voltage Coordinate 1 1783 0.044 Coordinate 1 1261 0.061Coordinate 2 1669 -0.027 Coordinate 2 1855 -0.017Mass 7.275Kg Mass 7.275kg time of impact 0.114S time of impact -0.594s Force 2.366667lbf Force 2.6lbf Force 10.52741N Force 11.56532N Impulse -1.20012Ns Impulse 6.8698Ns

Average Decel -1.44707M/s2 Average Decel -1.58973m/s2 kipr3 stg3 time Voltage time voltage Coordinate 1 1596 0.044 Coordinate 1 1723 0.046Coordinate 2 1508 -0.034 Coordinate 2 1638 -0.032Mass 7.275Kg Mass 7.275kg time of impact 0.088S time of impact 0.085s Force 2.6Lbf Force 2.6lbf Force 11.56532N Force 11.56532N Impulse -1.01775Ns Impulse -0.98305Ns Average Decel -1.58973m/s2 Average Decel -1.58973m/s2 kipr4 stg4 time Voltage time voltage Coordinate 1 1532 0.034 Coordinate 1 1159 0.049Coordinate 2 1407 -0.029 Coordinate 2 1064 -0.029Mass 7.275Kg Mass 7.275kg

131


Average Decel -1.28402m/s2 Average Decel -1.58973m/s2 stg5 time voltage Coordinate 1 1520 0.046 Coordinate 2 1420 -0.039 Mass 7.275kg time of impact 0.1s Force 2.833333lbf Force 12.60323N Impulse -1.26032Ns Average Decel -1.7324m/s2 Average Average time of impact 0.09675s time of impact -0.0412s Impact Force 10.305N Impact Force 11.53567N Deceleration -1.41649m/s2 Deceleration -1.58566m/s2

132


133


134


135


136


1 inch 2 inch red1 new1 Time voltage time Voltage Coordinate 1 1444 0.034 Coordinate 1 1245 0.063Coordinate 2 1309 -0.029 Coordinate 2 1115 -0.032Mass 7.275kg Mass 7.275Kg time of impact 0.135s time of impact 0.13S Force 2.1lbf Force 3.166667Lbf Force 9.34122N Force 14.08597N Impulse -1.26106Ns Impulse -1.83118Ns

Average Decel -1.28402m/s2 Average Decel -1.93622m/s2 red2 new2 Time voltage time Voltage Coordinate 1 1234 0.029 Coordinate 1 1453 0.046Coordinate 2 1124 -0.032 Coordinate 2 1377 -0.015Mass 7.275kg Mass 7.275Kg time of impact 0.11s time of impact 0.076S Force 2.033333lbf Force 2.033333Lbf Force 9.044673N Force 9.044673N Impulse -0.99491Ns Impulse -0.6874Ns

Average Decel -1.24325m/s2 Average Decel -1.24325m/s2 red3 new3 Time voltage time Voltage Coordinate 1 1305 0.034 Coordinate 1 1300 0.051Coordinate 2 1175 -0.029 Coordinate 2 1156 -0.032Mass 7.275kg Mass 7.275Kg time of impact 0.13s time of impact 0.144S Force 2.1lbf Force 2.766667Lbf Force 9.34122N Force 12.30669N Impulse -1.21436Ns Impulse -1.77216Ns Average Decel -1.28402m/s2 Average Decel -1.69164m/s2 red4 new4 Time voltage time Voltage Coordinate 1 1613 0.032 Coordinate 1 1258 0.051Coordinate 2 1479 -0.032 Coordinate 2 1100 -0.032Mass 7.275kg Mass 7.275Kg

137

time of impact 0.134s time of impact 0.158S Force 2.133333lbf Force 2.766667Lbf Force 9.489493N Force 12.30669N Impulse -1.27159Ns Impulse -1.94446Ns

Average Decel -1.3044m/s2 Average Decel -1.69164m/s2 red5 new5 Time voltage time Voltage Coordinate 1 1533 0.032 Coordinate 1 1139 0.051Coordinate 2 1391 -0.029 Coordinate 2 1005 -0.029Mass 7.275kg Mass 7.275Kg time of impact 0.142s time of impact 0.134S Force 2.033333lbf Force 2.666667Lbf Force 9.044673N Force 11.86187N Impulse -1.28434Ns Impulse -1.58949Ns Average Decel -1.24325m/s2 Average Decel -1.6305m/s2 Average Average time of impact 0.1302s time of impact 0.1284s Impact Force 9.252256N Impact Force 11.92118N

Deceleration -1.27179m/s2 Deceleration -1.63865m/s2

138


1.5 inch 2.5 inch red6 fine1 time voltage time voltage Coordinate 1 1308 0.034 Coordinate 1 1327 0.051Coordinate 2 1178 -0.039 Coordinate 2 1194 -0.032Mass 7.275kg Mass 7.275kg time of impact 0.13s time of impact 0.133s Force 2.433333lbf Force 2.766667lbf Force 10.82395N Force 12.30669N Impulse -1.40711Ns Impulse -1.63679Ns

Average Decel -1.48783m/s2 Average Decel -1.69164m/s2 red7 fine2 time voltage time voltage Coordinate 1 1249 0.029 Coordinate 1 970 0.068Coordinate 2 1147 -0.042 Coordinate 2 796 -0.022Mass 7.275kg Mass 7.275kg time of impact 0.102s time of impact 0.174s Force 2.366667lbf Force 3lbf Force 10.52741N Force 13.3446N Impulse -1.0738Ns Impulse -2.32196Ns

Average Decel -1.44707m/s2 Average Decel -1.83431m/s2 red8 fine3 time voltage time voltage Coordinate 1 1317 0.037 Coordinate 1 1453 0.044Coordinate 2 1182 -0.039 Coordinate 2 1325 -0.037Mass 7.275kg Mass 7.275kg time of impact 0.135s time of impact 0.128s Force 2.533333lbf Force 2.7lbf Force 11.26877N Force 12.01014N Impulse -1.52128Ns Impulse -1.5373Ns Average Decel -1.54897m/s2 Average Decel -1.65088m/s2 red9 fine4 time voltage time voltage Coordinate 1 1204 0.044 Coordinate 1 1408 0.056Coordinate 2 1120 -0.024 Coordinate 2 1274 -0.024Mass 7.275kg Mass 7.275kg

139


Average Decel -1.38592m/s2 Average Decel -1.6305m/s2 fine5 time voltage Coordinate 1 1165 0.049 Coordinate 2 1068 -0.027 Mass 7.275kg time of impact 0.097s Force 2.533333lbf Force 11.26877N Impulse -1.09307Ns Average Decel -1.54897m/s2 Average Average time of impact 0.11275s time of impact 0.1332s Impact Force 10.67568N Impact Force 12.15841N


140


141


142


143


144

HORIZONTAL ROCKER BOGIE MIDDLE WHEEL 1m/s

1 inch 2 inch you1 hello1 time Voltage time voltage Coordinate 1 1064 0.039 Coordinate 1 1258 0.044Coordinate 2 886 -0.039 Coordinate 2 1147 -0.042Mass 7.275Kg Mass 7.275kg time of impact 0.178S time of impact 0.111s Force 2.6Lbf Force 2.866667lbf Force 11.56532N Force 12.75151N Impulse -2.05863Ns Impulse -1.41542Ns

Average Decel -1.58973m/s2 Average Decel -1.75278m/s2 you2 hello2 time Voltage time voltage Coordinate 1 1139 0.034 Coordinate 1 1289 0.049Coordinate 2 988 -0.037 Coordinate 2 1177 -0.039Mass 7.275Kg Mass 7.275kg time of impact 0.151S time of impact 0.112s Force 2.366667Lbf Force 2.933333lbf Force 10.52741N Force 13.04805N Impulse -1.58964Ns Impulse -1.46138Ns

