SECTION 3...launch in 2015, multiple CubeSats are being developed to demonstrate the utility of multiple small spacecraft working together. The specific goal of this mission, the Edison

UAB School of Engineering – Mechanical Engineering - ECTC 2015 Proceedings – Vol. 14 Page 65

SECTION 3

DYNAMIC SYSTEMS

& CONTROL



Proceedings of the Fifteenth Annual Early Career Technical Conference The University of Alabama, Birmingham ECTC 2015

November 7, 2015 - Birmingham, Alabama USA

ORBITAL MECHANIC SIMULATION OF A 1U CUBESAT

Alicia Ratcliffe

University of South Alabama Mobile, Alabama, USA

Carlos Montalvo

University of South Alabama Mobile, Alabama, USA

ABSTRACT

The overall goal of this program is to investigate sending

multiple CubeSats discretely into orbit and connecting them to

form a monolithic system. Composite satellites have greater

abilities in areas such as data collection, mission, and

surveillance capabilities. The work investigated here will be a

start for a much larger program to build the tools necessary to

perform research in this area. Initial work will be done on

analyzing the orbit of a single satellite with the potential to

expand the simulation to multiple CubeSats.

INTRODUCTION CubeSats, small satellites found in low or medium Earth

orbit (LEO/MEO), typically collect data such as atmospheric,

radiation, and geographic readings. With a volume of one liter

and a mass up to 1.33 kilograms, they were originally designed

to set a standard for future picosatellites. Since these satellites

have a comparatively low price tag, there has been an increase

in demand for new technologies and research. Multiple

universities and institutes around the world have sent their own

CubeSats into space for development, research, earth science,

and other uses. For example, Auburn University’s CubeSat,

AubieSat -1, tested how well different solar panels endured

against the environment as well as transmitting Auburn

University’s motto, “War Eagle” back to Earth in Morse code

[1]. CubeSats were not originally designed to a set standard.

The concept began in 1999 as a design challenge for graduate

students and, as the program evolves, now building on sixteen

years of direct experience and 58 years of small satellite

technology [2], it is updated regularly to improve efficiency and

availability [3].There have been 341 missions identified by

Saint Louis University, including the first CubeSat sent into

space by the military just a year after the CubeSat concept was

proposed. PicoSAT 1 and 2, weighing 250 grams each, were

launched into orbit from the rocket Minotaur-1 on February 6,

2000. The PicoSATs’ primary mission was to demonstrate the

feasibility of deployable space technology and in addition, to

act as an amateur radio transmitter. Their primary mission was

a success, and as a result Universities deploy their own

satellites to facilitate research instead of attaching devices to

other spacecraft or designing systems for another agency [4].

Government agencies such as the National Aeronautics and

Space Administration as well as the European Space Agency

are also interested in these picosatellites, assisting various

teams’ CubeSats into orbit around Earth

[5]. In particular

NASA Ames Research Center’s project, PhoneSat, makes it

possible to control a CubeSat from a generic smartphone [6].

Looking to push farther afield, NASA also issued a challenge in

2013 to design a CubeSat which operates in Mars’ environment

and furthers our knowledge. They provided a list of potential

science or infrastructure objectives [7]. So far, little work has

investigated the possibility of physically connecting, not

tethering, multiple CubeSats while in orbit, but quite a bit of

work has been accomplished regarding defining and modeling

discrete flight and formation flight.

Although little work has been done on physical connection,

except tethers, quite a bit of research and development is being

accomplished. The Quakesat was sent into orbit by Quake

Finder, a company based in California. It provided a “proof of

concept,” collecting ULF (earthquake precursor) signals from

space. The NEE- 01 Pegaso was launched by the Ecuadorian

Space Agency and was the first CubeSat to transmit real time

video from orbit to be broadcast over the internet [8]. Due to

launch in 2015, multiple CubeSats are being developed to

demonstrate the utility of multiple small spacecraft working

together. The specific goal of this mission, the Edison

Demonstration of Smallsat Networks (EDSN), is to acquire

data from multiple points on Earth simultaneously [5].

Distributed satellite systems like the EDSN mission present a

faster and less expensive method of retrieving data while

allowing greater flexibility in formation. The ability to dock

two autonomous satellites for them to work jointly would

increase the likelihood that monolithic systems previously

unsuited to formation flight could be assembled in space. The

Hawaii Space Flight Laboratory has developed flight-like

software that may be used in real time simulation environments

to dock small satellites in a cooperative manner [9]. To help

further the goal of cost effective and capable satellites; orbital

mechanics, control law and simulation will be implemented.

Orbital Mechanics is a broad subject encompassing many

topics including the orbital environment, flight mechanics, type

of orbit, and constellation architecture [10]. The orbital

environment in LEO or MEO provides high bandwidth (data

transfer rate) and low communication lag, making it an ideal

area to maintain a satellite; however, it is becoming congested

with space debris, which increases the possibility of collision

[11]. Such matters may be avoided using a control system to


help the satellite system behave in a desired manner [12]. As a

subject, control is concerned with operating a dynamic system

at minimal cost. Operating the system requires an output

(typically pointing direction or relative position) that is sent to

an onboard controller, which dynamically compensates for

unwanted disruptions such a floating missiles of space junk.

Attitude orbit and control systems (AOCS) are required for all

space missions, and the more specialized functions on a control

system may include formation flying or orbital rendezvous

[13]. To solve this problem, one must specify which

performance function should be optimized within specified

parameters [14]. The general solutions to the optimal control

problem have been thoroughly documented in [15] and AOCS

in [14]. Some common ways the motion of a picosatellite is

controlled is using whip antennas, deployable arrays, tethers,

reaction wheels and moment gyros. Since CubeSats are

relatively new, there is no common qualification standard and

these mechanisms are largely custom made for a single mission

[16].

This paper will attempt to analyze a single 1U CubeSat

with the goal of simulating multiple satellites in orbit. Once a

model is built, control laws will be implemented to connect

each satellite in orbit. In order to analyze a 1U CubeSat, the

MATLAB programming language will be used to create a

sophisticated three degree of freedom simulation tool. A

satellite dynamic model will be placed in first order form for

successful implementation to be carried out by the software.

NOMENCLATURE Ek Kinetic energy

Ep Potential energy

mi Mass of body i

First derivative of position

G Gravitational constant

Lagrangian set

MATHEMATICAL MODEL

I. CIRCULAR ORBIT

Johannes Kepler was a pioneer of elliptical orbits and came

up with “three empirical laws of planetary motion:

1. The planets orbit the sun in elliptical orbits, with the

sun at one focus of the ellipse.

2. The radius vector sweeps out equal areas in equal

times.

3. The period of the orbit is proportional to the

semimajor axis cubed.

These laws constitute a complete solution to the two-body

problem of orbital motion [17]. The problem is that of

mathematically depicting the motion of two separate bodies in

space, such as a planet and a satellite. It begins with the

equations for kinetic and potential energy:

(1)

(2)

The center of gravity is defined as the point about which

all the gravitational torques vanish regardless of the orientation

of the body with respect to the gravitational field. The

equations shown above are a linearly independent set of

coordinates that can be used to formulate the Lagrangian

equations of motion [17]. Conventional Lagrange equations of

motion are defined in equations (3)-(5):

(3)

(4)

(5)

where r is defined as:

(6)

Performing this calculation for both bodies leads to the

following equations:

(7)

(8)

(9)

Equation (9) is simply the result of combining equations

(7) and (8). Integrating equation (9) twice yields two constants.

The significance of these two constants is that the system as a

whole is fixed in an inertial frame that follows a straight path

where the center of mass of the system is not accelerating.

Thus, the two body problem can be reduced to a single system

by combining equations (7) and (8):

(10)

Substituting the variable leads to the much

more compact form for the two body problem.

(11)

It is further noted in [14] that it is much easier to accurately

determine than it is to determine G (Earth’s gravitational

constant), so it may be preferable to use . This system is

modeled with two degrees of freedom such that

(12)

The equations of motion in vector form are then


(13)

Software has been implemented to allow the simulation of

multiple satellites. Constellation architecture and formation

flight are commonly used in communication systems and GPS

to provide full coverage of Earth’s surface. However, a limit of

a monolithic satellite of multiple CubeSats would only be

capable of scanning part Earth’s surface at any one moment and

as such is unsuited to act as a positioning system.

II. CONTROL SYSTEM

In order to perform a docking maneuver, the satellites must

be brought close together in orbit without damaging the

spacecraft. For the purpose of this simulation, velocity is

assumed to change instantaneously. The most efficient method

of bringing two spacecraft close in circular orbit is by

accelerating tangent to orbit, thus entering a faster, elliptical

orbit. This new orbit has a larger period ( ). Equation (14)

implies that the two satellites will rendezvous after one orbit

has occurred for the control satellite denoted .

(14)

represents the time it takes to traverse the distance at the

specified radius shown in Figure 1- Sample phase angle

between two representative satellites.

Figure 1- Sample phase angle between two representative

satellites

This time may be calculated using Equation (15).

(15)

The craft uses two engine impulses, which require two changes

in velocity: and to match orbits. The first impulse

moves the craft into the transfer orbit, and the second redirects

into the final, matched orbit. To calculate these changes in

velocity:

where the first change in velocity is the difference of the

maximum elliptical velocity and the lead satellite’s

initial velocity.

(16)

(17)

The semi-major axis, , is defined as:

(18)

Once has decreased for rendezvous, a burn is performed by

to match the velocity and direction of ,

entering into circular orbit.

SIMULATION SET UP: A candidate case has been run with two satellites of mass

and Due to the magnitude of the

mass, radius, and gravitational constant of Earth, the equations

of motion in [14] have been nondimensionalized using the

following parameters: and

This leads to being roughly equivalent to

which, when nondimensionalized, is denoted , and in this case

is equivalent to [18]. Geostationary orbit (GSO)

has the chosen orbital period of one day, intentionally matching

Earth’s sidereal rotation period. The initial conditions of the

satellite are set in GSO with an average orbital velocity of

.

RESULTS:

An example simulation has been run using the parameters

defined in the section above. Figure 2 shows the

nondimensional orbit of two separate CubeSats orbiting the

Earth. The CubeSats have been enlarged to show detail and are

in their initial positions.

Since the radius of is constant, a graph depicting

the radius or velocity over time would be a straight line with

components sinusoidal in nature and a phase difference of .

The radius of however is not a straight line; it is

parabolic in nature with the maximum taking place once the

satellite takes a phase angle of with respect to the rendezvous

point. As seen in Figure 3, the velocity decreases parabolically

over time until it has traveled half of its period. The velocity

then increases at the same rate along the transfer orbit’s larger


circuit and period. As the phase angle decreases the control

system is initiated and the velocities of the two spacecraft take

the same value.

Figure 2- Unit Orbit for a two satellite system

Figure 3- Velocity of

Figure 4 shows the phase angle over the course of one

orbit. Initially, the absolute value of the angle increases due to

the burn performed that places the CubeSat into the transfer

orbit. The operation causes the secondary CubeSat to lose

velocity so that the distance and phase angle between the two

satellites decrease.

CONCLUSION: This work verifies that multiple CubeSats may be docked

in orbit. A case study is generated of the rendezvous and

docking of two satellites in geostationary orbit. In future work,

more satellites may be added and a more sophisticated control

system and docking maneuver implemented. Four more degrees

of freedom should also be incorporated to model the tumbling

and altitude of a spacecraft as it is deployed and a control

system created to orient the structure towards Earth correctly.

Figure 4- as the control system is implemented and

rendezvous occurs.

ACKNOWLEDGMENTS This research was supported by the University Committee

on Undergraduate Research as well as the Mechanical

Engineering department at the University of South Alabama.

REFERENCES [1] “Auburn University Student Space Program,” Auburn

Univ. Stud. Space Program [Online]. Available:

http://www.space.auburn.edu/. [Accessed: 17-Jun-2015].

[2] Kramer, H. J., and Cracknell, A. P., 2008, “An overview of

small satellites in remote sensing,” Int. J. Remote Sens., 29(15),

pp. 4285–4337.

[3] 2015, “CubeSat Design Specification Revision 13.”

[4] “CubeSat Database - swartwout” [Online]. Available:

https://sites.google.com/a/slu.edu/swartwout/home/cubesat-

database. [Accessed: 17-Jun-2015].

[5] Mahoney, E., 2013, “CubeSats Initiative,” NASA [Online].

Available:

http://www.nasa.gov/directorates/heo/home/CubeSats_initiative

.html. [Accessed: 17-Jun-2015].

[6] Wall, M., “Tiny Cubesats Set to Explore Deep Space,”

Space.com [Online]. Available: http://www.space.com/29306-

cubesats-deep-space-exploration.html. [Accessed: 17-Jun-

2015].


[7] “Home | 2015 SpaceApps Challenge” [Online]. Available:

https://2015.spaceappschallenge.org/. [Accessed: 17-Jun-2015].

[8] WiSP Information Update, 1993, “WiSP Information

Update” [Online]. Available:

http://www.ne.jp/asahi/hamradio/je9pel/.

