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Micro-controller Ball Thrower Machine
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Dalhousie University-Mechanical EngineeringMECH 4010 – Senior Design Project – Fall 2011
Term Report
The Canine Ball Thrower
Group #2 Canine Ball Thrower
Group member names Randy Jordan
Michael Pyne
Corey Stewart
Evan Macadam
Submission Date December 07, 2011
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Executive SummaryThe report provides the design requirements, the designs considered, and the final build designselected with detail information, as well as the budget. The calculations which prove the finaldesign selection is viable are shown in the report, and AUTO CAD drawings are attached in theappendix. The current status of the build process is be stated. The purpose is to design andconstruct a canine tennis ball thrower to launch a tennis ball a distances of at least 50 ft. This devicewill be powered by an ordinary outlet, be safe for the dog and the surrounding humans, and it mustbe operated by the dog without human interference. The design is focuses on the training of the dogas a major aspect of the design considerations. The budget has been submitted and is $1471.57 forthe cost of the unit.
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Table of contents1. Introduction ...................................................................................................................................................................12. Design Background .....................................................................................................................................................22.1. Problem Definition.............................................................................................................................................22.2. Design Requirements ........................................................................................................................................23. Design Selection............................................................................................................................................................33.1. Spring loaded .........................................................................................................................................................33.2. Lever Arm ..............................................................................................................................................................33.3. Compressed Air ...................................................................................................................................................43.4. Dual Spinning Disks ...........................................................................................................................................53.5. Comparison ...........................................................................................................................................................54. Final Design ....................................................................................................................................................................74.1. Device Operation.................................................................................................................................................84.2. Launching Mechanism ......................................................................................................................................84.2.1. Flywheel Decision.......................................................................................................................................94.2.2. Motor Sizing and Justification ............................................................................................................104.3. Treat Dispensing System ..............................................................................................................................134.4. Training System................................................................................................................................................144.4.1. Sensors......................................................................................................................................................... 144.4.2. Arduino Controller Applications .......................................................................................................144.5. Safety Considerations of the Design.........................................................................................................155. Progress Report .........................................................................................................................................................166. Bibliography................................................................................................................................................................17Appendix A Gantt Chart ..................................................................................................................................................18Appendix B Budget ...............................................................................................................................................................20Appendix C MATLAB for Projectile ................................................................................................................................21Appendix D CAD Drawings ................................................................................................................................................23
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List of figuresFigure 1 Spring loaded design.............................................................................................................................................3Figure 2 Lever arm design ....................................................................................................................................................4Figure 3 Compressed air design .........................................................................................................................................4Figure 4 Dual spinning disks design.................................................................................................................................5Figure 5 Full design with all components ......................................................................................................................7Figure 6 Relation between flywheel characteristics and tennis ball velocity .................................................9Figure 7 Pneumatic tire from McMaster-Carr ...........................................................................................................10Figure 8 Theoretical projectile profiles with the desired motor .......................................................................13List of tablesTable 1 Comparison of launcher designs........................................................................................................................6Table 2 Motor requirements and specifications.......................................................................................................11Table 3 Proof of Concept Motor Characteristics.......................................................................................................16
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1. Introduction
The purpose of this report is to provide a complete description of the work completed by Group #2
during the fall semester. The report provides a problem statement, design requirements, the selection
process, the final design and calculations to justify specifications are provided. Final CAD drawings, final
budget and the winter Gantt chart are provided in the appendices.
This report includes the design selection, description of parts, detailed build drawings, a winter
schedule, work completed thus far and a detailed budget. This report will first detail the design problem
and the requirements of the final design. The criteria for design selection are provided and the chosen
design includes sizes, materials and testing. A full set of CAD drawings are attached in the appendix and
outline work to be completed by the Dalhousie University technical staff and which are off the shelf
parts requiring only assembly. The basis of the included information will be used to determine and
justify a working budget for this particular design project. The final inclusion within this report will be a
schedule that is presented in the form of a Gantt chart.
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2. Design Background
The function of this project is to design an automated device to play fetch with a dog. The design focus is
on training the dog, automation and safety to eliminate any required human intervention.
The device will be initially loaded by a person. The device will launch a ball using and encourage the dog
to retrieve it through various audio queues. An Arduino control system using infrared and ultrasonic
sensors will determine which audio queues are used. The device will include safety measures to ensure
the user and nearby persons and dogs will not be injured. When the ball is returned, a treat is dispensed
while the ball proceeds to the launching mechanisms.