Average Decel -1.44707m/s2 Average Decel -1.79355m/s2 you3 hello3 time Voltage time voltage Coordinate 1 1221 0.034 Coordinate 1 1370 0.053Coordinate 2 1047 -0.034 Coordinate 2 1272 -0.02Mass 7.275Kg Mass 7.275kg time of impact 0.174S time of impact 0.098s Force 2.266667Lbf Force 2.433333lbf Force 10.08259N Force 10.82395N Impulse -1.75437Ns Impulse -1.06075Ns Average Decel -1.38592m/s2 Average Decel -1.48783m/s2 you4 hello4 time Voltage time voltage Coordinate 1 1178 0.042 Coordinate 1 1132 0.046Coordinate 2 1005 -0.032 Coordinate 2 1031 -0.032Mass 7.275Kg Mass 7.275kg

145

time of impact 0.173S time of impact 0.101s Force 2.466667Lbf Force 2.6lbf Force 10.97223N Force 11.56532N Impulse -1.8982Ns Impulse -1.1681Ns

Average Decel -1.50821m/s2 Average Decel -1.58973m/s2 you5 time voltage Coordinate 1 1436 0.044 Coordinate 2 1310 -0.022 Mass 7.275Kg time of impact 0.126S Force 2.2Lbf Force 9.78604N Impulse -1.23304Ns Average Decel -1.34516m/s2 Average Average time of impact 0.1604S time of impact 0.1055s Impact Force 10.58672N Impact Force 12.04721N Deceleration -1.45522m/s2 Deceleration -1.65597m/s2

146

HORIZONTAL ROCKER BOGIE MIDDLE WHEEL 1m/s

1.5 inch 2.5 inch ha1 dk1 time voltage time voltage Coordinate 1 1001 0.037 Coordinate 1 985 0.034Coordinate 2 915 -0.022 Coordinate 2 820 -0.049Mass 7.275kg Mass 7.275kg time of impact 0.086s time of impact 0.165s Force 1.966667lbf Force 2.766667lbf Force 8.748127N Force 12.30669N Impulse -0.75234Ns Impulse -2.0306Ns

Average Decel -1.20249m/s2 Average Decel -1.69164m/s2 ha2 dk2 time voltage time voltage Coordinate 1 1136 0.051 Coordinate 1 1373 0.059Coordinate 2 982 -0.032 Coordinate 2 1233 -0.02Mass 7.275kg Mass 7.275kg time of impact 0.154s time of impact 0.14s Force 2.766667lbf Force 2.633333lbf Force 12.30669N Force 11.71359N Impulse -1.89523Ns Impulse -1.6399Ns

Average Decel -1.69164m/s2 Average Decel -1.61012m/s2 ha3 dk3 time voltage time voltage Coordinate 1 984 0.049 Coordinate 1 1141 0.054Coordinate 2 871 -0.032 Coordinate 2 1017 -0.029Mass 7.275kg Mass 7.275kg time of impact 0.113s time of impact 0.124s Force 2.7lbf Force 2.766667lbf Force 12.01014N Force 12.30669N Impulse -1.35715Ns Impulse -1.52603Ns Average Decel -1.65088m/s2 Average Decel -1.69164m/s2 ha4 dk4 time voltage time voltage Coordinate 1 1078 0.054 Coordinate 1 1413 0.061Coordinate 2 922 -0.024 Coordinate 2 1290 -0.024Mass 7.275kg Mass 7.275kg

147


Average Decel -1.58973m/s2 Average Decel -1.7324m/s2 dk5 time voltage Coordinate 1 1243 0.059 Coordinate 2 1087 -0.024 Mass 7.275kg time of impact 0.156s Force 2.766667lbf Force 12.30669N Impulse -1.91984Ns Average Decel -1.69164m/s2 Average Average time of impact 0.12725s time of impact 0.1416s Impact Force 11.15757N Impact Force 12.24738N Deceleration -1.53369m/s2 Deceleration -1.68349m/s2

148


149


150


151


152

Appendix C TILTED ROCKER-BOGIE FRONT WHEEL 0.5m/s 1 inch 2 inch t1 isay1 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 940 0.017 Coordinate 1 663 0.027Coordinate 2 896 -0.012 Coordinate 2 611 -0.005Mass 7.332kg Mass 7.332kg time 0.044s time 0.052s Force 2.9lbf Force 3.2lbf Force 12.89978N Force 14.23424N Impulse -0.56759Ns Impulse -0.74018Ns V(final) 0.422587m/s V(final) 0.399048m/s

Average Decel -1.75938m/s2 Average Decel -1.94139m/s2 t4 isay2 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 929 0.015 Coordinate 1 928 0.027Coordinate 2 890 -0.015 Coordinate 2 879 -0.005Mass 7.332kg Mass 7.332kg time 0.039s time 0.049s Force 3lbf Force 3.2lbf Force 13.3446N Force 14.23424N Impulse -0.52044Ns Impulse -0.69748Ns V(final) 0.429018m/s V(final) 0.404872m/s

Average Decel -1.82005m/s2 Average Decel -1.94139m/s2 t5 isay3 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 922 0.015 Coordinate 1 911 0.024Coordinate 2 885 -0.015 Coordinate 2 865 -0.007Mass 7.332kg Mass 7.332kg time 0.037s time 0.046s Force 3lbf Force 3.1lbf Force 13.3446N Force 13.78942N Impulse -0.49375Ns Impulse -0.63431Ns V(final) 0.432658m/s V(final) 0.413487m/s


153

t6 isay4 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1078 0.015 Coordinate 1 1009 0.024Coordinate 2 1042 -0.012 Coordinate 2 956 -0.007Mass 7.332kg Mass 7.332kg time 0.036s time 0.053s Force 2.7lbf Force 3.1lbf Force 12.01014N Force 13.78942N Impulse -0.43237Ns Impulse -0.73084Ns V(final) 0.44103m/s V(final) 0.400322m/s

Average Decel -1.63804m/s2 Average Decel -1.88072m/s2 t7 isay5 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1113 0.012 Coordinate 1 677 0.027Coordinate 2 1068 -0.015 Coordinate 2 628 -0.005Mass 7.332kg Mass 7.332kg time 0.045s time 0.049s Force 2.7lbf Force 3.2lbf Force 12.01014N Force 14.23424N Impulse -0.54046Ns Impulse -0.69748Ns V(final) 0.426288m/s V(final) 0.404872m/s


154

TILTED ROCKER-BOGIE FRONT WHEEL 0.5m/s 1.5 inch 2.5 inch usay1 hu1 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 871 0.027 Coordinate 1 944 0.024Coordinate 2 826 -0.005 Coordinate 2 887 -0.005Mass 7.332kg Mass 7.332kg time 0.045s time 0.057s Force 3.2lbf Force 2.9lbf Force 14.23424N Force 12.89978N Impulse -0.64054Ns Impulse -0.73529Ns V(final) 0.412638m/s V(final) 0.399715m/s Average Decel -1.94139m/s2 Average Decel -1.75938m/s2 usay2 hu2 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 604 0.02 Coordinate 1 749 0.024Coordinate 2 553 -0.007 Coordinate 2 695 -0.01Mass 7.332kg Mass 7.332kg time 0.051s time 0.054s Force 2.7lbf Force 3.4lbf Force 12.01014N Force 15.12388N Impulse -0.61252Ns Impulse -0.81669Ns V(final) 0.41646m/s V(final) 0.388613m/s Average Decel -1.63804m/s2 Average Decel -2.06272m/s2 usay3 hu3 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 698 0.022 Coordinate 1 1076 0.027Coordinate 2 649 -0.007 Coordinate 2 1029 -0.005Mass 7.332kg Mass 7.332kg time 0.049s time 0.047s Force 2.9lbf Force 3.2lbf Force 12.89978N Force 14.23424N Impulse -0.63209Ns Impulse -0.66901Ns V(final) 0.41379m/s V(final) 0.408755m/s Average Decel -1.75938m/s2 Average Decel -1.94139m/s2

155

usay4 hu4 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 924 0.02 Coordinate 1 1208 0.027Coordinate 2 822 -0.012 Coordinate 2 1149 -0.005Mass 7.332kg Mass 7.332kg time 0.102s time 0.059s Force 3.2lbf Force 3.2lbf Force 14.23424N Force 14.23424N Impulse -1.45189Ns Impulse -0.83982Ns V(final) 0.301979m/s V(final) 0.385458m/s