[9] Nunes, M. A., Sorensen, T. C., and Pilger, E. J., “On the

development of a 6DoF GNC framework for docking multiple

small satellites,” AIAA Guidance, Navigation, and Control

Conference, American Institute of Aeronautics and

Astronautics.

[10] Logsdon, T., 1998, Orbital Mechanics: Theory and

Applications, John Wiley & Sons.

[11] Working Group 2, 2013, Stability of the Future LEO

Environment, Inter-Agency Space Debris Coordination

Committee.

[12] Nicholas, A. K., 2013, “Attitude and formation control

design and system simulation for a three-satellite CubeSat

mission,” Thesis, Massachusetts Institute of Technology.

[13] “Control Systems,” Eur. Space Agency [Online].

Available:

http://www.esa.int/Our_Activities/Space_Engineering_Technol

ogy/Control_Systems. [Accessed: 17-Jun-2015].

[14] Graham C. Goodwin, S. F. G., and Mario E. Salgado,

2001, “Linear Quadratic Regulator,” Control System Design,

Prentice Hall.

[15] Palacios, L., Ceriotti, M., and Radice, G., 2013,

“Autonomous distributed LQR/APF control algorithms for

CubeSat swarms manoeuvring in eccentric orbits” [Online].

Available: http://www.iac2013.org/dct/page/1. [Accessed: 17-

Jun-2015].

[16] Paul Oppenheimer, 2009, “CubeSat Mechanisms

Workgroup.”

[17] George W. Collins, II, 2004, The Foundations of Celestial

Mechanics, Pachart Foundation dba Pachart Publishing House.

[18] California Institute of Technology, “Astrodynamic

Constants” [Online]. Available:

http://ssd.jpl.nasa.gov/?constants.




A BEGINNER’S GUIDE TO CONTROLLER AREA NETWORK BUS ACCESS IN MODERN VEHICLES

Timothy D. Fisher

Kennesaw State University Kennesaw, GA, USA

Kevin McFall

Kennesaw State University Kennesaw, GA, USA

ABSTRACT

A controller area network (CAN) is a communication

system designed so that a microcontroller governing multiple

systems (nodes) on the network can function effectively. This

network can be accessed, interpreted, and manipulated by an

external computer. The purpose of this paper is to provide a

basic working knowledge of CAN architecture and protocols,

as well as show how to connect to and decode a vehicular

controller area network.

INTRODUCTION CAN protocol was introduced by the Society of

Automotive Engineers (SAE) in February of 1986 [1] as a

multiplexed system for sending messages between devices in

an automobile. The first production vehicle implementing the

system was the BMW 8 Series line, starting in 1989. In 1992,

CAN 2.0 was published with provisions for devices with both

11-bit and 29-bit identifiers (often referred to as CAN 2.0A and

CAN 2.0B, respectively). CAN 2.0 remains the foundation of

present day CAN architecture. The most recent update to the

CAN protocol, published in 2012, is CAN FD 1.0, or CAN with

Flexible Data-Rate. [2] This new format allows variation in

both the size of the data package and in the bit rate. CAN FD

1.0 is fully back-compatible with CAN 2.0.

CAN 2.0 is also used in the on-board diagnostics (OBD-II)

system, which allows an external device to communicate with

an automobile and assess its functionality. Starting in 1996, the

OBD-II system was made mandatory in many types of vehicles

throughout the world, and specifically those sold in the United

States and the European Union (which uses a marginally

different standard called EOBD).

Though CAN FD 1.0 was the last major update to the CAN

protocol, the technology continues both to improve and to

provide a basis for other improvements. In 2007, the New

Jersey State Police integrated the pursuit light package in its

patrol cars into the CAN bus in order to reduce extraneous

wiring in the cockpit, and to integrate more subsystems so that

maintenance time could be reduced. [3] In 2014, General

Motors introduced a wireless connection system called ViCAN

with the goals of making it possible to connect devices to the

network without physically wiring them into the bus, and to

further reduce the amount of wiring needed in the vehicle by

removing the need for a common wire pair connecting every

device. [4] Earlier this year, a new safety system that

automatically dims headlights for oncoming traffic, checks for

short circuits in vehicle wiring that can cause fires and rapid

battery drain, detects flammable fumes near the engine, and

monitors engine temperature was introduced at a conference at

Hindustan University. [5] Most recently, Kennesaw State

University began research into autonomously controlling a

2012 Kia Optima via manipulation of the CAN bus. This is the

project that generated the information presented in this paper.

BACKGROUND The CAN bus itself is really very simple. It consists of two

wires connected to every CAN device in the vehicle. Instead of

one wire carrying a signal and the other functioning as ground,

one carries high voltage and one carries low voltage. A signal

on the low voltage line is designated as a logical 1 (recessive),

and a signal on the high voltage line is designated as a logical 0

(dominant).

An individual message that a CAN node sends is called a

frame. Every frame begins with an identification number

unique to each node. The ID numbers also set message priority

on the CAN bus, with lower ID numbers taking precedence

over higher numbers. For instance, a high-priority system such

as the Engine Control Unit would have a very low ID number,

and low-priority systems such as power locks would have a

higher ID number. This precedence is established through the

following protocol, known as arbitration.

When one or more CAN nodes transmits a logical 0, all

nodes receive a logical 0. When one or more CAN nodes

transmit a logical 1 and at least one other node transmits a

logical 0, all nodes receive a logical 0, including the ones

transmitting a logical 1. When a node transmits a 1 and sees a 0

during identification, this tells the node that there is a higher

priority message being transmitted by a different node, and it

will wait until it receives an End-of-Frame signal before

reattempting transmission.


Priority on the CAN bus is indicated by a node’s

identification number, as noted above. A lower identification

number will have a lower binary value, and it will win

arbitration over nodes with higher ID numbers. If a node

completes its ID transmission without interruption, it will

transmit the rest of its message.

Take, for instance, a conflict between two hypothetical

nodes with IDs of 47 and 11, respectively, which starts on the

same clock cycle. The CAN bus arbitration for their 11-bit ID

transmission is displayed in Table 1. ID Arbitration.

Table 1. ID Arbitration

Bit: 10 9 8 7 6 5 4 3 2 1 0

Node

11 0 0 0 0 0 0 0 1 0 1 1

Node

47 0 0 0 0 0 1 Not transmitting

CAN 0 0 0 0 0 0 0 1 0 1 1

Table 2. Can Base Frame Format

0 0 0 0 0 0 0 0 1 0 1 1 0 0

0 0 0 0 1 0 1 1 1 0 0 1 0 0

1 1 0 1 0 1 0 0 1 0 1 0 0 0

1 1 1 1 1 1 1 1 1 1 Inter-frame space

Table 3. CAN Extended Frame Format

0 0 0 0 0 0 0 0 1 0 1 1 1 1

1 0 0 0 0 1 1 0 0 1 1 1 0 0

0 1 0 1 0 0 0 0 0 0 1 0 1 1

1 0 0 1 0 0 1 1 0 1 0 1 0 0

1 0 1 0 0 0 1 1 1 1 1 1 1 1

1 1 Inter-frame space

ID

IDE

DLC

DATA

CRC

ACK

EOF

Misc. Figure 1. Legend for Shading in Tables 2 and 3

A standard frame can have between 55 and 131 data bits in it,

depending on whether it uses a base frame with 11 ID bits or an

extended frame with 29 ID bits. How much DATA is included

in the frame (between 1 and 8 bytes, or 8 and 64 bits) also has

an effect. Aside from the ID and DATA bits, the frames are

mostly similar.

The first bit of a frame is always a dominant 0 to cut

through the recessive background and alert other nodes that a

frame is beginning. The next 11 bits are the node ID.

The subsequent bit changes depending on whether the base

frame format (BFF, seen in Table 2) or extended frame format

(EFF, seen in Table 3) is used. The shading key for Table 2 and

Table 3 can be found in Figure 1. In BFF, this bit after the node

ID is the remote transmission request (RTR) bit, which is

dominant for data frames and recessive for remote requests.

Normally nodes transmit information as a matter of routine, but

if a node wishes to query a different node for information, it

will set the RTR bit to 1 as an alert to other nodes that it is

requesting information. In EFF, this bit instead becomes the

substitute remote request (SRR), and will always be recessive.

After the RTR/SRR bit comes the identifier extension bit

(IDE). This will be dominant if using BFF, and recessive if

using EFF. If the IDE bit is recessive, the next 18 bits will be

the remainder of the ID, and the 19th will be the RTR. In BFF,

the IDE will be followed by 1 dominant bit, and in EFF, the

RTR will be followed by 2 dominant bits.

From this point, BFF and EFF are formatted the same way.

The next 4 bits are the data length code (DLC), which describe

how many bytes the following DATA field will be (up to 8).

The DATA field contains the message that the rest of the frame

acts as an envelope for, ensuring its integrity and that it goes to

the correct destination. The contents of the DATA frame will

change depending on which node it was generated by or

addressed to (e.g. lock all doors, activate right turn signal, set

tachometer to 4500 RPM).

Following this is a 15 bit cyclic redundancy check (CRC)1

to test data integrity, and 1 recessive CRC delimiter bit. The

frame then drops to a recessive acknowledgement (ACK) bit,

during which any other node which has been paying attention

will transmit a dominant bit if it has read the current frame as

valid. A recessive ACK delimiter bit follows this, followed by a

total of 7 recessive end-of-frame (EOF) bits to indicate that the

frame is complete and that another node may begin

transmitting.

While a normal frame will typically contain between 55

and 131 useful bits, it may occasionally contain more due to an

error-checking method known as “bit stuffing.” Six sequential

bits of the same type (dominant or recessive) will be read as an

error by any receiving nodes, so when this occurs naturally, an

opposing bit will be inserted between the fifth and sixth

repeated bit. This does not occur with the CRC delimiter, either

ACK bit, or the end-of-frame bits, all of which are of fixed size

and value.

None of this information is strictly necessary in order to

interpret the CAN bus using the methods described below, but

it can help to understand why the network behaves as it does.

1 See Appendix for computation


PROCEDURE The most reliable way to get started with the CAN system

is to dismantle part of a car and hook up to the CAN bus that

way. However, sometimes an expendable vehicle may not be

available. In such cases, there are commercial CAN simulators

available that are useful for training, troubleshooting, and to

some degree, debugging. [6]

The easiest way to access the CAN bus in a modern

vehicle is via the On-Board Diagnostics port (OBD-II) under

the driver’s side dashboard. This port is installed in most

modern vehicles as a way of directly communicating with the

microcontroller running the network, and includes both the high

and low (i.e. CAN-H, CAN-L) terminals needed to access the

CAN network.

However, on occasion this method may not work. During

the course of the research that led to this paper, it was

discovered that the OBD-II port of the project’s Kia Optima

was unresponsive. In such a situation, the next course of action

is to find a CAN-connected device whose wire harness can be

used to read the CAN bus. Qualifying devices will vary from

vehicle to vehicle, but the instrument cluster (speedometer,

odometer, etc.) will typically have a CAN line if it is not

mechanically actuated.

Once the CAN bus has been located, it will be necessary to

connect it to a computer. A PEAK-System OBD-II to D-sub

adapter was used with accompanying software for this research,

but any compatible combination of adapters and software

would function adequately. After a physical connection has

been established, the bit rate must be synchronized. A modern

computer will often have a clock speed of several GHz,

whereas a CAN microcontroller will typically have a

transmission rate in the kHz to MHz range.

Upon accessing the CAN bus and synchronizing the bitrate

with the computer, decoding the bus is as simple as

manipulating equipment in the vehicle and recording the

changes in the data values for whatever addresses are present

on the bus. This process of experimentation is necessary

because the DATA field is so densely packed with information

that it has to be reduced to machine code in order to fit inside a

standard CAN frame. The formatting and meaning of this code

will vary from node to node, so the only way to interpret it

without proprietary information or software from the

manufacturer is via trial and error.

RESULTS Connection to the car was made via the CAN ports on pins

31 and 32 of the instrument cluster harness at a bit rate of 100

kHz. The general state of the CAN bus immediately after

ignition can be seen below in Table 4.

Table 4. Vehicle After Ignition

ID DATA

100h 31 1C 00 00 08 20 00 00

101h 80 40 11 00 00 00 00 00

104h 05 6E 00 00 00 00 00 00

10Ch 00 00 00 12 00 00 00 00

10Dh 16 83 C8 20 06 00 00 00

400h 01 02 00 00 00 00 FF FF

401h 0F 02 00 00 00 00 FF FF

40Fh 00 02 00 00 00 00 FF FF

501h 00 03 48 00 00 00 00 00

The first observation that was made when the car had

finished its power-on procedures was that bytes 2 and 3 in word

501h fluctuated slightly when the vehicle was completely idle

and parked. It is hypothesized that these two bytes, and

possibly byte 1, are tachometer readings. Converting 0348 from

hexadecimal to decimal yields 840, which is believable for an

RPM reading from an engine recently started. Further research

will be made when a splitter has been fashioned that will allow

the computer and the instrument cluster to read from the cluster

harness at the same time. This will confirm whether the raw

number corresponds to the RPM.