2.1. Problem DefinitionFetch devices for dogs currently exist which can be used by a dog and are mostly autonomous in that
they require limited human interaction. These devices are not completely safe for the dog, require
supervision and can only be used by dogs trained to fetch. The devices require that the dog be trained to
stand in certain positions and be supervised by a person. The device also does not provide
encouragement to return or reward for doing so. The device proposed in this report will alleviate these
issues by meeting the design requirements below.
2.2. Design Requirements
The design must:
· Be safe for use around dogs and humans
· Train the dog with minimal human assistance
· Be operable solely by the dog
· Be compatible with a regulation size tennis ball
· Be transportable by one person
· Throw a tennis ball a distance of at least 50 feet
· Be robust enough to withstand prolonged operation (dry cycle of two hours)
· Be powered by a standard outlet
These design requirements were deemed acceptable through a group deliberation.
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3. Design Selection
The possible designs for the launching mechanism are provided below. A comparison of the design is
provided in Table 1.
3.1. Spring loadedA motor compresses a spring to build potential energy. The ball is placed into the barrel and the spring is
released, launching the ball. See sketch below.
Why it was rejected: this design was rejected because of the low robustness of the spring which would
make the final product unreliable.
Figure 1 Spring loaded design
3.2. Lever ArmA long arm is bent backwards and the ball is placed at the tip. The arm is released and the ball is
launched. See sketch below.
Why it was rejected: this design was rejected because of the inherent danger the arm presented when it
is released.
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Figure 2 Lever arm design
3.3. Compressed AirAn air compressor is used to build pressure behind a piston cylinder arrangement. The piston would be
propelled forward using the pressure generated in the air compressor. See sketch below.
Why it was rejected: the noise caused by the compressed air may frighten the dog, as well as the
potential danger of a pressure vessel.
Figure 3 Compressed air design
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3.4. Dual Spinning DisksThe launching mechanism chosen is a dual rotating disk system. The design consists of two rotating disks
that spin in opposing directions at approximately the same speed. Two disks were chosen over a single
similarly sized disk to provide a higher exit velocity. This system allows the moving parts to be encased
so that there is no potential for contact between the moving parts and the dog or its owner. The
spinning disk design is considered to be the most robust because there are fewer moving parts involved
in its operation (motor, gears, bearings, and the disks themselves). This also contributes to the reliability
of the system. The cost is also considered to be the least compared to the other ideas as there are few
intermediary steps/parts between the motor and the disks. The noise generated by this design will be
more consistent and less likely to shock the dog than the compressed air or spring design. The figure 4
shows the design.
Figure 4 Dual spinning disks design
3.5. ComparisonThe design selection process was done using a selection matrix. The criteria were ranked in order of best
performance to worst performance for the various design possibilities. This makes the higher the score
the better option in this matrix.
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Table 1 Comparison of launcher designs
Launcher Robustness Safety Controllability Cost Reliability Total
Two Spinning Disks 4 4 4 2 4 18
Spring 1 3 2 4 2 12
Compressed Air 3 2 3 1 3 12
Lever Arm 2 2 1 3 2 10
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4. Final Design
The following describes the device operation as well as the function of each individual component. The
associated CAD drawings can be found in Appendix B. The whole design was broken down into three
working systems. These systems are the launching mechanism, treat dispenser, and training system.
These are explained at length within their respective sections below.
Figure 5 shows a representation of the design. The ball is returned on the right side where a treat is
dispensed. The ball is then gravity fed to the launching mechanism.
Figure 5 Full design with all components
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4.1. Device OperationThe device is operated through the following process:
1. The device is connected to an AC outlet.
2. The motor will be turned on and will allow variable distances.
3. The motor will transmit power through a pulley and belt system to two rubber disks.
4. The tennis ball is placed in the receiving area.
5. The ball is gravity fed to the rotating disks.
6. The ball will then be propelled after contact with the disks.
7. The device uses audio queues based on the ball position to encourage the dog to retrieve the ball
(audio queues are pre-recorded by the owner using an onboard microphone).
8. When the dog returns the ball, the process is repeated and should be able to run continuously
without intervention.
4.2. Launching MechanismThe launching mechanism uses a dual flywheel system. The two flywheels will be rotating in opposite
directions and spaced apart by slightly less than the diameter of a regulation size tennis ball. A space less
than that of the tennis balls diameter will reduce slip between the ball and the flywheel. The ball is
passed through the space and propelled forward by the rotating disks. Using a basic understanding of
rotational mechanics and assuming slip within the system is negligible the following diagram outlines
the physical relation of the flywheels geometry and rotation speeds to the output velocity of the tennis
ball itself.