Average Decel -1.94139m/s2 Average Decel -1.94139m/s2 usay5 hu5 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 774 0.024 Coordinate 1 1015 0.032Coordinate 2 714 -0.005 Coordinate 2 960 -0.002Mass 7.332kg Mass 7.332kg time 0.06s time 0.055s Force 2.9lbf Force 3.4lbf Force 12.89978N Force 15.12388N Impulse -0.77399Ns Impulse -0.83181Ns V(final) 0.394437m/s V(final) 0.38655m/s


156

Output excitation voltage of the Tilted Front motor mount at speed 0.5 m/s over 1” height wedge

157

Output excitation voltage of the Tilted Front motor mount at speed 0.5 m/s over 1.5” height wedge

158


159


160

TILTED ROCKER-BOGIE FRONT WHEEL 0.7m/s 1 inch 2 inch deal1 tfk1 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 723 0.024 Coordinate 1 711 0.024Coordinate 2 677 -0.005 Coordinate 2 665 -0.007Mass 7.332kg Mass 7.332kg time 0.046s time 0.046s Force 2.9lbf Force 3.1lbf Force 12.89978N Force 13.78942N Impulse -0.59339Ns Impulse -0.63431Ns V(final) 0.619068m/s V(final) 0.613487m/s Average Decel -1.75938m/s2 Average Decel -1.88072m/s2 deal2 tfk2 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 906 0.022 Coordinate 1 639 0.024Coordinate 2 856 -0.007 Coordinate 2 591 -0.007Mass 7.332kg Mass 7.332kg time 0.05s time 0.048s Force 2.9lbf Force 3.1lbf Force 12.89978N Force 13.78942N Impulse -0.64499Ns Impulse -0.66189Ns V(final) 0.612031m/s V(final) 0.609726m/s Average Decel -1.75938m/s2 Average Decel -1.88072m/s2 deal3 tfk3 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 968 0.02 Coordinate 1 692 0.027Coordinate 2 923 -0.01 Coordinate 2 637 -0.007Mass 7.332kg Mass 7.332kg time 0.045s time 0.055s Force 3lbf Force 3.4lbf Force 13.3446N Force 15.12388N Impulse -0.60051Ns Impulse -0.83181Ns V(final) 0.618098m/s V(final) 0.58655m/s Average Decel -1.82005m/s2 Average Decel -2.06272m/s2

161

deal4 tfk4 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1001 0.022 Coordinate 1 826 0.027Coordinate 2 945 -0.007 Coordinate 2 748 -0.007Mass 7.332kg Mass 7.332kg time 0.056s time 0.078s Force 2.9lbf Force 3.4lbf Force 12.89978N Force 15.12388N Impulse -0.72239Ns Impulse -1.17966Ns V(final) 0.601475m/s V(final) 0.539108m/s

Average Decel -1.75938m/s2 Average Decel -2.06272m/s2 deal5 tfk5 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 952 0.022 Coordinate 1 665 0.024Coordinate 2 901 -0.007 Coordinate 2 616 -0.01Mass 7.332kg Mass 7.332kg time 0.051s time 0.049s Force 2.9lbf Force 3.4lbf Force 12.89978N Force 15.12388N Impulse -0.65789Ns Impulse -0.74107Ns V(final) 0.610272m/s V(final) 0.598927m/s


162

TILTED ROCKER-BOGIE FRONT WHEEL 0.7m/s 1.5 inch 2.5 inch diu1 fin1 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 718 0.024 Coordinate 1 841 0.032Coordinate 2 671 -0.007 Coordinate 2 781 -0.002Mass 7.332kg Mass 7.332kg time 0.047s time 0.06s Force 3.1lbf Force 3.4lbf Force 13.78942N Force 15.12388N Impulse -0.6481Ns Impulse -0.90743Ns V(final) 0.611606m/s V(final) 0.576237m/s Average Decel -1.88072m/s2 Average Decel -2.06272m/s2 diu2 fin2 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1129 0.024 Coordinate 1 529 0.034Coordinate 2 1066 -0.007 Coordinate 2 480 0Mass 7.332kg Mass 7.332kg time 0.063s time 0.049s Force 3.1lbf Force 3.4lbf Force 13.78942N Force 15.12388N Impulse -0.86873Ns Impulse -0.74107Ns V(final) 0.581515m/s V(final) 0.598927m/s Average Decel -1.88072m/s2 Average Decel -2.06272m/s2 diu3 fin3 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 769 0.022 Coordinate 1 537 0.034Coordinate 2 707 -0.007 Coordinate 2 487 0Mass 7.332kg Mass 7.332kg time 0.062s time 0.05s Force 2.9lbf Force 3.4lbf Force 12.89978N Force 15.12388N Impulse -0.79979Ns Impulse -0.75619Ns V(final) 0.590918m/s V(final) 0.596864m/s Average Decel -1.75938m/s2 Average Decel -2.06272m/s2

163

diu4 fin4 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 745 0.024 Coordinate 1 623 0.036Coordinate 2 693 -0.007 Coordinate 2 580 0.005Mass 7.332kg Mass 7.332kg time 0.052s time 0.043s Force 3.1lbf Force 3.1lbf Force 13.78942N Force 13.78942N Impulse -0.71705Ns Impulse -0.59295Ns V(final) 0.602203m/s V(final) 0.619129m/s

Average Decel -1.88072m/s2 Average Decel -1.88072m/s2 diu5 fin6 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 752 0.024 Coordinate 1 435 0.032Coordinate 2 701 -0.007 Coordinate 2 378 -0.002Mass 7.332kg Mass 7.332kg time 0.051s time 0.057s Force 3.1lbf Force 3.4lbf Force 13.78942N Force 15.12388N Impulse -0.70326Ns Impulse -0.86206Ns V(final) 0.604083m/s V(final) 0.582425m/s


164


165


166


167


168

TILTED FRONT WHEEL 0.8m/s 1 inch 2 inch j1 y1 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 546 0.027 Coordinate 1 1201 0.036Coordinate 2 478 -0.002 Coordinate 2 1152 -0.002Mass 7.332kg Mass 7.332kg time 0.068s time 0.049s Force 2.9lbf Force 3.8lbf Force 12.89978N Force 16.90316N Impulse -0.87719Ns Impulse -0.82825Ns V(final) 0.680362m/s V(final) 0.687036m/s Average Decel -1.75938m/s2 Average Decel -2.3054m/s2 j2 y2 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 542 0.024 Coordinate 1 584 0.032Coordinate 2 493 -0.005 Coordinate 2 524 -0.002Mass 7.332kg Mass 7.332kg time 0.049s time 0.06s Force 2.9lbf Force 3.4lbf Force 12.89978N Force 15.12388N Impulse -0.63209Ns Impulse -0.90743Ns V(final) 0.71379m/s V(final) 0.676237m/s Average Decel -1.75938m/s2 Average Decel -2.06272m/s2 j3 y3 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 722 0.039 Coordinate 1 395 0.033Coordinate 2 652 -0.005 Coordinate 2 345 -0.002Mass 7.332kg Mass 7.332kg time 0.07s time 0.05s Force 4.4lbf Force 3.5lbf Force 19.57208N Force 15.5687N Impulse -1.37005Ns Impulse -0.77844Ns V(final) 0.613142m/s V(final) 0.69383m/s Average Decel -2.66941m/s2 Average Decel -2.12339m/s2

169

j4 y4 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 742 0.029 Coordinate 1 439 0.035Coordinate 2 690 -0.005 Coordinate 2 384 -0.002Mass 7.332kg Mass 7.332kg time 0.052s time 0.055s Force 3.4lbf Force 3.7lbf Force 15.12388N Force 16.45834N Impulse -0.78644Ns Impulse -0.90521Ns V(final) 0.692738m/s V(final) 0.67654m/s

Average Decel -2.06272m/s2 Average Decel -2.24473m/s2 j5 y5 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 538 0.027 Coordinate 1 593 0.034Coordinate 2 425 -0.005 Coordinate 2 544 -0.002Mass 7.332kg Mass 7.332kg time 0.113s time 0.049s Force 3.2lbf Force 3.6lbf Force 14.23424N Force 16.01352N Impulse -1.60847Ns Impulse -0.78466Ns V(final) 0.580623m/s V(final) 0.692981m/s