When the brake pedal was pressed, byte 4 of word 10Dh

changed from 00 to 02, setting bit 3 of the word high. This is

likely the bit that controls the brake lights, or the sensor

indicating that the brakes are engaged. Bytes 1 and 2 of the

same word appear to keep track of the current state of the

power system and the motor, respectively.

Word 104h seems to deal mainly with safety features such

as locks and flashers. Word 1 changes states depending on the

state of the driver’s side back door (open or closed, locked or

unlocked), and word 2 performs the same function for both

front doors. No data was collected on word 3, but logically, it

might relate to the passenger side back door. Word 4 controls

the hazard lights, and likely the turn signals.

CONCLUSION Preliminary results on this project are encouraging. By

mapping some of the more easily-accessible CAN codes, less

important data generated by normal operation of devices in the

car can be filtered out, and more useful codes such as those for

cruise control or ABS can be more easily isolated. The 2012

Kia Optima is lacking in what would traditionally be

considered drive-by-wire systems, but it may yet become

unmanned via more unconventional means.


APPENDIX A CRC check is performed on the data in every CAN

frame to ensure data integrity. This is accomplished by adding a

number of 0s to the end of the DATA field equal to the size of

the CRC field (15 bits) and performing an XOR operation on

the DATA field with a predetermined divisor (for CAN

applications, 0x4599), aligning with the leftmost 1 and working

to the right until the remainder is 0. Each progression aligns the

first 1 in the divisor with the first 1 in the dividend. The process

for the CRC field in Table 2 and Table 3 is shown below in

Table 5.

Table 5. CRC Calculations

0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1

0 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0

0 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0

0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1

0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0

0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0

0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1

0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0

0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1

0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0

Since the remainder of the DATA field is 0, the process is

now complete, and the result becomes the CRC field seen in

Table 2 and Table 3.

REFERENCES [1] Embedded Systems Academy, "Almost 25 Years of

CAN," [Online]. Available: http://www.canopen.us/history.htm.

[Accessed 12 August 2015].

[2] Robert Bosch GmbH, "CAN with Flexible Data-Rate,"

in 13th International CAN Conference, Neustadt an der Haardt,

Rhineland-Palatinate, Germany, 2012.

[3] A. Marino and J. Schmalzel, "Controller Area

Network for In-Vehicle Law Enforcement Applications," in

IEEE Sensors Applications Symposium, San Diego, California,

USA, 2007.

[4] M. Laifenfeld and T. Philosof, "Wireless Controller

Area Network For In-Vehicle Communication," in IEEE 28-th

Convention of Electrical and Electronics Engineers in Israel,

Hertzelia, Israel, 2014.

[5] K. Kalaiyarasu and C. Carthikeyan, "Design of an

Automotive Safety System using Controller Area Network," in

International Conference on Robotics, Automation, Control and

Embedded Systems, Kelambakam, Chennai, India, 2015.

[6] H. Guo, J. J. Ang and Y. Wu, "Extracting Controller

Area Network Data for Reliable Car Communications," IEEE,

Singapore, 2009.




DYNAMIC SYSTEM ANALYSIS USING RECURRENCE QUANTIFICATION ANALYSIS AND RECURRENCE PLOTS IN MATHEMATICA

Serkan Güldal

Interdisciplinary Engineering University of Alabama at Birmingham

Birmingham, AL, USA

Veronica L. Baugh Electrical and Computer Engineering University of Alabama at Birmingham

Birmingham, AL, USA

ABSTRACT Recurrence quantification analysis and recurrence plots

are techniques of non-linear data analysis used for various

mechanical engineering analyses. The recurrence plot reveals

all the times when the phase space trajectory of the dynamical

system visits roughly the same area in the phase space. The

Euclidean distance between each state is used as a measure of

in n-dimensional space. The Recurrence Plot measures that are

considered are Percent Recurrence, Percent Determinism, and

Deterministic Ratio of the state matrix. These derived

measures are used to better understand the states of the sys-

tem. There are relatively few software options available for

creating recurrence plots and recurrence quantification analy-

sis. We proposed and developed a new algorithm in

Mathematica for creating recurrence plots and recurrence

quantification measures (see Appendix).

INTRODUCTION Recurrence plots are used as a technique of non-linear da-

ta analysis. In 1987, Eckmann et al. introduced the method of

recurrence plots to visualize the recurrences of dynamical sys-

tems [1]. Later in order to quantify the lines in a recurrence

plot, a way of measuring quantitative information was intro-

duced [2] to define measures of complexity including percent

recurrence, percent determinism, and deterministic ratio. The-

se measures have been used in various engineering disciplines

including mechanical engineering. Recurrence quantification

analysis has been used to compare the machinability of steels

[3], to assess the damage of mechanical systems [4], detecting

flank wear in face milling [5], and detection of two-phase flow

patterns [6].

EUCLIDEAN DISTANCE Consider two n-dimensional states, points, p1 = (x1,1, x 1,2,

…, x 1,n) and p2 = (x 2,1, x 2,2, .,.., x 2,n). The Euclidean distance

between these two points corresponds to the length of the

straight line drawn from one point to the other and is defined

in Equation (1).

(1)

Every particular state can be representing in vector form

as a point in n-dimensional space. Equation (1) can be used to

calculate the distance between any state and the origin or the

distance between any pair of solutions.

For each given state of size n and m number of states,

each row represents a point in n-dimensional space. The corre-

sponding state matrix of size m x n is given by Equation (2).

(2)

We define the Euclidean distance, d, between points

and as

(3)

where and The matrix of dis-

tances is of the form as shown in Equation (4).

(4)

The difference of two n-dimensional states is defined as

(5)

where and . The matrix of differ-

ences between a point and the next point has a size of .

RECURRENCE QUANTIFICATION ANALYSIS We consider a state space matrix representing the time

evolution of a dynamical system. The recurrence plot reveals

all the times when the phase space trajectory of the dynamical

system visits roughly the same area in the phase space.

Suppose we have a trajectory {xk}k=1…m of a system in its

phase space where m is the number of states with each state

being represented as an n-dimensional vector. The develop-

ment of the system is then described by a series of these vec-

tors representing each state and thus the trajectory in an ab-

stract mathematical n dimensional space. Each component of

the recurrence matrix RP = (RPij) is one if xj is contained in a

“ball” Bε(xi) of radius ε >0 centered at state and zero other-

wise as shown in [7]. The method of selecting the threshold,


the radius of the n-dimensional sphere, is based on the meth-

odology explained in [7]. The threshold, ε, is set to r x

std(data), where r = 0.25 is a common usage. We set r = 3 due

to the nature of our data and since our data is already “embed-

ded” and we use the maximum column-wise standard devia-

tion of the state matrix.

Figure 1. of radius centered at state used to determine value of

The recurrence plot shows the spatial dependence of the

system in its state space and it is not affected by the non-

stationarities in the signal. The lines formed by points that are

parallel to the main diagonal line represent the determinism of

the system.

The recurrence plot measures derived from recurrence

plots that we will discuss are Percent Recurrence (PR), Per-

cent Determinism (PD), and Deterministic Ratio (DR). Per-

cent recurrence is defined as the number of points x(i) and x(j)

closer to one another than the threshold, ε, over the total num-

ber of points in the recurrence plot. Percent determinism is

defined as the number of diagonal lines of a minimum length

of two points divided by the total number of points in the re-

currence plot. The deterministic ratio is defined as the ratio of

the percent determinism to the percent recurrence. The calcu-

lation of these parameters is based on the methodology by

Webber [8].

TESTING USING N-QUEENS DATA The N-Queens problem has been studied for over a centu-

ry and originated from the 8-Queens problem which was first

posed in 1848 by a German chess player, Max Bazzel [9, 10,

11] . The problem was proposed in Illustrirte Zeitung in 1850

[10, 11]. The goal of the 8-Queens problem is to achieve an

arrangement of 8 queens such that there is only one queen in

each column, row, diagonal, and anti-diagonal1. The problem

was eventually extended to the N-Queens problem for placing

queens on the general × board size. The problem has

been studied extensively and has attracted the attention of

many mathematicians, including Gauss [9, 11], Pólya [12],

and Lucas [13]. During the last five decades, the problem has

been discussed in the context of computer science and used as

an example of backtracking algorithms, permutation genera-

tion, divide and conquer paradigm, program development

methodology, constraint satisfaction problems, integer pro-

gramming, specification, and neural networks [14].

The N-Queens problem is classified as non-deterministic

polynomial time hard (NP-hard) [15]. This is a class of prob-

lems that are “at least as hard as the hardest problems in NP”.

Currently, no closed-form formula exists for the number of

solutions of the N-Queens problem as a function of the grid

size n. The number of solutions is determined through various

algorithms that are process intensive for large .

The solutions to the N-Queens problem form a group. The

notations of isomorphic and fundamental solutions follow the

methodology of Erbas [16]. From a particular solution, one

can generate other solutions by simple rotations. Two solu-

tions are said to be equivalent or isomorphic if either can be

transformed into the other by rotations of 90, 180, or 270 de-

grees and/or reflections about the horizontal, vertical, diago-

nal, or anti-diagonal axes. These rotations partition the solu-

tions into a set of equivalence classes. The set of solutions

consisting of exactly one representative from each equivalence

class is called a set of fundamental solutions. The number of

fundamental solutions and the number of all solutions for the

N-Queens problem are known for grid sizes less than or equal

to 26 and are listed in are listed in Table 2. These solutions are

obtained by backtracking algorithm separately, and the solu-

tion matrices from 8-Queens to 12-Queens are used in the fol-

lowing analysis. For example, 8-Queens solution matrix is 8

by 92 matrix, so it produces 8-dimentional 92 states. Figure 1

demonstrates the polynomial growth of the number of solu-

tions as a function of board-size in logarithmic scale.

The N-Queens solution matrices were used to test the re-

currence quantification analysis. Table 1 shows the recurrence

plot parameters calculated for all states and for the fundamen-

tal states respectively for grid sizes 8 to 12. For n smaller than

8, there is not a sufficient number of states to achieve reliable

results. The fundamental solutions have larger parameter val-

ues (PR, PD, and DR) compared to all states. This shows that

determinism of the fundamental states is higher than that of all

the states. In both the fundamental and all of the states, as the

grid size increases, determinism decreases. Hence, we can

claim that the states for higher grid sizes behave less determin-

istically. In other words, determinism is inversely proportion-

al to the grid size.

Table 1. Recurrence Plot Parameters

i) States of Grid Size, n Grid Size

n

Percent

Recurrence

Percent

Determinism

Deterministic

Ratio

8 0.2580 0.0484 0.1877

9 0.1590 0.0269 0.1691

10 0.1058 0.0150 0.1414

11 0.0683 0.0081 0.1181

12 0.0400 0.0042 0.1047

ii) Fundamental Solutions of Grid Size, n

Grid Size n Percent

Recurrence Percent

Determinism Deterministic

Ratio

8 .5972 .1528 .2558

9 .3875 .0907 .2341

10 .2540 .0477 .1879

11 .1473 .0221 .1497

12 .1012 .0133 .1310


Table 2. Number of Solutions for the N-Queens Problem [17, 18].

n Number of

Fundamental

Number of

All Solutions

1 1 1

2 01 0

1

3 01 0

1

4 1 2

5 2 10

6 12 4

2

7 6 40

8 12 92

9 46 352

10 92 724

11 341 2,680

12 1,787 14,200

13 9,233 73,712

14 45,752 365,596

15 285,053 2,279,184

16 1,846,955 14,772,512

17 11,977,939 95,815,104

18 83,263,591 666,090,624

19 621,012,754 4,968,057,848

20 4,878,666,808 39,029,188,884

21 39,333,324,973 314,666,222,712

22 336,376,244,042 2,691,008,701,644

23 3,029,242,658,210 24,233,937,684,440

24 28,439,272,956,934 227,514,171,973,736

25 275,986,683,743,434 2,207,893,435,808,350

26 2,789,712,466,510,280 22,317,699,616,364,000

Figure 2 shows the relationship between the grid-size and

the Percent Recurrence.

1 There are no solutions for board-sizes of 2x2 or 3x3.

2 The 6-Queens problem has fewer solutions than the 5-

Queens problem.

Figure 2. Percent Recurrence by Grid-size, n

Figure 3 and Figure 4 show the relationship between the

grid-size and the Percent Determinism and the Deterministic

Ratio respectively.

Figure 3. Percent Determinism by Grid-size, n

Figure 4. Deterministic Ratio by Grid-size, n.

RECURRENCE PLOTS A recurrence plot is a two-dimensional representation

technique to visualize distance correlations in a time series.

Recurrence plots easily demonstrate whether a system is peri-

odic or chaotic.

The recurrence plots for the 8-Queens through 10-Queens

solutions are shown in Figure 5. The recurrence plots for the

8-Queens through 10-Queens fundamental solutions are

shown in Figure 6.