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Figure 6 Relation between flywheel characteristics and tennis ball velocity
The two flywheels will be mounted onto a transmitted from an AC motor to the
shaft via a belt pulley system. The two flywheels will spin in opposite directions because one belt will be
crossed and the other will not. This will allow both flywheels to be powered by the same motor and the
speeds of the two flywheels will be approximately the same.
If the flywheels were not spinning at the same angular velocity the ball would exhibit a characteristic
known as spin. Spin is defined as the following equation.
= −This is an interesting result and would make the launching mechanism able to throw curve balls but was
deemed unnecessary as it makes the system require two motors which would require a controller as
well. This would also decrease the horizontal displacement as not all of the components of the velocity
vector would be in the forward direction.
4.2.1. Flywheel DecisionFlywheel designs considered include foam castings, grooved steel wheels, cart wheels, and pneumatic
wheels. Pneumatic wheels were found to be the best option. The major factors that affected the
decision were traction and survivability. A major benefit for the pneumatic wheels is that they offer
some control over the contact pressure that will be exhibited on the tennis ball. This will allow testing to
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determine the best air pressure to reduce slip between the tennis ball and the flywheels. Having
pneumatic flywheels also increases our tolerance with the spacing associate with them which is a major
benefit.
Figure 7 Pneumatic tire from McMaster-Carr
An 8” diameter flywheel was selected since its size provides appropriate speeds, is not too large for a
motor to accelerate adequately and is available locally.
4.2.2. Motor Sizing and JustificationThe motor size was selected considering the design requirement that the ball reach a distance of 50 ft.
Matlab was used to model projectile motion for no drag, constant drag and variable drag. Little
difference was found between the two drag models with constant drag providing a slightly smaller
maximum distance. One concern was motor slip providing a lower than expected maximum distance so
a motor was found that would provide more than 50ft. This led us to motor speeds of approximately
1800 rpm. This rotation speed leads to theoretical values of approximately 85 ft.
A major motor sizing consideration for the system is the required torque to accelerate the system
adequately. This is done by calculating the inertia of the entire rotational system and defining an
adequate time at which the system should reach top speed. This analysis was done using excel and Table
2 below.
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determine the best air pressure to reduce slip between the tennis ball and the flywheels. Having
pneumatic flywheels also increases our tolerance with the spacing associate with them which is a major
benefit.
Figure 7 Pneumatic tire from McMaster-Carr
An 8” diameter flywheel was selected since its size provides appropriate speeds, is not too large for a
motor to accelerate adequately and is available locally.
4.2.2. Motor Sizing and JustificationThe motor size was selected considering the design requirement that the ball reach a distance of 50 ft.
Matlab was used to model projectile motion for no drag, constant drag and variable drag. Little
difference was found between the two drag models with constant drag providing a slightly smaller
maximum distance. One concern was motor slip providing a lower than expected maximum distance so
a motor was found that would provide more than 50ft. This led us to motor speeds of approximately
1800 rpm. This rotation speed leads to theoretical values of approximately 85 ft.
A major motor sizing consideration for the system is the required torque to accelerate the system
adequately. This is done by calculating the inertia of the entire rotational system and defining an
adequate time at which the system should reach top speed. This analysis was done using excel and Table
2 below.
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determine the best air pressure to reduce slip between the tennis ball and the flywheels. Having
pneumatic flywheels also increases our tolerance with the spacing associate with them which is a major
benefit.
Figure 7 Pneumatic tire from McMaster-Carr
An 8” diameter flywheel was selected since its size provides appropriate speeds, is not too large for a
motor to accelerate adequately and is available locally.
4.2.2. Motor Sizing and JustificationThe motor size was selected considering the design requirement that the ball reach a distance of 50 ft.
Matlab was used to model projectile motion for no drag, constant drag and variable drag. Little
difference was found between the two drag models with constant drag providing a slightly smaller
maximum distance. One concern was motor slip providing a lower than expected maximum distance so
a motor was found that would provide more than 50ft. This led us to motor speeds of approximately
1800 rpm. This rotation speed leads to theoretical values of approximately 85 ft.
A major motor sizing consideration for the system is the required torque to accelerate the system
adequately. This is done by calculating the inertia of the entire rotational system and defining an
adequate time at which the system should reach top speed. This analysis was done using excel and Table
2 below.