170

TILTED ROCKER-BOGIE FRONT WHEEL 0.8m/s 1.5 inch 2.5 inch p1 u1 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 511 0.033 Coordinate 1 710 0.032Coordinate 2 468 0 Coordinate 2 668 -0.005Mass 7.332kg Mass 7.332kg time 0.043s time 0.042s Force 3.3lbf Force 3.7lbf Force 14.67906N Force 16.45834N Impulse -0.6312Ns Impulse -0.69125Ns V(final) 0.713912m/s V(final) 0.705721m/s Average Decel -2.00205m/s2 Average Decel -2.24473m/s2 p2 u2 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 552 0.034 Coordinate 1 783 0.029Coordinate 2 504 0 Coordinate 2 746 -0.007Mass 7.332kg Mass 7.332kg time 0.048s time 0.037s Force 3.4lbf Force 3.6lbf Force 15.12388N Force 16.01352N Impulse -0.72595Ns Impulse -0.5925Ns V(final) 0.700989m/s V(final) 0.71919m/s Average Decel -2.06272m/s2 Average Decel -2.18406m/s2 p3 u3 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 531 0.035 Coordinate 1 749 0.037Coordinate 2 480 0 Coordinate 2 706 -0.002Mass 7.332kg Mass 7.332kg time 0.051s time 0.043s Force 3.5lbf Force 3.9lbf Force 15.5687N Force 17.34798N Impulse -0.794Ns Impulse -0.74596Ns V(final) 0.691707m/s V(final) 0.698259m/s Average Decel -2.12339m/s2 Average Decel -2.36606m/s2

171

p4 u4 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 501 0.035 Coordinate 1 601 0.039Coordinate 2 439 0 Coordinate 2 550 -0.002Mass 7.332kg Mass 7.332kg time 0.062s time 0.051s Force 3.5lbf Force 4.1lbf Force 15.5687N Force 18.23762N Impulse -0.96526Ns Impulse -0.93012Ns V(final) 0.66835m/s V(final) 0.673143m/s

Average Decel -2.12339m/s2 Average Decel -2.4874m/s2 p5 u5 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 423 0.019 Coordinate 1 767 0.039Coordinate 2 367 -0.017 Coordinate 2 713 -0.002Mass 7.332kg Mass 7.332kg time 0.056s time 0.054s Force 3.6lbf Force 4.1lbf Force 16.01352N Force 18.23762N Impulse -0.89676Ns Impulse -0.98483Ns V(final) 0.677693m/s V(final) 0.66568m/s


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176

TILTED ROCKER-BOGIE FRONT WHEEL 1m/s 1 inch 2 inch no1 miss1 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 621 0.029 Coordinate 1 593 0.033Coordinate 2 580 -0.002 Coordinate 2 537 -0.005Mass 7.332kg Mass 7.332kg time 0.041s time 0.056s Force 3.1lbf Force 3.8lbf Force 13.78942N Force 16.90316N Impulse -0.56537Ns Impulse -0.94658Ns V(final) 0.922891m/s V(final) 0.870898m/s Average Decel -1.88072m/s2 Average Decel -2.3054m/s2 no2 miss2 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 595 0.024 Coordinate 1 570 0.037Coordinate 2 555 -0.005 Coordinate 2 527 -0.005Mass 7.332kg Mass 7.332kg time 0.04s time 0.043s Force 2.9lbf Force 4.2lbf Force 12.89978N Force 18.68244N Impulse -0.51599Ns Impulse -0.80334Ns V(final) 0.929625m/s V(final) 0.890433m/s Average Decel -1.75938m/s2 Average Decel -2.54807m/s2 no3 miss3 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 400 0.051 Coordinate 1 533 0.036Coordinate 2 356 -0.002 Coordinate 2 482 -0.002Mass 7.332kg Mass 7.332kg time 0.044s time 0.051s Force 5.3lbf Force 3.8lbf Force 23.57546N Force 16.90316N Impulse -1.03732Ns Impulse -0.86206Ns V(final) 0.858522m/s V(final) 0.882425m/s Average Decel -3.21542m/s2 Average Decel -2.3054m/s2

177

no4 miss4 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 434 0.029 Coordinate 1 630 0.036Coordinate 2 386 -0.005 Coordinate 2 588 0Mass 7.332kg Mass 7.332kg time 0.048s time 0.042s Force 3.4lbf Force 3.6lbf Force 15.12388N Force 16.01352N Impulse -0.72595Ns Impulse -0.67257Ns V(final) 0.900989m/s V(final) 0.90827m/s

Average Decel -2.06272m/s2 Average Decel -2.18406m/s2 no5 miss5 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 615 0.027 Coordinate 1 411 0.032Coordinate 2 570 -0.002 Coordinate 2 359 -0.002Mass 7.332kg Mass 7.332kg time 0.045s time 0.052s Force 2.9lbf Force 3.4lbf Force 12.89978N Force 15.12388N Impulse -0.58049Ns Impulse -0.78644Ns V(final) 0.920828m/s V(final) 0.892738m/s

Average Decel -1.75938m/s2 Average Decel -2.06272m/s2 1 inch height wedge 2 inch height wedge v(initial) 1m/s v(initial) 1m/s time of impact 0.04425s time of impact 0.047s Impact Force 16.12473N Impact Force 16.72523N V(final) 0.902491m/s V(final) 0.893466m/s Deceleration -2.19923m/s2 Deceleration -2.27506m/s2

178

TILTED ROCKER-BOGIE FRONT WHEEL 1m/s 1.5 inch 2.5 inch yo1 nihao1 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 521 0.033 Coordinate 1 535 0.042Coordinate 2 476 -0.005 Coordinate 2 484 0Mass 7.332kg Mass 7.332kg time 0.045s time 0.051s Force 3.8lbf Force 4.2lbf Force 16.90316N Force 18.68244N Impulse -0.76064Ns Impulse -0.9528Ns V(final) 0.896257m/s V(final) 0.870048m/s Average Decel -2.3054m/s2 Average Decel -2.54807m/s2 yo2 nihao2 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 500 0.035 Coordinate 1 499 0.037Coordinate 2 445 0 Coordinate 2 454 -0.002Mass 7.332kg Mass 7.332kg time 0.055s time 0.045s Force 3.5lbf Force 3.9lbf Force 15.5687N Force 17.34798N Impulse -0.85628Ns Impulse -0.78066Ns V(final) 0.883214m/s V(final) 0.893527m/s Average Decel -2.12339m/s2 Average Decel -2.36606m/s2 yo3 nihao3 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 730 0.029 Coordinate 1 654 0.037Coordinate 2 670 -0.007 Coordinate 2 595 -0.002Mass 7.332kg Mass 7.332kg time 0.06s time 0.059s Force 3.6lbf Force 3.9lbf Force 16.01352N Force 17.34798N Impulse -0.96081Ns Impulse -1.02353Ns V(final) 0.868956m/s V(final) 0.860402m/s Average Decel -2.18406m/s2 Average Decel -2.36606m/s2

179

yo4 nihao4 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 498 0.032 Coordinate 1 449 0.042Coordinate 2 444 -0.005 Coordinate 2 395 0Mass 7.332kg Mass 7.332kg time 0.054s time 0.054s Force 3.7lbf Force 4.2lbf Force 16.45834N Force 18.68244N Impulse -0.88875Ns Impulse -1.00885Ns V(final) 0.878785m/s V(final) 0.862404m/s

Average Decel -2.24473m/s2 Average Decel -2.54807m/s2 yo5 nihao5 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 563 0.032 Coordinate 1 622 0.035Coordinate 2 503 -0.005 Coordinate 2 563 -0.005Mass 7.332kg Mass 7.332kg time 0.06s time 0.059s Force 3.7lbf Force 4lbf Force 16.45834N Force 17.7928N Impulse -0.9875Ns Impulse -1.04978Ns V(final) 0.865316m/s V(final) 0.856823m/s

Average Decel -2.24473m/s2 Average Decel -2.42673m/s2 1.5 inch height wedge 2.5 inch height wedge v(initial) 1m/s v(initial) 1m/s time of impact 0.0548s time of impact 0.0536s Impact Force 16.28041N Impact Force 17.97073N V(final) 0.878506m/s V(final) 0.868641m/s Deceleration -2.22046m/s2 Deceleration -2.451m/s2