0

0.5

1

13 9 10 11 12

Percent Recurrence

PR (All) PR (Fundamental)

0

0.1

0.2

8 9 10 11 12

Percent Determinism

PD (All) PD (Fundamental)

0

0.1

0.2

0.3

8 9 10 11 12

Deterministic Ratio

DR (All) DR (Fundamental)


i. 8-Queens All Solutions

ii. 9-Queens All Solutions

iii. 10-Queens All Solutions

Figure 5. Recurrence plot of from 8, 9 and 10-Queens’ solutions

i. 8-Queens Fundamental Solutions

ii. 9-Queens Fundamental Solutions

iii. 10-Queens Fundamental Solutions

Figure 6. Recurrence plot of fundamental solutions of 8, 9, and 10-Queens

OBSERVATIONS

Analysis of the recurrence plot of the N-Queens solution

matrix reveals a characteristic which is known as drift and also

reveals a checkerboard texture. Drift can be seen by the paling

of the recurrence plot away from the central diagonal. The

checker-board texture which is found in the N-Queens recur-

rence plot is a distinguishing trait of a Lorenz system in which

the points move in a spiral around one of the two symmetric

fixed points of the system [8]. A plot of an arbitrary Lorenz

System trajectory and the associated recurrence plot with a

checkerboard texture is shown in Figure 7 [19].

Figure 7. Arbitrary Lorenz System Trajectory and Asso-ciated Recurrence Plot [20].

The results obtained from the recurrence plot derived

measures suggest that the system’s complexity increases as the

grid size increases. This implies that it becomes more difficult

to speculate the position of the next solution as the grid size


increases. These results confirm observations over many dec-

ades in trying to solve the N-Queens problem.

FUTURE WORK A new area of interest would include creation of an asso-

ciated Lorenz System Trajectory.

ACKNOWLEDGEMENT We are grateful to Dr. Tanik for his encouragement and

inspiration.

REFERENCES

[1] N. Marwan, M. C. Romano, M. Thiel and j. Kurths,

"Recurrence plots for the analysis of complex systems,"

Science Direct, pp. 237-306, 3 November 2006.

[2] J. P. Zbilut and C. L. Webber, "Embeddings and delays

as derived from quantification of recurrence plots," Ph, vol.

171, pp. 199-203, 1992.

[3] Ravish, K. S. Umashankar, A. Abhinav, K. V.

Gangadharan and D. Vijay, "Recurrence Quantification

Analysis to Compare the Machinability of Steels," ARPN

Journal of Engineering and Applied Sciences, vol. 6, no. 1, pp.

8-13, 2011.

[4] Y. Qian, R. Yan and M. Shan, "Damage Assessment of

Mechanical Systems Based on Recurrence Quantification

Analysis," in Prognostics & System Health Management

Conference, Beijing, 2012.

[5] S. D. Mhalsekar, S. S. Rao and K. V. Gangadharan,

"Investigation of feasibility of recurrence quantficiation

analysis for detecting flank wear in face milling,"

International Journal of Enginering, Science, and Technology,

vol. 2, no. 5, pp. 22-38, 2010.

[6] R. Mosdorf and G. Gorski, "Detection of Two-Phase

Flow Patterns in a Vertical Minichannel using the Recurrence

Quantficiation Analysis," AMA, vol. 9, no. 2, pp. 99-102,

2015.

[7] R. Seker, M. M. Tanik and D. Callahan, "Analysis of N-

Queens Solutions: A Dynamical System Approach," in

Integrated Design and Process Technology, 2002.

[8] C. L. Webber, Jr. and J. P. Zbilut, "Dynamical

assessment of physiological systems and states using

recurrence plot strategies," American Physiological Society,

pp. 965-973, 1994.

[9] C. F. Gauss and H. C. Schumacher, Briefwechsel

zwischen, pp. 105-122, 1865.

[10] J. Gingsburg, "Gauss's arithmetrization of the problem of

n queens," Scripta Math. 5, pp. 63-66, 1939.

[11] S. Gunther, "Zur mathematisches theorie des

Schachbretts," Archiv der Mathematik und Physik, vol. 56, pp.

281-292, 1874.

[12] G. Polya, "Uber die 'doppelt-periodischen' losungen des

n-damen-problems," Mathematische Unterhaltungen und

Spiele, pp. 364-374, 1918.

[13] E. Lucas, Recreations mathematiques, 1891.

[14] C. Erbas, S. Sarkeshik and M. M. Tanik, "Different

Perspectives of the N-Queens Problem," ACM, pp. 99-108,

1992.

[15] Z. Wang, D. Huang, J. Tan, T. Liu, K. Zhao and L. Li,

"A parallel algorithm for solving the n-queens problem based

on inspired computational model," BioSystems, pp. 22-29,

2013.

[16] C. Erbas, S. Sarkeshik and M. M. Tanik, "Different

Perspectives of the N-Queens Problem," ACM, pp. 99-108,

1992.

[17] N. J. A. Sloane and S. Plouffe, "Number of ways of

placing n nonattacking queens on nxn board (symmetric

solutions count only once)," Academic Press, 17 April 2015.

[Online]. Available: http://oeis.org/A002562. [Accessed 17

June 2015].

[18] N. J. A. Sloane and S. Plouffe, "Number of ways of

placing n nonattacking queens on nxn board.," 17 June 2015.

[Online]. Available: http://oeis.org/A000170. [Accessed 17

April 2015].

[19] J. P. Eckmann, S. O. Kamphorst and D. Ruelle,

"Recurrence Plots of Dynamical Systems," Europhysics

Letters, pp. 973-977, November 1987.

[20] "Recurrence Plots and Dynamical System Analysis,"

[Online]. Available:

http://www.cs.colorado.edu/~lizb/rps.html. [Accessed 17 June

2015].


APPENDIX Recurrence plot code in Mathematica language

SetDirectory[$UserDocumentsDirectory]; data=Import["8.dat","CSV"]; n =Length[data]; size = Length[data[[1,All]]]; (* Threshold = R x the max standard deviation of the columns of the solution matrix*) R=3; stdev = {}; maxstdev = 0; For [i=1, i<= size, i++, AppendTo[stdev,N[StandardDeviation[data[[All,i]]]]]; ]; maxstdev = Max[stdev]; epsilon = R*maxstdev; (* Euclidean Distance and Recurrence Plot*) eucdis=Table[0,{n},{n}]; rp=Table[0,{n},{n}]; For[i=1, i<= n, i++, For[j=1, j< i, j++, eucdis[[i,j]]=N[EuclideanDistance[Take[data,{i,i}],Take[data, {j,j}]]]; If [eucdis[[i,j]]<epsilon , rp[[i,j]]=1;rp[[j,i]]=1 ] ]; rp[[i,i]]=1 ]; MatrixPlot[rp] (*Recurrence Plot Measures*) countlines=0; countpoints = 0; For[j=0, j< n ,j++, linelength = 0; For[i=1, i+j< n,i++, If[rp[[i,i+j+1]]==1, linelength++, If[linelength >=2,countlines++, If[linelength == 1, countpoints++ ]; ]; linelength = 0(* reset for a diagonal*) ]; ]; If[linelength >=2,countlines++, If[linelength == 1, countpoints++ ]; ]; ]; pr = N[(Total[Total[rp]])/(n*n)]; pd = N[2*countlines/(n*n)]; dr = N[pd/pr]; Print[StringJoin["Percent Recurrence (PR): ", ToString[pr]]]; Print[StringJoin["Percent Determinism (PD): ", ToString[pd]]]; Print[StringJoin["Deterministic Ratio (DR): ", ToString[dr]]];




SIMULATED LVAD PUMP MIMIC DEVICE FOR ANALYZING SAFETY, RISK AND RELIABILITY OF DESIGNS

Jacob King Department of Mechanical Engineering

University of Louisiana at Lafayette Lafayette, Louisiana

Clint Bergeron Department of Mechanical Engineering

University of Louisiana at Lafayette Lafayette, Louisiana

Krishna Chaitanya Manthripragada

Department of Mechanical Engineering University of Louisiana at Lafayette

Lafayette, Louisiana

Charles Taylor, Ph.D.

Department of Mechanical Engineering University of Louisiana at Lafayette

Lafayette, Louisiana

ABSTRACT

Congestive heart failure (CHF) is one of the most common

forms of debilitating illness that threatens the health and safety

of countless victims worldwide. Due to the severity of this

disease, victims must seek alternatives in hopes of improving

their quality of life. One such alternative is the support from a

left ventricular assist device (LVAD) to directly assist with

meeting the blood flow demands of the body.

The medical device design challenge answered within this

research lies in the inaccessibility of LVAD designs currently

being used on the market. It is very difficult to determine the

effectiveness of other medical device designs that may impact

the performance and reliability of an LVAD when the

functionality of these devices are so proprietary. As a result, in

order to assess potentially correlated medical device

performance and safety, it would be beneficial to replicate the

functionality of an LVAD, both numerically and empirically.

Thus, in order to accurately replicate the functionality of an

LVAD, for the purposes of analyzing the possible impacts of

external factors on the performance and reliability of the

device, an LVAD simulator or “mimic” would be critical for in

vitro use within a mock circulatory loop (MCL).

INTRODUCTION

Congestive heart failure (CHF) is the medical condition

that occurs when the heart is no longer capable of pumping

enough blood to maintain the adequate amount of blood flow

needed to meet the demands of the body. According to the

2013 heart disease and stroke statistical report by the American

Heart Association, approximately 5.1 million people in the

United States suffer from varying degrees of CHF and nearly

half of the people who develop CHF will die within 5 years of

being diagnosed [1-2]. A procedure developed in an effort to

combat this common and deadly condition is the replacement of

the damaged heart by means of a total heart transplant. It is

estimated that approximately 70,000 patients may benefit from

a heart transplant; however, only 2,000 hearts become available

per year [3]. Due to the severity of this condition, patients must

seek other alternatives in hopes of improving their quality of

life. One such alternative is to receive support from a left

ventricular assist device (LVAD) to directly assist with the

blood flow demands of systemic circulation, and consequently

pulmonary circulation. An LVAD’s primary function is to

effectively pump blood directly to the aorta, from the impaired

left ventricle, essentially bypassing the aortic valve. This is

typically due to the aortic valve being weakened or damaged,

which directly contributes to CHF.

To comply with the Food and Drug Administration’s

(FDA) regulations and standards, in vitro testing is utilized in

order to accurately and safely analyze device reliability and

performance, prior to in vivo trials. In vitro testing is primarily

utilized prior to in vivo in order to limit the complications and

coupled risks associated with experimentation on a living

organism.

Although a circulatory loop model cannot replace in vivo

testing, an LVAD’s design may be efficiently refined

beforehand by determining its effect on circulatory

hemodynamics. This is achieved through the use of a mock

circulatory loop (MCL), which simulates the human circulatory

system by accurately representing cardiovascular conditions in

a bench-top hydraulic circuit. Due to the complexity of the

circulatory system and the dynamics associated with cardiac

function, the MCL is an essential in vitro tool for testing

ventricular assist devices and other cardiac assist technologies.

In 1998, an article was published in the ASAIO Journal

from a joint collaboration with the FDA, The American Society

for Artificial Internal Organs (ASAIO), the Society of Thoracic

Surgeons (STS), and the National Heart, Lung and Blood

Institute entitled, “Long-Term Mechanical Circulatory Support

System Reliability Recommendation” [4]. In this article,

suggested conditions that must be accounted for in a circulatory

model are outlined. Additional guidance documents used for


assessment reaffirm this article’s recommendation: ISO 5198,

ISO 14791, and ISO 14708. Given the state of technology

when these documents were written and the many

advancements since then, these conditions need to be re-

evaluated for increased safety. Coupled with the increasing

need for these medical devices, a more rigorous and robust in

vitro analysis should be necessary before an LVAD design

begins in vivo trials.

The challenge lies in the inaccessibility of the LVAD

designs currently on the market. It is difficult to analyze

LVAD functionality on a broad range of circulatory conditions

and determine the effectiveness of other medical device designs

that may intentionally or unintentionally interact with an

implanted LVAD, when the information on LVAD

functionality is very proprietary.

For the empirical V&V aspect of this work, a pump mimic

device that could be included in a hydraulic test apparatus

would be necessary. This pump mimic would have to replicate

the hydraulic performance dictated by the affinity curves of the

chosen LVAD design being simulated. A higher performance

pump (the mimicking device), one with an operating range

encompassing that of the LVAD, could be controlled to

replicate the pressure-flow relationships of a constant RPM

LVAD through manipulation of the mimicking pump’s own

operating speed. Essentially, once the LVAD mimic is

implemented into the hydraulic system, the MCL, with all its

supplemental elements, will function as if it is operating with

the assistance of an LVAD directly from the manufacturer.

The purpose of this report is to outline the process and

methods developed in order to accurately simulate LVAD

performance for use within a MCL, to describe the

development of the in silico nested loop hydraulic testing

system used to determine the effectiveness of the LVAD

simulator or “mimic”, and to outline the simulated data to

substantiate that this verification and validation (V&V)

methodology is an effective means of addressing a key medical

device design challenge.

MATERIALS AND METHODS

The published affinity curves, following ISO 5198

specifications, for various pump designs enable the hydraulic

performance to be replicated through the use of a parameterized

pump model. These pumping curves communicate the

hydraulic performance of the LVAD without divulging the

driveline characteristics, which implies that the LVAD must

maintain constant RPM in its function. The SimHydraulics™

toolbox, in the Simulink® Simscape™ product line, contains a

pump-modeling block element that could replicate the pumping

profiles of many different types of pumps, including LVADs.