180

Output excitation voltage of the Tilted Front motor mount at speed 1 m/s over 1.0” height wedge

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Appendix D TILT ROCKER-BOGIE MIDDLE WHEEL 0.5m/s 1 inch 2 inch w1 d1 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1850 0.017 Coordinate 1 2181 0.029Coordinate 2 1789 -0.015 Coordinate 2 2048 -0.022Mass 7.275kg Mass 7.275kg time of impact 0.061s time of impact 0.133s Force 1.066667lbf Force 1.7lbf Force 4.744747N Force 7.56194N Impulse -0.28943Ns Impulse -1.00574Ns V(final) 0.460216m/s V(final) 0.361754m/s

Average Decel -0.6522m/s2 Average Decel -1.03944m/s2 w2 d2 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1736 0.032 Coordinate 1 2150 0.017Coordinate 2 1582 -0.024 Coordinate 2 2037 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.154s time of impact 0.113s Force 1.866667lbf Force 1.466667lbf Force 8.303307N Force 6.524027N Impulse -1.27871Ns Impulse -0.73722Ns V(final) 0.324232m/s V(final) 0.398665m/s

Average Decel -1.14135m/s2 Average Decel -0.89677m/s2 w3 d3 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1577 0.02 Coordinate 1 1873 0.022Coordinate 2 1522 -0.01 Coordinate 2 1744 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.055s time of impact 0.129s Force 1lbf Force 1.633333lbf Force 4.4482N Force 7.265393N Impulse -0.24465Ns Impulse -0.93724Ns V(final) 0.466371m/s V(final) 0.37117m/s


185

w4 d4 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1984 0.02 Coordinate 1 1955 0.022Coordinate 2 1876 -0.024 Coordinate 2 1822 -0.024Mass 7.275kg Mass 7.275kg time of impact 0.108s time of impact 0.133s Force 1.466667lbf Force 1.533333lbf Force 6.524027N Force 6.820573N Impulse -0.70459Ns Impulse -0.90714Ns V(final) 0.403148m/s V(final) 0.375308m/s

Average Decel -0.89677m/s2 Average Decel -0.93754m/s2 w5 d5 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 2342 0.017 Coordinate 1 1967 0.022Coordinate 2 2206 -0.022 Coordinate 2 1862 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.136s time of impact 0.105s Force 1.3lbf Force 1.633333lbf Force 5.78266N Force 7.265393N Impulse -0.78644Ns Impulse -0.76287Ns V(final) 0.391898m/s V(final) 0.395139m/s

Average Decel -0.79487m/s2 Average Decel -0.99868m/s2 time of impact 0.1028s time of impact 0.1226s Impact Force 5.374908N Impact Force 7.087465N V(final) 0.409173m/s V(final) 0.380407m/s Deceleration -0.81932m/s2 Deceleration -0.97422m/s2

186

TILT ROCKER-BOGIE MIDDLE WHEEL 0.5m/s

1.5 inch 2.5 inch pcc1 g1 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1981 0.012 Coordinate 1 2141 0.024Coordinate 2 1843 -0.022 Coordinate 2 2000 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.138s time of impact 0.141s Force 1.133333lbf Force 1.7lbf Force 5.041293N Force 7.56194N Impulse -0.6957Ns Impulse -1.06623Ns V(final) 0.404371m/s V(final) 0.353439m/s Average Decel -0.69296m/s2 Average Decel -1.03944m/s2 pcc2 g2 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1769 0.024 Coordinate 1 2013 0.017Coordinate 2 1644 -0.01 Coordinate 2 1924 -0.024Mass 7.275kg Mass 7.275kg time of impact 0.125s time of impact 0.089s Force 1.133333lbf Force 1.366667lbf Force 5.041293N Force 6.079207N Impulse -0.63016Ns Impulse -0.54105Ns V(final) 0.41338m/s V(final) 0.425629m/s Average Decel -0.69296m/s2 Average Decel -0.83563m/s2 pcc3 g3 V(initial) 0.5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 2038 0.026 Coordinate 1 1973 0.054Coordinate 2 1916 -0.01 Coordinate 2 1842 -0.007Mass 7.275kg Mass 7.275kg time of impact 0.122s time of impact 0.131s Force 1.2lbf Force 2.033333lbf Force 5.33784N Force 9.044673N Impulse -0.65122Ns Impulse -1.18485Ns V(final) 0.410486m/s V(final) 0.337134m/s Average Decel -0.73372m/s2 Average Decel -1.24325m/s2

187

pcc6 g4 V(initial) 5m/s V(initial) 0.5m/s time voltage time voltage Coordinate 1 1736 0.017 Coordinate 1 2012 0.054Coordinate 2 1640 -0.024 Coordinate 2 1838 -0.005Mass 7.275kg Mass 7.275kg time of impact 0.096s time of impact 0.174s Force 1.366667lbf Force 1.966667lbf Force 6.079207N Force 8.748127N Impulse -0.5836Ns Impulse -1.52217Ns V(final) 0.41978m/s V(final) 0.290766m/s

Average Decel -0.83563m/s2 Average Decel -1.20249m/s2 pcc5 V(initial) 0.5m/s time voltage Coordinate 1 1749 0.022 Coordinate 2 1616 -0.02 Mass 7.275kg time of impact 0.133s Force 1.4lbf Force 6.22748N Impulse -0.82825Ns V(final) 0.386151m/s

Average Decel -0.85601m/s2 time of impact 0.1228s time of impact 0.13375s Impact Force 5.545423N Impact Force 7.463091N V(final) 0.406833m/s V(final) 0.351742m/s Deceleration -0.76226m/s2 Deceleration -1.0802m/s2

188

Output excitation voltage of the Tilted Middle motor mount at speed 0.5 m/s over 1.0” height wedge

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TILT ROCKER-BOGIE MIDDLE WHEEL 0.7m/s 1 inch 2 inch ag1 mo1 V(initial) 0.7m/s V(initial) 0.7 m/s time voltage time voltage Coordinate 1 1666 0.022 Coordinate 1 1519 0.032Coordinate 2 1493 -0.015 Coordinate 2 1481 -0.017Mass 7.275kg Mass 7.275 kg time of impact 0.173s time of impact 0.038 s Force 1.233333lbf Force 1.633333 lbf Force 5.486113N Force 7.265393 N Impulse -0.9491Ns Impulse -0.27608 Ns V(final) 0.56954m/s V(final) 0.66205 m/s Average Decel -0.7541m/s2 Average Decel -0.99868 m/s2 ag2 mo2 V(initial) 0.7m/s V(initial) 0.7 m/s time voltage time voltage Coordinate 1 1679 0.027 Coordinate 1 1748 0.027Coordinate 2 1554 -0.012 Coordinate 2 1614 -0.024Mass 7.275kg Mass 7.275 kg time of impact 0.125s time of impact 0.134 s Force 1.3lbf Force 1.7 lbf Force 5.78266N Force 7.56194 N Impulse -0.72283Ns Impulse -1.0133 Ns V(final) 0.600642m/s V(final) 0.560715 m/s Average Decel -0.79487m/s2 Average Decel -1.03944 m/s2 ag3 mo3 V(initial) 0.7m/s V(initial) 0.7 m/s time voltage time voltage Coordinate 1 1743 0.029 Coordinate 1 1511 0.024Coordinate 2 1621 -0.01 Coordinate 2 1435 -0.029Mass 7.275kg Mass 7.275 kg time of impact 0.122s time of impact 0.076 s Force 1.3lbf Force 1.766667 lbf Force 5.78266N Force 7.858487 N Impulse -0.70548Ns Impulse -0.59724 Ns V(final) 0.603026m/s V(final) 0.617904 m/s Average Decel -0.79487m/s2 Average Decel -1.0802 m/s2

193

ag4 mo4 V(initial) 0.7m/s V(initial) 0.7 m/s time voltage time voltage Coordinate 1 1514 0.029 Coordinate 1 1207 0.032Coordinate 2 1349 -0.01 Coordinate 2 1096 -0.017Mass 7.275kg Mass 7.275 kg time of impact 0.165s time of impact 0.111 s Force 1.3lbf Force 1.633333 lbf Force 5.78266N Force 7.265393 N Impulse -0.95414Ns Impulse -0.80646 Ns V(final) 0.568847m/s V(final) 0.589147 m/s