DEVELOPMENT OF THE HYDRAULIC SIMULATION

MODEL USING MATHWORKS’ MATLAB® AND

SIMULINK®

The most dominant pumping methods in the ventricular

assist research space are axial and centrifugal; the scope of this

research was limited to those two types of rotary blood pumps.

Using Simulink® Simscape™, computational models were

developed for the HeartMate II and the Jarvik 2000 using a

parameterized pump block. These two LVAD designs were

chosen for their well-documented use and performance

capabilities; the affinity curves of both are publically accessible

[5-6]. An MP Pumps FRX-50 centrifugal pump was chosen as

the pump mimicking device for its operating range, driveline

response, and published affinity curves [7].

Figure 1 is a compilation of all published pump

performance affinity curve data documented by the

manufacturer at each published operating speed for the

HeartMate II, Jarvik 2000, and the MP Pumps FRX-50. This

pump performance data was digitized for use within the model

using the program DataThief. Noted is that each pump was

tested under varying conditions, such as different fluid

properties, described by the manufacturer. Thus careful

consideration had to be made when developing a parameterized

pump model that replicates the exact conditions under which

the data was collected.

The manufacturers of the Jarvik 2000, the Heartmate II,

and the FRX-50 published data on the parameters of the fluid

used in the performance trials of each respective pump. For the

Jarvik 2000, the manufacturer specified that the fluid used was

a glycerol/water mixture with a kinematic viscosity of 3.3

centistokes (cSt). For the Heartmate II, the manufacturer

specified that the fluid used was bovine blood with a dynamic

viscosity of 3.8 centipoise (cp); the dynamic viscosity and

density of the fluid was calculated based on an average specific

gravity of 1.05 for bovine blood [8]. For the FRX-50, the

manufacturer specified that the trials were performed using

water; it was assumed that the trials were completed at room

temperature. Table 1 displays the manufacturer’s data along

with the calculated data of the aforementioned fluids at room

temperature (22° C).

A control architecture was created using Simulink®

Simscape™ based on a nested loop control structure. Figure 2

shows the hydraulic loop created for testing the performance of

the FRX-50 and the two selected LVADs in silico.

Through simulation, it was found that the Simscape™

modeling tools were able to precisely replicate the affinity

curves of the chosen LVAD designs and the MP Pumps FRX-

50 centrifugal pump as shown in Figure 3. The control

architecture, based on a nested loop control structure, enabled

the FRX-50 to successfully reproduce the function described by

the LVAD’s affinity curves. This forces the assumption that

the FRX-50 pump mimic’s differential pressure output can be

controlled to replicate any pump’s affinity curve that is below

the characteristic affinity curve of the FRX-50.


Figure 1. Affinity curves for (a) Heartmate II, (b) JARVIK 2000, (c) MP PUMPS FRX-50 at given operating speeds

Table 1. Pump fluid properties

Pumps (22° C) Kinematic

Viscosity

Density

Jarvik 2000 3.3 cst 1107.1 kg/m3

Heartmate II 3.627 cst 1047.66 kg/m3

FRX-50 0.9565 cst 997.8 kg/m3

Implementation of a discrete-time PID controller into the

nested loop control architecture was necessary for the FRX-50

to effectively track and replicate the performance of an LVAD.

Using the control elements in Simulink®, a PID control

structure was developed that enabled a computational model of

the FRX-50 to vary its operating RPM such that it could

reproduce an affinity curve of one of the LVADs, given an

operating speed. This controller setup is illustrated in Figure 4.

The PID controller that was utilized for this application is

an ideal, discrete-time, forward Euler, PID controller with a

sampling time of 0.01 seconds [9]. Table 2 displays the gains

for the PID controller. Table 3 displays the controller

performance based on the gains:

Table 2. PID controller gains

Table 3. PID controller performance

After tuning the PID controller to produce the desired

response believed to be effective at controlling the plant (Figure

2), the implementation of a Lookup Table from the Simulink®

library was necessary for matching a specific flow rate with the

corresponding differential pressure, given a specified LVAD

and operating speed.

An operating structure written in Matlab® was created in

order to construct and organize the sequence of events

necessary to simulate the FRX-50 pump mimicking the affinity

curve of a selected LVAD at a particular operating speed.

RESULTS The operating structure and the PID control architecture

was successful at simulating the FRX-50 pump mimicking both

LVADs at the eight different operating speeds published by

each manufacturer. As can be seen from Figure 5, the LVAD

mimic very closely tracks the actual LVAD’s affinity curve.

PID Controller Parameters Gain Value

Proportional (P) 0.8689

Integral (I) 200

Derivative (D) 0

PID Controller Specifications Performance Value

Rise Time 0.16 s

Settling Time 0.28 s

Overshoot 0 %


Figure 2 - SIMULINK® SIMSCAPE™ created nested loop model for simulating pump performance. The nested loop reflects a simple hydraulic circuit with three subassemblies: Reservoir, Resistance Valve and Hydraulic pump. The SIMSCAPE™ block library provided all components necessary to create a realistically functioning model, such as

pressure sensors, flow rate sensors, hydraulic pipes, reservoirs, valves, pumps, etc.

Figure 3. SIMULINK® SIMSCAPE™ simulated affinity curves for (a) Heartmate II AND (b) JARVIK 2000. Values published by the manufacturer. The valves are specified in Figure 1. Simulations performed with 60/40 glycerol / water

moisture at 22° C to represent blood flow at room temperature. The FRX-50’s performance curves (simulated from 200 to 900 rpm) completely encompass the curves of the specified LVADS, verifying that the operating speed capabilities of the

FRX-50 cover the necessary differential pressure and flow rate ranges needed to mimic LVAD’s affinity curve.

(a) (b)


Figure 4. PID control architecture featuring flow rate vs differential pressure lookup table block (to deliver a specific LVAD differential pressure, given a particular flow rate), an initial condition block, a discrete-time PID controller block, a ramp

input block connected to a needle valve (to increase flow rate over time), and two feedback loops for differential pressure and flow rate (to provide the control system with real-time sensor data). The control architecture was created using

Mathworks SIMULINK®.

Figure 5. Comparison of the simulated Heartmate II affinity curve and the MP PUMPS FRX-50 mimicking the affinity curve of the Heartmate II at 15,000 RPM. The FRX-50’s performance data reflects the PID controller adjusting to track the

target affinity curve based on a specified sampling time. This is a reflection of the PID control architecture logic illustrated in Figure 4.


Figure 6. (a) Differential pressure vs time, (b) Flow rate vs time, (c) PID-Controlled pump speed vs time, and (d) Controller

signal error vs time for the FRX-50 mimicking the Heartmate II at 15,000 rpm

The HeartMate II operating at a speed of 15,000 RPM was

chosen in this example; however, every condition tested

behaved exactly in the same manner, implying that this

heuristic model does produce results that are concurrent with

the theory that a higher performance pump can be programmed

to mimic an LVAD’s affinity curve using MathWorks’

Matlab® and Simulink®.

Figure 6 reflects the performance data of the FRX-50

mimicking the HeartMate II at 15000 RPMs. Provided is the

differential pressure, flow rate, PID-controlled pump speed, and

the controller signal error versus time for the FRX-50

mimicking the HeartMate II at 15000 RPM.

In silico verification (of the FRX-50 performance) and

validation (of the control architecture) support this modeling

and control method as an effective means of reproducing pump

performance and mimicking functionality. It was found that

the Simscape™ modeling tools were able to precisely replicate

the affinity curves of the chosen LVAD pumps and the FRX-50

pump as shown in Figure 3. The control architecture, based on

a nested loop PID control structure, enabled the FRX-50 pump

(a) (b)

(c) (d)


to successfully reproduce the function described by the

LVAD’s affinity curves in silico, Figure 5.

DISCUSSION AND CONCLUSION

The final product of this study is a hydraulic pump that can

mimic the functionality of any lower performance pump with

known affinity curves, e.g. an LVAD, by producing the

requisite flow rate against a prescribed differential pressure,

given a fixed rotational speed. Utilizing established V&V

techniques from the aerospace and automotive industries, these

in silico system modeling tools were shown to be effective at

establishing baseline performance specifications for subsequent

in vivo testing, while assisting in confirming proof of concept

prior to spending time, money, and effort developing a

hydraulic testing system. Furthermore, this medically novel

V&V methodology successfully assisted in addressing a key

medical device design challenge, proving this to be a viable

method for use within the medical device design industry.

The limitations of this methodology are restricted to the

accuracy and precision of the information necessary for

Simulink® SimscapeTM

to perform realistically. The

parameters which define the system, such as pumping profiles,

tubing length and inner diameter, etc., were all meticulously

investigated in order to provide this in silico system analysis

with the most realistic and mechanically practical design for

future in vitro studies.

FUTURE WORK

The success met in this study provides a useful model of

how to apply the outlined V&V methodology on future medical

device research, while illuminating a path to further

development in this area. Further research of this topic may

result in advances in the V&V methodology for evaluating

medical device designs prior to in vitro and in vivo trials, due to

the quick and affordable ease of application of this in silico

method.

This V&V methodology could be implemented as an

effective means of analyzing the safety and performance of

many different types of hydraulic systems, such as those used

in the manufacturing industry. These studies would lead to

further knowledge regarding LVAD performance and reliability

under conditions that have never been properly tested in vitro,

but have caused serious injury and death in vivo. Additionally,

this research will assist in producing a testing methodology and

MCL design that will advance the V&V process for LVAD

research. The overall intent of this work is to decrease the

number of device recalls in future LVAD designs through more

thorough in silico tools and in vitro methods.

REFERENCES

[1] A. S. Go, et al., and on behalf of the American Heart

Association Statistics Committee and Stroke Statistics

Subcommittee, “Heart Disease and Stroke Statistics--2013

Update: A Report From the American Heart Association,”

Circulation, vol. 127, no. 1, pp. e6–e245, Jan. 2013.

[2] K. D. Kochanek, J. Xu, S. L. Murphy, A. M. Miniño, and

H.-C. Kung, “National vital statistics reports,” National Vital

Statistics Reports, vol. 59, no. 4, p. 1, 2011.

[3] “New Heart, New Hope.” [Online]. Available:

http://www.newsweek.com/new-heart-new-hope-153439.

[Accessed: 16-Feb-2015].

[4] F. Altieri, A. Berson, H. Borovetz, K. Butler, G. Byrd, A.

A. Ciarkowski, R. Dunn, B. Griffith, D. W. Hoeppner, and J. S.

Jassawalla, “Long-Term Mechanical Circulatory Support

System Reliability Recommendation American Society for

Artificial Internal Organs and Society of Thoracic Surgeons:

Long-Term Mechanical Circulatory Support System Reliability

Recommendation,” ASAIO journal, vol. 44, no. 1, p. 108, 1998.

[5] M. D. Macris, P. Michael, S. M. Parnis, M. D. Frazier, J.

M. Fuqua Jr, M. D. Jarvik, and K. Robert, “Development of an

implantable ventricular assist system,” The Annals of thoracic

surgery, vol. 63, no. 2, pp. 367–370, 1997.

[6] Thoratec® Corporation, “HeartMate® II Left Ventricular

Assist System (LVAS),” Food & Drug Administration,

Circulatory System Devices Panel, FDA EXECUTIVE

SUMMARY MEMORANDUM, Nov. 2007.

[7] “FRX 50 1/2‘ x 1/2’ End Suction Centrifugal Pump.”

[Online]. Available: http://mppumps.com/Product/FRX-50-

End-Suction-Centrifugal-Pump. [Accessed: 16-Oct-2013].

[8] R. K. Chaplin, D. E. Waldern, and O. L. Frost, “Specific

gravity of bovine blood as affected by breed and age,”

American Journal of Veterinary Research, vol. 31, pp. 1887 –

1888, 1970.

[9] R. C. Dorf and R. H. Bishop, Modern control systems, 12th

ed. Prentice Hall: Pearson, 2010.




A LASER SENSOR FOR TIRE REAL-TIME PARAMETER ESTIMATION

Mostafa Salama (PhD Candidate) Mechanical Engineering Department University of Alabama at Birmingham

Birmingham, Alabama, USA

Marc A. Parker Mechanical Engineering Department University of Alabama at Birmingham


Vladimir V. Vantsevich

Mechanical Engineering Department University of Alabama at Birmingham


ABSTRACT As more demands are made on the automotive industry for

energy efficiency, more physical conditions must be

continuously monitored on vehicles in order to find areas to

make efficiency gains. One such dynamic condition that is not

yet monitored is the changing of wheel rolling radius while in

driving mode. This project demonstrates the feasibility of

continuously monitoring dynamic wheel radius in a single tire

by experimentally measuring the tire’s deflection from inside a

tire. A laser displacement sensor mounted to the rim of the

wheel measured the rubber’s deflection. A housing structure is

also designed to mount the sensor, amplifier, myRIO data

acquisition device, and power source.

The goal of this project is to monitor tire deflection from

inside the tire, transmit the information to the software, and

allow the user to monitor the tire deflection. Operators will be

able to monitor their tires continuously in real-time and make

informed decisions to improve their vehicle performance.