Average Decel -0.79487m/s2 Average Decel -0.99868 m/s2 ag5 mo5 V(initial) 0.7m/s V(initial) 0.7 m/s time voltage time voltage Coordinate 1 1303 0.027 Coordinate 1 1366 0.037Coordinate 2 1227 -0.007 Coordinate 2 1226 -0.01Mass 7.275kg Mass 7.275 kg time of impact 0.076s time of impact 0.14 s Force 1.133333lbf Force 1.566667 lbf Force 5.041293N Force 6.968847 N Impulse -0.38314Ns Impulse -0.97564 Ns V(final) 0.647335m/s V(final) 0.565892 m/s

Average Decel -0.69296m/s2 Average Decel -0.95792 m/s2 time of impact 0.1322s time of impact 0.0998 s Impact Force 5.575077N Impact Force 7.265393 N V(final) 0.597878m/s V(final) 0.599142 m/s Deceleration -0.76633m/s2 Deceleration -1.01498 m/s2

194

TILT ROCKER-BOGIE MIDDLE WHEEL 0.7m/s k1 bd1 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1433 0.027 Coordinate 1 1559 0.046Coordinate 2 1262 -0.02 Coordinate 2 1397 -0.012Mass 7.275kg Mass 7.275kg time of impact 0.171s time of impact 0.162s Force 1.566667lbf Force 1.933333lbf Force 6.968847N Force 8.599853N Impulse -1.19167Ns Impulse -1.39318Ns V(final) 0.536196m/s V(final) 0.508498m/s

Average Decel -0.95792m/s2 Average Decel -1.18211m/s2 k2 bd2 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1356 0.029 Coordinate 1 1807 0.049Coordinate 2 1189 -0.015 Coordinate 2 1632 -0.007Mass 7.275kg Mass 7.275kg time of impact 0.167s time of impact 0.175s Force 1.466667lbf Force 1.866667lbf Force 6.524027N Force 8.303307N Impulse -1.08951Ns Impulse -1.45308Ns V(final) 0.550239m/s V(final) 0.500264m/s

Average Decel -0.89677m/s2 Average Decel -1.14135m/s2 k3 bd3 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1466 0.032 Coordinate 1 1560 0.042Coordinate 2 1268 -0.015 Coordinate 2 1421 -0.007Mass 7.275kg Mass 7.275kg time of impact 0.198s time of impact 0.139s Force 1.566667lbf Force 1.633333lbf Force 6.968847N Force 7.265393N Impulse -1.37983Ns Impulse -1.00989Ns V(final) 0.510332m/s V(final) 0.561184m/s

Average Decel -0.95792m/s2 Average Decel -0.99868m/s2 k4 bd4

195

V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1147 0.024 Coordinate 1 1621 0.041Coordinate 2 1004 -0.022 Coordinate 2 1487 -0.005Mass 7.275kg Mass 7.275kg time of impact 0.143s time of impact 0.134s Force 1.533333lbf Force 1.533333lbf Force 6.820573N Force 6.820573N Impulse -0.97534Ns Impulse -0.91396Ns V(final) 0.565932m/s V(final) 0.57437m/s Average Decel -0.93754m/s2 Average Decel -0.93754m/s2 k5 bd5 V(initial) 0.7m/s V(initial) 0.7m/s time voltage time voltage Coordinate 1 1074 0.024 Coordinate 1 1660 0.051Coordinate 2 984 -0.027 Coordinate 2 1504 -0.01Mass 7.275kg Mass 7.275kg time of impact 0.09s time of impact 0.156s Force 1.7lbf Force 2.033333lbf Force 7.56194N Force 9.044673N Impulse -0.68057Ns Impulse -1.41097Ns V(final) 0.60645m/s V(final) 0.506052m/s Average Decel -1.03944m/s2 Average Decel -1.24325m/s2 time of impact 0.1538s time of impact 0.1532s Impact Force 6.968847N Impact Force 8.00676N V(final) 0.55383m/s V(final) 0.530074m/s


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TILT ROCKER-BOGIE MIDDLE WHEEL 0.8m/s

1 inch 2 inch re1 v1 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1496 0.029 Coordinate 1 1393 0.029Coordinate 2 1423 -0.012 Coordinate 2 1263 -0.024Mass 7.275kg Mass 7.275kg time of impact 0.073s time of impact 0.13s Force 1.366667lbf Force 1.766667lbf Force 6.079207N Force 7.858487N Impulse -0.44378Ns Impulse -1.0216Ns V(final) 0.738999m/s V(final) 0.659573m/s Average Decel -0.83563m/s2 Average Decel -1.0802m/s2 re2 v2 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1195 0.029 Coordinate 1 1479 0.02Coordinate 2 1045 -0.024 Coordinate 2 1393 -0.032Mass 7.275kg Mass 7.275kg time of impact 0.15s time of impact 0.086s Force 1.766667lbf Force 1.733333lbf Force 7.858487N Force 7.710213N Impulse -1.17877Ns Impulse -0.66308Ns V(final) 0.637969m/s V(final) 0.708855m/s Average Decel -1.0802m/s2 Average Decel -1.05982m/s2 re3 v3 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1294 0.022 Coordinate 1 1249 0.027Coordinate 2 1207 -0.027 Coordinate 2 1133 -0.024Mass 7.275kg Mass 7.275kg time of impact 0.087s time of impact 0.116s Force 1.633333lbf Force 1.7lbf Force 7.265393N Force 7.56194N Impulse -0.63209Ns Impulse -0.87719Ns V(final) 0.713115m/s V(final) 0.679425m/s Average Decel -0.99868m/s2 Average Decel -1.03944m/s2

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re5 v4 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1420 0.024 Coordinate 1 1480 0.029Coordinate 2 1316 -0.017 Coordinate 2 1353 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.104s time of impact 0.127s Force 1.366667lbf Force 1.866667lbf Force 6.079207N Force 8.303307N Impulse -0.63224Ns Impulse -1.05452Ns V(final) 0.713095m/s V(final) 0.655049m/s

Average Decel -0.83563m/s2 Average Decel -1.14135m/s2 re6 v5 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1231 0.029 Coordinate 1 1245 0.017Coordinate 2 1129 -0.007 Coordinate 2 1197 -0.024Mass 7.275kg Mass 7.275kg time of impact 0.102s time of impact 0.048s Force 1.2lbf Force 1.366667lbf Force 5.33784N Force 6.079207N Impulse -0.54446Ns Impulse -0.2918Ns V(final) 0.72516m/s V(final) 0.75989m/s


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TILT ROCKER-BOGIE MIDDLE WHEEL 0.8m/s 1.5 inch 2.5 inch j1 x1 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1481 0.022 Coordinate 1 1529 0.049Coordinate 2 1344 -0.027 Coordinate 2 1376 -0.02Mass 7.275kg Mass 7.275kg time of impact 0.137s time of impact 0.153s Force 1.633333lbf Force 2.3lbf Force 7.265393N Force 10.23086N Impulse -0.99536Ns Impulse -1.56532Ns V(final) 0.663181m/s V(final) 0.584836m/s Average Decel -0.99868m/s2 Average Decel -1.4063m/s2 j2 x2 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1430 0.027 Coordinate 1 1491 0.049Coordinate 2 1304 -0.024 Coordinate 2 1346 0.007Mass 7.275kg Mass 7.275kg time of impact 0.126s time of impact 0.145s Force 1.7lbf Force 1.4lbf Force 7.56194N Force 6.22748N Impulse -0.9528Ns Impulse -0.90298Ns V(final) 0.66903m/s V(final) 0.675878m/s Average Decel -1.03944m/s2 Average Decel -0.85601m/s2 j3 x3 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1290 0.029 Coordinate 1 1589 0.051Coordinate 2 1145 -0.024 Coordinate 2 1423 -0.017Mass 7.275kg Mass 7.275kg time of impact 0.145s time of impact 0.166s Force 1.766667lbf Force 2.266667lbf Force 7.858487N Force 10.08259N Impulse -1.13948Ns Impulse -1.67371Ns V(final) 0.64337m/s V(final) 0.569937m/s Average Decel -1.0802m/s2 Average Decel -1.38592m/s2