Measuring axial tire deflection is chosen specifically because it

has a direct measurement of the tire’s actual shape, while tire

pressure only is a rough indicator of shape, which is ultimately

the property that influences tire performance and reliability.

There are a number of challenges inherent in this project.

Since the sensor unit is inside the tire, it will be unserviceable.

The proposed designed device will be durable enough to go

without maintenance for extended periods of time, and its

battery able to be recharged through the wheel’s valve stem. It

must also be wirelessly connected to the controller due to the

rotating nature of the wheel.

Benefits of device are, but are not limited to, allowing for

easy measuring of tire deflections, allowing for monitoring of

deflections while on the road (on-line measurement), and

facilitating the detection of the length of the contact patch of

the tire.

INTRODUCTION The kinematic and force factors of a pneumatic wheel and

their functional mathematical description are determined by the

tire’s ability to deform in the normal, tangential and lateral

directions. To understand the manner in which the driveline

system affects the vehicle performance, it is important to

compile functional relationships that relate the kinematic and

force factors of the wheel. This is, in fact, important, because

the force factors of the wheel depend on the torque that is fed to

the wheel by the driveline system.

The kinematic, together with the force factors, determine

the power that is supplied to the wheel and its part that is lost in

the wheel. It should be emphasized that these factors are highly

affected by the properties of the surface of motion: the type and

state of the solid cover; presence of a wet layer (water and

snow) on a solid road and the physical and mechanical

properties of the terrain under off-road conditions.

Benefits of properly inflated tires

Improved vehicle energy efficiency

Longer tire life

Superior traction

Less compaction on soil (when moving on deformable

surfaces)

Features

Device will increase the life of the tire

Energy Efficient

System displays the percentage of tire deflection

This project is to continuously monitor the deflection of a

tire wall in an operating vehicle and to continuously

comprehend the surface underneath the vehicle through the


acquired data. The scope of this paper only involves a proof of

concept and some design work for the overall project. The first

goal is to determine, acquire, assemble, and test the necessary

hardware to accomplish this goal. Second is to create the

necessary software tool using LabVIEW to operate the data

acquisition hardware and record the results in a format that can

be analyzed. Third is to design a housing structure that can

protect and hold the electronic hardware in place inside of a

tire. The final goal of this project is to temporarily mount the

sensor inside of a test tire, deflect the tire, and analyze the

numerical results to identify the deflection within the readings

in order to verify the entire system up to this point.

Figures 1 and 2 demonstrate a layout of a proposed

intelligent tire system and components. A laser displacement

sensor is mounted inside the tire to continuously monitor the

tire deflection and connected to a data acquisition system which

has the capability to be connected to a computer using a WIFI.

Figure 1. Layout of intelligent tire system

Figure 2. Intelligent tire system components

Once the MyRIO detects laser sensor readings it sends

these data wirelessly to a computer host in the vehicle to

monitor and save tire deflection data.

LITERATURE REVIEW Armstrong et al. used low-cost piezoelectric film sensors

between the inner tube and the tire to characterize the surface of

motion. They suggested that the sensors were capable of

detecting normal pressure, deflection, and/or longitudinal

strain. However, their results were less consistent for larger

tires [1]. Erdogan et al. introduced a simple approach for the

analysis of tire deformation and proposed a new piezoelectric

tire sensor to physically measure tire deformation to estimate

slip angle [2]. Tuononen used a tire laser sensor based on a

laser triangulation technology, which can measure the carcass

deflections of a rolling tire. The results were shown for several

wheel loads and inflation pressures, which have linear influence

on both tire radius mean value and radius amplitude [3]. Xiong

et al. presented a laser-based sensor system to measure tire-

tread block deformation. Validation experiments were

conducted on a chassis dynamometer, and an asymmetric tire

tread deformation along the contact patch was observed. They

proposed that asymmetric tread deformation is due to rolling

resistance [4]. Erdogan et al. proposed a tire-road friction

coefficient estimation approach, which makes use of the

uncoupled lateral deflection profile of the tire carcass measured

from inside the tire through the entire contact patch [5].

EFFECTIVE ROLLING RADIUS AND SLIP RATIO The rolling radius of a wheel with a pneumatic tire is one

of the most important concepts of wheel kinematics. The rolling

radius that links the actual velocity of the center of the wheel

to the wheel angular velocity is given by

(1)

Since the rolling radius of a pneumatic wheel is not

equal to its free radius , a pneumatic wheel and a rigid wheel

of the same radius with no slip or skid will make different

numbers of revolutions for the same traveled distance [6].

The rolling radius of a pneumatic wheel is not constant

because the wheel will make different numbers of revolutions

on the same travel distance when loaded by different

combinations of moments and longitudinal forces at the wheel

axis and at the tire/terrain contact patch [6].

Any change in the wheel loads changes the rolling radius

and the angular velocity of the wheel. This leads to a definition

of the slip ratio,

(2)

where

is the theoretical linear velocity of the wheel

is the actual linear velocity of the wheel

When a wheel moves in the free mode and the slip ratio is

zero, the actual and theoretical velocities are equal and the

rolling radius is . The rolling radius in free mode can be

determined analytically [6]. However, it is more convenient to

use the rolling radius in the driven mode instead for the

following reasons:

The difference between radii and

can be neglected

for hard-surface roads, and the radius can be used as the

reference for zero slip ratio [6].


DESCRIPTION OF THE SYSTEM COMPONENTS 1. Wheel and Tire

The wheel chosen for study is a passenger car with

Michelin MXV4 tires. The tire size is 195/60R15 with load

index 88 and speed symbol H. This means that the maximum

load on the tire is 560 kg (1235 lbs.), maximum inflation

pressure is 300 kPa (44 psi) and maximum speed is 210 km/h

(130 mph). See Figures 3 and 4.

Figure 3. Wheel and tire

Figure 4. Tire dimensions

The most important factor in tire dimensions is the aspect

ratio where higher aspect ratio means more space to mount all

system equipment (data acquisition system, sensor, wires,

batteries, etc.) on the wheel.

2. Laser Displacement Sensor (LDS)

A laser tire sensor can measure the carcass deflection of a

rolling tire. The sensor’s output is red using one of the

controller’s analog pins. This sensor gives a voltage output

related to the distance of the tire from the sensor’s location.

The sensor used to measure deflections is a Keyence IL-

065 analog laser sensor with an IL-1000 amplifier. The sensor

head produces a single laser and also intercepts its reflection off

of whatever surface is being measured. Before purchase it was

evaluated for compatibility with the equipment already in hand.

It was evaluated for output signal and power requirements to

make sure that a myRIO could intercept the sensor’s analog

output and run on the same power source. See Figure 5.

Figure 5. Keyence IL-065 Laser sensor [7]

The IL-1000 sensor amplifier provides an analog output

signal between -5 V and 5 V, but it can be limited to a range of

0 V to 5 V. The myRIO system can process 0 V to 5 V analog

signals. The sensor also requires a power source between 10

VDC to 30 VDC and up to 18 W. The myRIO device requires

between 6 VDC and 16VDC and up to 14 W. Therefore, the

Keyence sensor and amplifier are compatible with the NI

myRIO, and any shared power source must be within 10 V and

16 V. See Figure 6.

Figure 6. Laser sensor amplifier IL-1000 connections [7]

Table 1 shows laser sensor and amplifier specifications.

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCL3fpeO028cCFQuoHgodSPgMZw&url=http://www.keyence.com/products/measure/laser-1d/il/models/il-065/index.jsp&psig=AFQjCNGC5-vS1zYxA528RqXlo2tECPj-1Q&ust=1441388508739785

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0CAcQjRxqFQoTCL3fpeO028cCFQuoHgodSPgMZw&url=http://www.keyence.de/products/sensor/laser/il/models/il-1050/index.jsp&psig=AFQjCNGC5-vS1zYxA528RqXlo2tECPj-1Q&ust=1441388508739785


Table 1: Laser sensor and amplifier specifications [7]

Model IL-065

Mounting distance 65 mm

Measurement range 55 to 105 mm

Mass 75 g

repeatability 2 m

Linearity 0.1%

Light source output 560 W

Model IL-1000

Amplifier type DIN rail mount

Analog voltage output 0 to 5 V

Analog current output 4 to 20 mA

Power voltage 10 to 30 VDC

Power consumption (no

load) 2300 mW

Mass 150 g

3. Data Acquisition System

A signal transmitter will take the information sent by the

sensor and send it to an external receiver connected to a

MyRIO and input to a PC station equipped with LabVIEW

software. Up to this moment, laser sensor, sensor amplifier, and

MyRIO are installed inside the tire. The MyRIO is already

equipped with built-in wireless characteristics with ISM 2.4

GHz frequency band and 20 MHz channel width while the

outdoor range is up to 150 m. The laser sensor and amplifier are

connected directly to the MyRIO mounted inside the tire.

The National Instruments (NI) myRIO was selected to be

the data acquisition system to be used in this project. It is a new

product designed with students in mind that makes creating

systems embedded with sensors and actuators more accessible.

It can also be controlled using NI’s LabVIEW, a graphical

programming software system licensed to UAB’s School of

Engineering. LabVIEW uses a block-diagram design that

should be familiar to mechanical engineering students who

have studied system modeling and controls.

4. Power Source

A self-contained power source such as a battery pack will

eventually be needed to carry out a tire deflection experiment in

a moving vehicle. Because lithium-ion and lithium-polymer

batteries have a relatively high ratio of energy storage over

mass, those two types of battery packs were considered. The

minimum numbers of hours were calculated based on each

component consuming the maximum amount of power

possible, but that would not be the actual case since the

majority of myRIO functions would not be utilized.

Instead of using a battery pack at this stage in the tire

deflection monitoring project, a DC power supply provides

energy to the sensor and amplifier, while the myRIO is plugged

into an AC wall socket. The battery pack is not necessary until

the housing structure is built and the entire system can be

integrated in the tire. Figure 7 shows all of the electronic

hardware utilized in this project except for a personal computer

used to run LabVIEW, perform research, and analyze results.

5. User Interface (LabVIEW)

LabVIEW software installed on the host computer will

display the output deflection of the tire signal for several wheel

loads and inflation pressure and terrain conditions. LabVIEW

has the capability to display, save, and signal condition the

sensor readings using the host computer mounted in the

vehicle.

Figure 7. Electronic equipment used in tire deflection monitoring proof of concept including myRIO (1), DC

power supply (2), laser sensor (3), and sensor amplifier (4).

RING STRUCTURE DESIGN Before designing the ring structure, which will hold all

system components inside the tire, measurement of the wheel

rim dimension is essential. Three dimensional scanner is used

to scan the rim and create a 3D model. See Figures 8 and 9.

Figure 8. 3D scanner in Enabling Technology Lab

The rim was scanned from three different perspectives. The

results of this process are multiple three-dimensional point

clouds representing the measured displacements across the


object. The three perspective views were stitched together from

the same points on the object for different images from

different perspectives by the scanner’s software. These point

cloud representations were then converted into a mesh as

shown in Figure 9. The mesh file was then exported to Creo

CAD software to get wheel rim dimensions.

Figure 9. Mesh generation of wheel rim

Finally, the dimensions of the middle section of the tire

rim’s edge were obtained and a solid model was developed in

Creo Parametric 2.0 of a structure that can hold the laser sensor,

amplifier, power source, and myRIO. A wire tunnel between the

separate chambers was used to connect them. The modeled

object is in Figure 10 with a wire frame version in Figure 11.

The ring structure was designed to support the sensor,

amplifier, myRIO, and battery pack in a stationary position with

the laser oriented downward through a radial line from the axis

of rotation of the wheel. The device is intended to keep the

laser stationary when the wheel is turning at slow speeds.

It can be seen that there is a “cap” that spans the upper

component. This will be held on by the straps which will fit

into holes on the upper and lower sections. This cap allows for

components to be placed within the envelope. Notice that there

is a hole near the top of Figure 10. This is for the laser sensor to

take readings of the inner wall of the tire. Another point of

interest is that the bottom section houses none of the

equipment. It exists only to facilitate strapping the structure to

the rim and to balance the tire.

Figure 10. Ring 3D CAD design

Figure 11. Ring 3D dimensions

In the wire frame version the places where the straps hook

in are apparent. Also, the chambers which hold the different

electronic system components are visible. Starting with the

parallelogram at the far left is the chamber for the myRIO. Next

is the sensor head, the amplifier, and finally the power source.

Note that the myRIO will sit on its thin edge. This keeps the

entire structure shorter and helps to maintain its structural

integrity. Figure 11 is the orthographic mechanical drawings

created from this model.

COST ANALYSIS The desired objectives of the personnel implementing the

research and progression of the Tire Deflection Monitor project

are impeded by the remaining components required for the

correctly validated completion of the application. The grant that

is generously provided will assist the VREL and its aspiring

undergraduate researchers to obtain the necessary equipment to

further advance the research, application, and testing of the

proposed project. The research will allow the direct observation

and demonstration of the effects of proper tire deflection on the

tire slippage and vehicle energy efficiency.


Table 2: Cost Analysis

Part Quantity Price

MyRIO Controller 1 $499

Laser Displacement Sensor 1 $1750

Rechargeable NiMH Battery Back 1 $35

Charger Adapter 1 $40

Materials (Aluminum 18”x18”) 1 $115

Machining and Manufacturing 1 $300

17” 5 bolt pattern rim 1 $150

17” high profile tire 1 $100

total $2989

HARDWARE TESTING After choosing and acquiring components, it is always

necessary to test their functionality as well as any other

qualities related to fulfilling objectives such as durability. In

this case functionality and range of the sensor and amplifier

was needed. Exploring the functionality of the amplifier

showed that displacement is measured in millimeters and that

any sensible point can be set to equal zero so that the user can

more easily read changes instead of absolute distance. In

addition, it was discovered that when the amplifier creates an

analog output signal between 0 V and 5 V, the signal voltage is

scaled to one-tenth of the displacement when measured in

millimeters. Figure 12 shows a displacement reading on the

sensor amplifier. The voltage of the output signal is equal to

one tenth of that number.

Figure 12. Sensor amplifier (center) displaying displacement measured by sensor head (left).

SENSOR RANGE The setup in Figure 12 is actually the arrangement used for

determining the range in which the laser can measure distance.

The Keyence IL-065 can measure distances between 55 mm

and 105 mm away from the face of the sensor [7]; as shown in

Figure 12. In order to test this range a simple experiment was

conducted. The sensor head was taped to a piece of paper and a

line drawn at the edge of its face to mark its position. Next a

straight ruler was placed perpendicular to the sensor head with

0 at the edge. The ruler was taped down for stability. A box was

placed directly in front of the sensor head and slowly moved

away so that it was moving up the ruler. Once a reading

appeared on the amplifier, a line was drawn in front of the box

so to mark the beginning of the sensor’s sensible range. The

box continued to be slid down the ruler until readings stopped.

Another line was drawn to mark the end of the sensible range.

Then the lengths along the ruler were measured where the lines

were drawn to see how far and how close to the sensor head it

can read the distance. Figure 14 shows how the sensor and ruler

were arranged as well as the final lines had drawn demarcating

the sensible range.

Figure 13. IL-065 laser sensor operating range [7]

Figure 14. Sensor head and ruler setup for range test. Range demarcation is also shown

DATA ACQUISITION SYSTEM In order for voltage values that represent displacement

detected by the sensor to be received by the myRIO and for it to

be displayed and recorded, a software application must be

created. National Instruments’ LabVIEW was developed to

facilitate control and data acquisition projects such as this.

After connecting the myRIO device to a computer in the

laboratory, LabVIEW was made to detect it.


LabVIEW uses a block diagram structure to build control

and instrumentation software. The block diagram built for this

particular project is shown in Figure 15. LabVIEW

automatically creates a front panel that allows user

manipulation of the software components that correlate with

actions signified in the block diagram. This front panel can and

was further customized for clarity and aesthetics. The final

front panel is shown in Figure 16.

Figure 15. Block diagram of LabVIEW data acquisition, interpretation, display, and recording application

The block diagram is entirely closed in a loop so that the

program will run repeatedly. It does not run continuously,

however. There is a constant value connected to a watch

symbol in the top, left corner. The program will delay by the

number of milliseconds equal to the constant before executing

the loop again. This way, the user can control the rate at which

data is sampled. By not providing a stop condition as part of the

diagram itself, it will run until the user ends the program.

The block diagram begins with an analog input from the

sensor as a numerical value. This value will equal the voltage

output of the sensor. Next, a value specified by the user is

subtracted from the analog input to represent an offset, in

millimeters. This is where the user can define the distance

between the laser sensor head and the original position of the

tire rubber if the user wants an output that represents change in

displacement of the point on the tire rather than an absolute

value. Next, the information is scaled by multiplying the

numerical datum by 10. This is done because the numerical

value for the voltage output of the sensor is one-tenth of the

numerical value of the measured displacement.

Finally, the measured displacement value is displayed in

four different forms, which is how the system output is

communicated to the user on the front panel. One display

shows the current value in a box, and it is also shown in the

form of a circular gauge. The last ten values are plotted over

time, as well. Finally, every value is stored in a vertical table

which can then be exported to a spreadsheet or delimited file

and analyzed.

Figure 16. Front panel of LabVIEW data acquisition, interpretation, display, and recording application

UNCERTAINTY ANALYSIS The uncertainty of deflection measurements can fall into

four categories. The first source of uncertainty is due to sensor

calibration. This is provided by the vendor, Keyence, in the IL

Series User Manual and is ±2 µm. There is also uncertainty due

to measurement resolution, taken to be ± the last digit of the

readout. If using the amplifier this would mean 0.001 mm, but

the recorded measurements actually come from the LabVIEW

program. This results in an uncertainty of 0.01 mm.

An important source of uncertainty is due to the angle in

placement. Ideally there would be an exact right angle between

the laser and a line tangent to the curvature of the tire wall at

the point where the laser comes in contact with it. However,

that was seen to not be the case when analyzed before setting

the tire back on the rim. Therefore, this uncertainty must be

quantified. If real deflection is ΔS, the measured deflection is

ΔS*, and the angle between the actual placement of the laser

and the ideal placement is , then

(3)

It is assumed that the difference between the actual angle and

90º is less than 10º. If 10º is assumed then this means an

uncertainty of ±0.015 of the sensor’s measurements, or 1.5 %.

Table 3 is repeated again, taking all three of these uncertainties

into account.

The fourth source of uncertainty only applies in the cases

where the initial reading of the sensor is set to zero, and it is

virtually unquantifiable human error. This is because the tire

was held in place by a person, not a rigid structure. The

movement it took to set the initial value to zero could have

caused a slightly different deflection from the actual rest

position before loads were applied. This is why data sets begin

with a number other than zero for an unloaded state.

EXPERIMENTAL RESULTS Experimental results presented in this section provide

preliminary results for the developed data acquisition system

mounted inside the wheel with no inflation pressure. System

response is tested for several types of loads (steady and high

impact) and different sampling rate is examined in order to test

the developed system. For instance, a high velocity impact does

not allow for an adequate function to be derived that describes

deflection over the time domain when the sampling rate is only


0.1 sec. Radii were calculated using the undeflected tire radius

of 302.5 mm. The pressure inside of the tire was atmospheric

pressure in all cases. This means that it was not inflated. The

tire was not inflated because measurable deflections would

have required loads too large to safely apply given the available

equipment and resources. As a result, the tests indicate basic

properties of the tire material, but this is not as practical as if it

were inflated to normal operating pressure.

Figure 17 demonstrates wheel radius changes when

deflecting the tire with slow steady load while the sampling

time is 0.1 sec.

Figure 17. Wheel radius at slow steady load with sampling time of 0.1 sec

Figures 18, 19 and 20 show tire radius values in real-time

when high impact load is applied to the wheel using different

sampling time. Three consecutive high impact loads are applied

to the wheel with about 1 sec in between in Figure 18, with

sampling time of 0.01 sec. It is apparent that 0.01 sampling

time is not sufficient to capture all high impact loads

representing bumps in the road, as shown in the first and third

impact loads.

Figure 18. Wheel radius at high impact load to simulate bump with sampling time of 0.01 sec

Using sampling time of 0.1 sec to capture tire high impact

load is not suitable, as shown in Figure 19, when a tire is

subjected to six consecutive high impact loads with 1 second

interval time. It can be seen that only one impact load is

captured by the data acquisition system.

Figure 19. Wheel radius at high impact load with 0.1 sec sampling time

Figure 20 displays tire radius with two consecutive high

impact loads with less than 0.5 sec in between. The sampling

time is set to be 0.001 sec. It was found that 0.001 sec sampling

time is the best sampling time to capture tire deflection for high

impact loads.

Figure 20. Wheel radius at high impact load with 0.001 sec sampling time

From the results it is evident that quick, forceful impacts

must be monitored with more considerations than smoothly

applied forces. The sampling rate should be higher, ideally at

least 1000 samples per second. In the second final case with a

high velocity impact and sampling rate of 0.1 per second,

almost no impact was detected. In a real situation when a tire is

rolling, the only type of impact that can be read will likely be of

high velocity because the sensor will be rotating along with the

tire.

CONCLUSION In conclusion, a continuous tire monitoring system was

achieved as realistic and practical, but still much work needs to

be done. A beneficial next step will be to manufacture the ring

structure for component housing inside a tire. This will allow

for more robust testing, because the monitoring system will be

secured and protected. That will allow for the tire to be

professionally worked on, which will then allow for its internal

296

297

298

299

300

301

302

303

0 2 4 6 8 10

Tire

Rad

ius

(mm

)

Time (s)

275

280

285

290

295

300

305

0 2 4 6 8 10

Tire

Rad

ius

(mm

)

Time (s)

297

298

299

300

301

302

303

0 2 4 6 8 10

Tire

Rad

ius

(mm

)

Time (s)

280

285

290

295

300

305

0 0.5 1 1.5 2

Tire

Rad

ius

(mm

)

Time (s)


pressure to be increased. It will also ensure less error in

readings.

In addition, testing equipment should be acquired that can

apply well-controlled forces in order to establish a functional

relationship between deflection and load. It may also be worth

acquiring access to more recent three-dimensional printing

software or other expertise to create a more accurate model of

the tire rim’s dimensions.

REFERENCES [1] Armstrong, E. G., Sandu, C., and Taheri, S., "A Study on

Using Piezoelectric Sensors in a Wheeled Robot Tire For

Surface Characterization," Proc. 18th International Conference

of the ISTVS.

[2] Erdogan, G., Alexander, L., and Rajamani, R., 2010, "A

novel wireless piezoelectric tire sensor for the estimation of slip

angle," Measurement of Science and Technology, 21.

[3] Tuononen, A. J., 2011, "Laser triangulation to measure the

carcass deflections of a rolling tire," Measurement of Science

and Technology, 22.

[4] Xiong, Y., and Tuononen, A., 2014, "A laser-based sensor

system for tire tread deformation measurement," Measurement

Science and Technology, 25.

[5] Erdogan, G., Alexander, L., and Rajamani, R., 2011,

"Estimation of Tire-Road Friction Coefficient Using a Novel

Wireless Piezoelectric Tire Sensor," IEEE Sensors Journal,

11(2), pp. 267-279.

[6] Andreev, A. F., Kabanau, V. I., and Vantsevich, V. V., 2010,

Driveline Systems of Ground Vehicles Theory and Design,

Taylor and Francis Group/CRC Press.

[7] 2015, "Keyence Laser Sensor,"

http://www.keyence.com/products/measure/laser-

1d/il/index.jsp.

http://www.keyence.com/products/measure/laser-1d/il/index.jsp

http://www.keyence.com/products/measure/laser-1d/il/index.jsp




KINEMATIC ANALYSIS AND SIMULATION OF THEO JANSEN MECHANISM

Mehrdad Mohsenizadeh, Jenny Zhou

Department of Mechanical Engineering Lamar University

Beaumont, Texas, USA

ABSTRACT

Legged robots have come to researchers’ attention due to

their abilities to surmount or deal with complex obstacles, high

levels of mobility (changing direction while moving), active

suspension using force-controllable actuators in confronting

irregular terrains, maneuverability and terrain adaptability.

Within a few decades, Theo Jansen’s wind-powered beach

animals found their place among the other types of legged

machines. These autonomous creatures are able to live by their

own, storing wind energy to move their PVC-made legs,

detecting wet sands by the help of implanted nose feelers and

escaping from danger by anchoring themselves to the ground.

The advantage of these animals is that the required power of the

engine must be sufficient to transfer only the legs, and not the

transported elements. In this paper we employed the loop

closure equations method using MATLAB for kinematic

analysis of a Theo Jansen mechanism. Moreover, we performed

simulations in SolidWorks to validate the method.

INTRODUCTION Lately, there has been much work done on the synthesis,

analysis and optimization of Theo Jansen mechanisms using

programming software including Mathematica, MaTX and

Borland’s Delphi. Ghassaei [1] uses Mathematica for the design

of the Theo Jansen mechanism using the Chebyshev replication

and an approximation approach, where the latter simulates the

links’ movement as sine and cosine functions in order to

produce desired loci, and performs an optimization to extract

the optimal links length. However, no systematic approach for

the kinematic analysis is provided in [1]. Nansi. et al. [2]

implements a comprehensive dynamic analysis based on the

projection method using the MaTX, which is a continuation of

the proposed work by Blajer [3]. Ingram [4] examines a

genetic algorithm to optimize foot trajectory. Ingram [5] also

employs an elementary numerical algorithm for kinematic as

well as kinetic analysis using Borland’s Delphi software.

In this work, we present a complete, straightforward, yet

precise kinematic analysis of the Theo Jansen mechanism based

on the loop closure equations method, using MATLAB to

provide the preliminary kinematic data as a basis for future

examinations of this novel walking mechanism such as

dynamic analysis and optimization. To validate the analytical

data obtained in MATLAB, we performed simulations of the

paired legs using the SolidWorks Motion Study package.