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j4 x4 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1353 0.024 Coordinate 1 1511 0.047Coordinate 2 1248 -0.022 Coordinate 2 1342 0.005Mass 7.275kg Mass 7.275kg time of impact 0.105s time of impact 0.169s Force 1.533333lbf Force 1.4lbf Force 6.820573N Force 6.22748N Impulse -0.71616Ns Impulse -1.05244Ns V(final) 0.701559m/s V(final) 0.655334m/s

Average Decel -0.93754m/s2 Average Decel -0.85601m/s2 j5 x6 V(initial) 0.8m/s V(initial) 0.8m/s time voltage time voltage Coordinate 1 1469 0.022 Coordinate 1 1478 0.046Coordinate 2 1359 -0.027 Coordinate 2 1346 0.007Mass 7.275kg Mass 7.275kg time of impact 0.11s time of impact 0.132s Force 1.633333lbf Force 1.3lbf Force 7.265393N Force 5.78266N Impulse -0.79919Ns Impulse -0.76331Ns V(final) 0.690145m/s V(final) 0.695078m/s

Average Decel -0.99868m/s2 Average Decel -0.79487m/s2 x5 V(initial) 0.8m/s time voltage Coordinate 1 1479 0.044 Coordinate 2 1321 -0.002 Mass 7.275kg time of impact 0.158s Force 1.533333lbf Force 6.820573N Impulse -1.07765Ns V(final) 0.651869m/s

Average Decel -0.93754m/s2 time of impact 0.1215s time of impact 0.154s

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Impact Force 7.376598N Impact Force 7.710213N V(final) 0.676026m/s V(final) 0.649619m/s Deceleration -1.01397m/s2 Deceleration -0.96607m/s2

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TILT ROCKER-BOGIE MIDDLE WHEEL 1m/s

1 inch 2 inch fc1 do1 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1344 0.029 Coordinate 1 1347 0.024Coordinate 2 1216 -0.022 Coordinate 2 1310 -0.017Mass 7.275kg Mass 7.275kg time of impact 0.128s time of impact 0.037s Force 1.7lbf Force 1.366667lbf Force 7.56194N Force 6.079207N Impulse -0.96793Ns Impulse -0.22493Ns V(final) 0.866951m/s V(final) 0.969082m/s Average Decel -1.03944m/s2 Average Decel -0.83563m/s2 fc2 do2 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1369 0.027 Coordinate 1 962 0.027Coordinate 2 1269 -0.024 Coordinate 2 909 -0.016Mass 7.275kg Mass 7.275kg time of impact 0.1s time of impact 0.053s Force 1.7lbf Force 1.433333lbf Force 7.56194N Force 6.375753N Impulse -0.75619Ns Impulse -0.33791Ns V(final) 0.896056m/s V(final) 0.953551m/s Average Decel -1.03944m/s2 Average Decel -0.87639m/s2 fc3 do3 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1224 0.027 Coordinate 1 1249 0.044Coordinate 2 1106 -0.029 Coordinate 2 1143 -0.007Mass 7.275kg Mass 7.275kg time of impact 0.118s time of impact 0.106s Force 1.866667lbf Force 1.7lbf Force 8.303307N Force 7.56194N Impulse -0.97979Ns Impulse -0.80157Ns V(final) 0.865321m/s V(final) 0.889819m/s Average Decel -1.14135m/s2 Average Decel -1.03944m/s2

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fc4 do4 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1310 0.032 Coordinate 1 1460 0.024Coordinate 2 1158 -0.022 Coordinate 2 1347 -0.029Mass 7.275kg Mass 7.275kg time of impact 0.152s time of impact 0.113s Force 1.8lbf Force 1.766667lbf Force 8.00676N Force 7.858487N Impulse -1.21703Ns Impulse -0.88801Ns V(final) 0.832711m/s V(final) 0.877937m/s

Average Decel -1.10059m/s2 Average Decel -1.0802m/s2 fc5 do5 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1174 0.032 Coordinate 1 1149 0.034Coordinate 2 1061 -0.022 Coordinate 2 1041 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.113s time of impact 0.108s Force 1.8lbf Force 2.033333lbf Force 8.00676N Force 9.044673N Impulse -0.90476Ns Impulse -0.97682Ns V(final) 0.875634m/s V(final) 0.865729m/s


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TILT ROCKER-BOGIE MIDDLE WHEEL 1m/s

1.5 inch 2.5 inch gy1 mad1 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1314 0.037 Coordinate 1 1308 0.037Coordinate 2 1175 -0.005 Coordinate 2 1222 -0.034Mass 7.275kg Mass 7.275kg time of impact 0.139s time of impact 0.086s Force 1.4lbf Force 2.366667lbf Force 6.22748N Force 10.52741N Impulse -0.86562Ns Impulse -0.90536Ns V(final) 0.881014m/s V(final) 0.875552m/s Average Decel -0.85601m/s2 Average Decel -1.44707m/s2 gy2 mad2 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1181 0.032 Coordinate 1 1288 0.024Coordinate 2 1043 -0.015 Coordinate 2 1207 -0.029Mass 7.275kg Mass 7.275kg time of impact 0.138s time of impact 0.081s Force 1.566667lbf Force 1.766667lbf Force 6.968847N Force 7.858487N Impulse -0.9617Ns Impulse -0.63654Ns V(final) 0.867807m/s V(final) 0.912503m/s Average Decel -0.95792m/s2 Average Decel -1.0802m/s2 gy3 mad3 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1376 0.032 Coordinate 1 1181 0.027Coordinate 2 1235 -0.012 Coordinate 2 1114 -0.02Mass 7.275kg Mass 7.275kg time of impact 0.141s time of impact 0.067s Force 1.466667lbf Force 1.566667lbf Force 6.524027N Force 6.968847N Impulse -0.91989Ns Impulse -0.46691Ns V(final) 0.873555m/s V(final) 0.93582m/s Average Decel -0.89677m/s2 Average Decel -0.95792m/s2

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gy4 mad4 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1386 0.017 Coordinate 1 1550 0.032Coordinate 2 1217 -0.037 Coordinate 2 1425 -0.027Mass 7.275kg Mass 7.275kg time of impact 0.169s time of impact 0.125s Force 1.8lbf Force 1.966667lbf Force 8.00676N Force 8.748127N Impulse -1.35314Ns Impulse -1.09352Ns V(final) 0.814001m/s V(final) 0.849689m/s

Average Decel -1.10059m/s2 Average Decel -1.20249m/s2 gy5 mad5 V(initial) 1m/s V(initial) 1m/s time voltage time voltage Coordinate 1 1528 0.037 Coordinate 1 1191 0.034Coordinate 2 1347 -0.02 Coordinate 2 1052 -0.024Mass 7.275kg Mass 7.275kg time of impact 0.181s time of impact 0.139s Force 1.9lbf Force 1.933333lbf Force 8.45158N Force 8.599853N Impulse -1.52974Ns Impulse -1.19538Ns V(final) 0.789727m/s V(final) 0.835687m/s


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Output excitation voltage of the Tilted Middle motor mount at speed 1 m/s over 1.0” height wedge

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Appendix E – Instrumentation

H-Bridge

Apply power to the board using connector J1. To make a connection, a short

bit of black wire to the upper pin and a short bit of red wire to the lower pin, then

used clip leads to connect the bench power supply or a battery. Note that the upper

part of the connector is for the negative pin and the lower part of the connector is for

the positive connection. Once the voltage checks out, connect a small motor to J2.

The leads into J2 are not polarized so there is not a problem to worry about

connecting the motor "backwards." Then apply 5 volts to pin A of J3 and connect pin

B to ground. [10]

Strain Gauges Preparation

Preparing the surface

To remove any unevenness of the surface, by abrading with coarse grade

emery paper and abrade the surface to a fine finish using grade 400C abrasive paper.

The surface need to be wipe with a dry cloth for removing particles remaining from

the abrading. Thoroughly degrease the surface using a lint-free cloth dampened with

acetone [9]. At this stage, the surface was ready to put on strain gauges. Bond

strength between the strain gauge and the metal piece will be reduced if there is

surface contamination (including contact with fingers). Therefore, extra precaution

needs to be taken when installing the strain gauges.

Preparing the Gauges

The back of the strain gauges had to be abraded with a fine grade of abrasive

paper, such as 2/0. Degrease the back of the gauges by light wiping with a lint-free

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cloth slightly dampened with acetone [9]. Similar to the surface, this process is to

prevent any particles left behind the back of the strain gauge. Tweezers were used to

handle the gauges to prevent contamination from this stage onward.

Preparing the Adhesive

The steps to prepare the adhesive are fairly straightforward. Pour one bottle of

the hardener into one of the resin bottles and shake vigorously for one minute. The

mixture should then be allowed to stand for approximately five minutes until any air

bubbles that may have formed have cleared.

Bonding the Gauges

First, apply a thin coating of adhesive to both the prepared surface and the

back of the gauge using the brush provided. Allow to air dry for a minimum of 15

minutes. Place the gauge on the surface in the required position and orientation.

Position a small piece of PTFE (polytetrafluoroethylene or Teflon) tape over the

gauges and “roll out” the adhesive with a glass rod to give a thin glue line. Then,

remove the piece of PTFE tape. Clear the top of the gauge of any traces of adhesive

using a cotton bud dampened with acetone. This ensures that no adhesive will remain

on the tap of the gauge after baking, which could prevent easy soldering of lead

wires. During the process, acetone is not allowed to penetrate into the adhesive at the

side of the gauge, as this may lower the resulting bond strength. Place a clean piece of

PTFE tape over the gauge. Place a thin piece of silicon rubber over the PTFE tape.

Apply a pressure of approximately 10 psi. The rubber pad will ensure uniform

distribution of the clamping pressure. Heat the clamp installation slowly to 80o C

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(approximately 30 minutes) and hold at this temperature for three hours. Remove the

clamps from the gauges installation. [10]

Bridge-sensor Amplifier

AC Powered Signal Conditioner

Typical bridge output is 2 or 3mV/Volt of excitation. With the power supply

excitation voltage at 10 Volts an output of 20 or 30mV from the bridge can be

obtained. The common mode voltage of the bridge is 5 volts. This is well within the

6.5 Volt common mode voltage range of the amplifier. The gain must be set between

300 and 600 depending on the output of the bridge. The built-in potentiometer set to a

gain of 200 would achieve an output voltage of 4 to 6 volts. For a higher-level output

an external resistor must be used.

A standard 350 Ohm bridge is used, the current required from the excitation

supply would be 28.6mA. If the lead were long enough to have 10 Ohms of internal

resistance there would be a drop of over 0.25 V in both the plus and common side of

the bridge.

Application Suggestions

The model DMD-465 is designed to eliminate many of the ordinary problems

associated with bridge type measurements. Since the whole system is in one case the

common problem of ground loops or circulating currents caused by poor wiring

practices is eliminated. The manufacturer recommended that the lead wire length to

be kept to a minimum. The use of shielded twisted pairs for the input leads is

recommended for most of the applications.

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In order to minimize self-heating errors the use of minimum excitation power

is suggested as is sufficient heat sinking of the transducer wherever possible. For

optimum stability a one-hour warm up is recommended. Avoid large temperature

changes or stray magnetic fields.

Operation of the bridge-sensor amplifier

Hook Up Procedure

Connect the positive out (+ out) wire of the strain gauge to the positive

INPUT (+ INPUT) at pin 10. Connect the negative out (- out) of the strain gauge to

the negative INPUT (- INPUT). Connect B+, pin 4, to the + excitation of the strain

gauge jumper the + SENSE (pin 3) to B + (pin 4). Connect B-, pin 2, to the –

excitation of the strain gauge jumper the – SENSE (pin 1) to B – (pin 2). Connect the

VAC power supply to the AC input lines, pin 6 and pin 7.

Turn on Procedure

The experimenter needs to verify that the hook up procedure is complete, and

make sure the correct AC voltage is applied to the DMD-465. Turn on the AC source

supply to the DMD-465. Set the required EXCITATION supply voltage to the strain

gauge by adjusting B+ at Pot B.

Calibration Procedure for Zero Adjustment

Connect the + and – input terminals, pins 10 and 11, together. Connect a

voltmeter across the output, pins 8 and 9. Adjust the OUTPUT OFFSET, Pot A,

potentiometer for zero.

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Full Scale Voltage Adjustment

The experimenter needs to remove the jumper between the + and – input

terminals and apply a known load to the strain gauges, in most cases it would be

100% of full scale. Adjust the COARSE GAIN (Pot D), and FINE GAIN (Pot C),

potentiometers for the desired FULL SCALE output. The experimenter should

recheck the ZERO & FULL SCALE output before continuing.[15]

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Appendix F G-code for the wheel on CNC

% o00221(Lee’s wheels) N1 T1 M06 (CENTER DRILL) G00 G90 G54 X0 Y0 S2000 M03 G43 H01 Z1. G81 Z-0.15 F5. R0.25 G80 G91 G28 Z0 M01

N2 T2 M06 (6mm DRILL) G00 G90 G54 X0 Y0 S2000 M03 G43 H02 Z1 G83 Z-0.8 Q0.125 F5. R0.25 G80 G91 G28 Z0 M01

N3 T3 M06 (3/4” ENDMILL) G00 G90 G54 X0 Y0 S1000 m03 G43 H03 Z0.1 G01 Z0 F10. G13 G91 Z-0.1 F10. D00 I0.5 K3.39 Q0.5 L4 G00 G90 Z1. G91 G28 Z0 M01

N4 T1 M06 (CENTER DRILL) G00 G90 G54 X0 Y0 S2000 M03 G43 H01 Z1. G70 I0.45 J0 L4 G81 Z-0.55 F10. R-0.25 G80 G91 G28 Z0 M01

N5 T4 M06 (#33 DRILL) (DRILL FASTENER HOLE) G00 G90 G54 X0 Y0 S2000 M03 G43 H04 Z1. G70 I0.45 J0 L4 G81 Z-0.75 F5. R-0.25 G80 G91 G28 Z0 M01

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N6 T6 M06 (3/8 ENDMILL) (CUT THE WHEEL OUT OF THE WORK-PIECE) G00 G90 G54 X0 Y4.13 S1000 M03 G43 H06 Z0.25 G01 Z-0.125 F3. G02 J-4.13 F10. G01 Z-0.25 F3. G02 J-4.13 F10. G01 Z-0.375 F3. G02 J-4.13 F10. G01 Z-0.5 F3. G02 J-4.13 F10. G01 Z-0.625 F3. G02 J-4.13 F10. G01 Z-0.66 F3. Y4.125 G02 J-4.125 F10. G01 Z-0.7 F3. G02 J-4.125 F10. G00 Z3 G91 G28 Z0 G91 G28 Y0 M30 %

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Appendix G Interactive C programming Language for Handy-Board Wheelie Maneuver

#define THRESHOLD_A 200 /*define the location of the wood*/ #define THRESHOLD_B 230 #define SLOW 25 /*define slow speed*/ #define FAST 100 /*define fast speed*/

void main() {

while(!stop_button()) { printf("delay=%f\n", ((float)knob())/100.); sleep(0.05); } while (1) { printf("Push Start for wheelie\n"); while(!start_button()); /*to start the motor*/ motor(1, SLOW); motor(2, SLOW); motor(3, SLOW); while(analog(2)> THRESHOLD_A); /*to set the threshold*/ printf("Waiting for Obstacle\n"); motor(1, SLOW); motor(2, FAST); motor(3, -25); sleep(((float)knob())/100.); motor(3, 0);

while(analog(4)> THRESHOLD_B && !stop_button());/*after the bump was passed, run for 3 seconds, then stop*/

printf("Over the Bump \n"); motor(1, SLOW); motor(2, SLOW); motor(3, SLOW); sleep(0.1); motor(3,FAST); motor(1,-10);

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sleep(0.4); motor(1, SLOW); motor(3, SLOW); sleep(2.);

ao(); }

Documents

UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE BEHAVIOR …eml.ou.edu/paper/thesis/TZE-LIANG LEE.pdf · Figure 1-2: The original model pf the Rocker-Bogie suspension [courtesy by JPL]6 Figure