DESCRIPTION OF THEO JANSEN MECHANISM Figure 1 shows the Theo Jansen mechanism, which is a

single degree of freedom mechanism composed of eight or

more legs. Applications of this marvelous legged mechanism go

beyond human-powered machines such as multi terrain

personal transport [6], multi terrain wheel chair, beach vendor

carts, robotic house pets, and steampunk walking ship [7].

Figure 2 depicts a schematic of one leg of the Theo Jansen

mechanism which has a crank (m), two oscillating rockers

(b,c), and two couplers (j,k), all connected by pivot joints. This

linkage is very similar to a Klann linkage [8]. Each leg consists

of six parts (see Fig. 2): 1) two three-bar linkages (triangles)

“bde” and “ghi”, which are rigid bodies while the crank rotates;

2) an upper and lower four-bar linkages (crank-rocker) “nm-bj”

and “nm-ck”, respectively, whose governing equations of

motion are similar to any other crank-rocker mechanisms; 3) an

open four-bar linkage “dc-fg” called parallel-like linkage

because of its figurative resemblance to parallelogram; 4) a

rigid three-bar linkage “ghi” called foot; 5) a ground, which is

the link between the two pivoted fixed points ( ),

represented by the dashed vector “n”; and 6) the

interconnection point “P” of links “h” and “i”, which is called

the toe. Each leg is fixed at two points, O2 and O4 in Fig. 2.

Point O4 is where the crank is pivoted to the ground and point

O2 is located at the connection of the upper rocker link “b”, the

lower rocker link “c”, and the link “d” of the linkage “bde”.

Figure 1. A CAD of the Theo Jansen mechanism [9]


Figure 2. Links and linkages of the Theo Jansen mechanism

Moreover, each two legs are joined together at the point

where the crank is fixed to the ground (point O4), and they are

out of phase with each other for one-half cycle of rotation of

the crank.

The length of each link in the mechanism is defined to

make the foot movement (approximately) linear for one-half of

the rotation of the crank. The remaining rotation of the crank

allows the foot to raise to a predetermined height, which is

called the height of step (see Fig. 3) before returning to the

starting position, which is the beginning of the next cycle.

During each movement cycle of the Theo Jansen mechanism,

each leg experiences four different movement phases which

make a closed curve. These phases are called stride phase, lift

phase, return phase and lower phase as shown in Fig. 3. The

straight line “AB” is called the stride phase in which the leg is

in touch with the ground where it should move at a constant

velocity. The curve “BCA” consists of two portions, “BC” and

“CA”. The first portion “BC” is called the lift phase. During

this phase the leg moves toward its maximum height. As the leg

passes the point “C”, it enters into the second portion of the

“BCA” which is called the return phase. During the return

phase, the leg moves in the same direction as the whole

mechanism. The shape of this phase affects the maximum

acceleration of the leg. Any attempts to make the curve “CA”

as a straight line will ideally minimize the acceleration of the

leg. Lastly, the leg descends to the ground until it reaches to the

point “A” to complete the movement cycle.

Fig. 3 Movement phases of one leg for each cycle [10]

Figure 4. Numbering points for kinematic analysis

KINEMATIC ANALYSIS In this section we studied the kinematics of one leg of the

Theo Jansen mechanism. For this kinematic analysis, we are

interested in the position, velocity and acceleration of points 1,

2, 4, 5, 6 and 7 which are shown in Fig. 4. We obtained the

general equations of motion for the linkages “nm-bj”, “nm-ck”,

“dc-fg” and “cip” (see Fig. 2) using the loop closure method, in

which links are represented as position vectors (see Fig. 5), and

then we solved these analytical equations for one full rotation

of the crank, by numerical analysis at each degree of rotation.

The upper and lower linkages are categorized as crank-

rocker mechanisms because of conforming to the Grashof

condition [11]. As in the kinematic analysis we need the

dimensions of the links, we used the dimensions that are

provided in Theo Jansen’s book [12]. To write the equations of

motion for each linkage, we used complex numbers and the

Euler identity in polar coordinates, which simplifies the

calculations.

POSITION ANALYSIS For position analysis [13] we put the origin of the general

coordinate system (GCS) at point O2 as illustrated in Fig. 5.

The vector loop equation for a general four-bar linkage “dc-ab”

as shown in Fig. 6 will be:

using complex numbers Eq. 1 can be rewritten as:

(2)

where present the link lengths. Equation 2 can be

solved for two unknown parameters,the angular positions of the

rocker and coupler . These unknowns are functions of the

links length and the angle of the crank :

where means either or . As the parameters

and represent the parameters of the


(a)

(b)

(c)

(d)

Figure 5. Vector loops of the Theo Jansen mechanism;

(a) nm-bj (b) nm-ck (c) dc-fg (d) cip

general linkage “dc-ab”, they should be replaced by the

corresponding parameters in the linkages under study.

(5)

(6)

(7)

(8)

(9)

for example, Eq. 2 can be written in terms of the real and

imaginary parts for the upper linkage:

(11)

for the set of Eq. 10 and Eq. 11, the unknowns are .

From the Eq. 10 and Eq. 11 one can find:

where the constants “x”, “y”, “R”, “ ” and “ ” are:

(14)

(15)

In Eq. 12 and Eq. 15, only one subscript inside the curly

brackets will be considered at a time. Solving Eq. 12 will

determine the angular position of the coupler and rocker of the

upper linkage. A similar approach can be used to find the

unknown parameters for the lower linkage.

Figure 6. Vector loop of a four-bar linkage


(a)

(b)

Figure 7. Position of points 1, 2, 4, 5, 6 and 7 for one rotation of the crank; (a) x-components (b) y-components

Since the triangle “bde” has rigid body behavior, the angle

of can be obtained using the Law of Cosines where is

known and has obtained from solving Eq.12:

The outputs of the kinematic analysis of the upper and

lower linkages are used as the inputs of the parallel-like

linkage. In the parallel-like linkage “dc-fg”, link “d” is

presumed to play the same role as link “n” does in the analysis

of the upper and lower linkages. However, its angle is not

constant as the crank rotates. Similarly, applying the same

method to the parallel-like linkage; separating equations into

real and imaginary parts will give unknown parameters of this

linkage which are .

The angular position is the foot input. To depict the

trace path of the toe (see Fig. 8(f)), it is required to find angular

position of the variable dashed vector “p” for each increment of

rotation of the crank. This vector together with vectors “c” and

“i” creates the triangle “cip” on which the toe is located (see

Fig. 5 (d)). The angle can be found in a similar way as .

The vector loop equation for this triangle gives the angular

position of the toe as:

(a) (b)

(c) (d)

(e)

(f)

Figure 8. Loci of all points; (a) Point 1 (b) Point 2 (c) Point 4 (d) Point 5 (e) Point 6 (f) Point 7


The x and y components of the position vector for each

point for one full rotation of the crank are illustrated in Fig. 7.

Moreover, the locus for each point of interest is shown in Fig.

8.

VELOCITY ANALYSIS Taking the time derivative of Eq. 2 gives the velocity

equation:

For the upper and lower linkages, the first and second time

derivatives of the ground link “n” are zero. Moreover, the

angular velocity of the crank is assumed to be known and

constant at 1 rad/s. Writing the velocity equations in terms of

complex numbers for the upper and lower linkages and solving

them for unknown parameters and gives:

(20)

Correspondingly, the linear velocity for each link will be:

(21)

(22)

(23)

To find vectors of angular velocities for the parallel-like

linkage, Eq. 18 can be written in the form of known and

unknown matrices:

where:

(25)

As mentioned before, the triangle “bde” acts kinematically as a

rigid body, hence . Similar rigid body behavior is also

obtained for the linkage “ghi” where . The

components of linear velocity of the toe can be written as

(a)

(b)

Figure 9. Linear velocities of points 1, 2, 4, 5, 6 and 7 for one rotation of the crank;

(a) x-components (b) y-components


(a) (b)

Figure 10. Linear accelerations of points 1, 2, 4, 5, 6 and 7 for one rotation of the crank;


the summation of the x and y components of the linear

velocities of the link “c” and link “i” (see Fig. 5(d)):

The x and y components of the linear velocity for all points

(see Fig. 4) for one full rotation of the crank are shown in Fig.

9.

ACCELERATION ANALYSIS Acceleration equations are derived from differentiating of

the velocity equations. Simplifying along with grouping terms

gives:

All the links lengths, angles, and angular velocities have been

determined so far. If the input angular acceleration of the crank

is known, then the angular acceleration of the coupler and

rocker of the upper and lower linkages will be functions of only

aforementioned parameters:

(29)

Expanding the Eulerian form of Eq. 27 in terms of complex

numbers; rearranging real and imaginary parts solely to solve

for angular accelerations of the upper and lower linkages leads

to:

where:

Figure 11. Trace path (loci) of all points of a paired leg using SolidWorks Motion Study Package


(32)

(33)

(34)

(35)

(36)

Now the components of linear acceleration for each link will

be:

(37)

(38)

(39)

We also can employ the same method used in the velocity

analysis section to write the acceleration equations for the

parallel-like linkage and solve them for the unknown

parameters :

(40)

where:

(41)

(42)

(a)

(b)

Figure 12. Linear velocities of points 1, 2, 4, 5, 6 and 7

for the equivalent time for one rotation of the crank using SolidWorks Motion Study Package;



(a)

(b)

Figure 13. Linear accelerations of points 1, 2, 4, 5, 6 and 7 for the equivalent time for one rotation of the crank

using SolidWorks Motion Study Package; (a) x-components (b) y-components

Since the triangle “bde” moves rigidly, the angular

accelerations of all its links will be identical, meaning .

Likewise, for the foot linkage “ghi”, we have

Then linear acceleration of the point “P” can be simply

written as (see Fig. 5 (d)):

The x and y components of the linear acceleration for all

the points (see Fig. 4) for one full rotation of the crank are

shown in Fig. 10.

SOLIDWORKS SIMULATION In order to measure the precision of the analytical results,

we simulated the motion of the Theo Jansen mechanism using

SolidWorks Motion Study package. The position (loci), velocity

and acceleration results for the points 1, 2, 4, 5, 6 and 7 are

represented in Fig. 11, Fig. 12 and Fig. 13, respectively. The

linear velocities and the linear accelerations plots obtained from

SolidWorks are shown for the time of 6.28 seconds which is

equal to one full rotation of the crank at constant angular

velocity of 1 rad/s.

CONCLUSIONS In this paper we employed the loop closure method for

kinematic analysis of the Theo Jansen mechanism. Each leg of

this mechanism is divided into four linkages, which are called

upper, lower, parallel-like and “cip” linkages. Furthermore, the

kinematics is studied for six points of the leg for one full

rotation of the crank, using MATLAB. A simulation was

performed to evaluate the analytical results for each point of

interest using SolidWorks Motion Study package for the

equivalent time for one full rotation of the crank. The position

(loci), linear velocity and linear acceleration results for the

desired points obtained in SolidWorks were in good agreement

with those obtained from the analytical approach in MATLAB.

REFERENCES [1] Ghassaei, A., 2011, “The Design and Optimization of a

Crank-Based Leg Mechanism,” M.S. thesis, Pomona College,

Claremont, CA, www.amandaghassaei.com/files/thesis.pdf

[2] Estremera, J., J. A. Cobano, and Pablo Gonzalez de Santos.

”Continuous Free-Crab Gaits for Hexapod Robots on a Natural

Terrain with Forbidden Zones: An application to humanitarian

Demining.” Robotics and Autonomous Systems 58, no. 5

(2010): 700-711.

[3] Blajer, Wojciech. ”A Projection Method Approach to

Constrained Dynamic Analysis.” Journal of applied Mechanics

59, no. 3 (1992): 643-649.

[4] Ingram, A. J., 2006, “A New Type of Mechanical Walking

Machine,” Ph.D. thesis, University of Johannesburg, South

Africa,https://ujdigispace.uj.ac.za/bitstream/handle/10210/598/

A%20new%20type%20of%20mechanical%20walking%20mac

hine.pdf

[5] Ingram, A. J., 2004, “Numerical Kinematic and Kinetic

Analysis of a New Class of Twelve Bar Linkage for Walking

Machines,” M.S. thesis, Raand Afrikaans University, South

Africa,https://ujdigispace.uj.ac.za/bitstream/handle/10210/1738

/Numerical.pdf?sequence=39

[6] https://www.youtube.com/watch?v=JCPlczI3k-c

[7] https://www.youtube.com/watch?v=b5E-VyQOfNM

[8] https://en.wikipedia.org/wiki/Klann_linkage

[9]www.shapeways.com/product/YHNUXCWDB/grosman-

strandbeest


[10] Shigley, J. E., 1960, “The Mechanics of Walking Vehicles:

A Feasibility Study: Final Report”, The University of Michigan

Research Institute, Ann Arbor, MI.

[11] https://en.wikipedia.org/wiki/Four-bar_linkage

[12] Jansen, T., 2007, Theo Jansen: The Great Pretender, 010

Publishers, Rotterdam, Netherlands.

[13] Norton, R. L., 2011, Design of Machinery: An Introduction

to the Synthesis and Analysis of Mechanisms and Machines,

5th ed., McGraw-Hill, New York, USA, Chap. 4.