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Table 2 Motor requirements and specifications
Parameter Value Units Value UnitsMass of Flywheel 5.00 lb 2.27 kgDiameter of flywheel 8.00 in 0.20 mmoment of inertia per 0.28 lb-ft2 0.01 kg-m2
number of disks 2.00 N.A. 2.00 N.A.total inertia of flywheels 0.56 lb-ft2 0.02 kg-m2
rod Diameter 0.05 ft 0.02 mdensity of rod 498.00 lb/ft3 7980.00 kg/m3
length of rod 1.00 ft 0.30 mmass per rod 0.34 lb 0.15 kginertia per rod 0.00 lb-ft2 0.00 kg-m2
number of rods 3.00 N.A. 3.00 N.A.Total inertia for rods 0.00 lb-ft2 0.00 kg-m2
pulley Diameter 0.21 ft 0.06 mmass 0.84 lb 0.38 kginertia per pulley 0.00 lb-ft2 0.00 kg-m2
number of pulleys 4.00 N.A. 4.00 N.A.total inertia of pulleys 0.02 lb-ft2 0.00 kg-m2
system inertia 0.57 lb-ft2 0.02 kg-m2
angular velocity 1750.00 rpm 183.26 rad/sSpeed up time 1.50 s 1.50 sAngular acceleration 122.17 rad/s2 122.17 rad/s2
Torque 2.18 lbft 2.96 Nmpower required 0.48 hp 361.34 Watts
A motor providing 1 HP, a rotation speed of 1750 rpm and a max torque of 36 lb-in was selected. A
locally available 1 HP motor was priced lower than 0.5 HP motors available elsewhere. Using the motor
parameters for this particular motor the Matlab simulation file was run and Figure 8 gives the profile
with a launch angle of 45 degrees.
The following equations are for the horizontal and vertical displacement for projectile motion that is not
subjected to air drag.
( ) = + 12( ) = + 12
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The following equations are for the horizontal and vertical displacement for projectile motion that is
subjected to air drag.
==
= − 24= − 24 −
== 3
Defining a constant k allows the differential equations solution to be written as the following:
= − 24( ) = − 1
( ) = 1 − + − 1 −
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Figure 8 Theoretical projectile profiles with the desired motor
Benefits of moving up to the higher motor include less heat generation and more reliability as we intent
to run the device for long periods of time (2 hours). If we chose a motor of ½ HP this would likely be
running near its max torque and would generate heat at an accelerated rate, this would most likely lead
to the eventual overheating/shutdown of the motor which is unacceptable as stated by our design
criteria.
4.3. Treat Dispensing SystemThe dispenser activates when the dog retrieves the ball. A treat is released as positive reinforcement
and to encourage the dog to stay beside the machine away from the launching mechanism.
The treats will be loaded into a hopper and moved along with a circular conveyor (see attached
AutoCAD drawing of treat dispensing mechanism). The amount of turn required to drop the desired
amount of kibble is 60 degrees. The kibble that was measured had a maximum dimension of
approximately 13 mm so a hole that is one inch in diameter should be sufficient to ensure that at least
one treat is dispensed and that no blockages occur.
A statistical analysis was done on the dimensions of a sample of kibble to determine what size of a hole
was required in the treat dispenser for dispensing the kibble. The average size of kibble found was 12
mm +- 0.45mm, however the maximum size in the sample was 13 mm wide. It was decided to use a hole
larger than the maximum size of kibble found and therefore a diameter of one inch was chosen. This
also allows the option of using a treat of a slightly larger size in the treat dispenser without major
modification of the unit.
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120
Height(Feet)
Distance (Feet)
No Drag Projectile Profile
Drag Projectile Profile
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4.4. Training SystemAudio queues will be provided to the dog to encourage and reward it when retrieving the ball. The
owner’s voice will be recorded with various the commands the dog is familiar with or will become
familiar with. Alternatively a bell or clicker may be found to be more appropriate. The final decision will
depend on testing with a dog.
4.4.1. SensorsMultiple sensors will be used in this project in various applications. These sensors will include an
ultrasonic sensors and a simple infrared detector for detecting the ball.
The ultrasonic sensor will be used in multiple ways including safety and training. The sensor will be
attached to the front of the launcher where the barrel of the launcher is located. This sensor’s purpose
will be to detect for objects in the firing path of the launcher. The sensor will be mounted at the height
of the exit of the barrel and will be mounted to detect horizontally straight out from the end of the
barrel. The sensor to be used for this application will be a Parallax PING Ultrasonic Sensor. The choice of
this sensor is twofold, first is for the 3.3m range of the sensor, and second is the ability to detect
distance to an object and to determine is an object is approaching the sensor. The 3.3 meter range of
the sensor will provide adequate distance to protect from any animal or person from being struck by a
launched ball, by actuating the safety mechanism in the barrel.
The ball will be detected by the infrared sensor when it has been returned; this way the dog can be
rewarded for successfully fetching the ball. This will be accomplished by using an infrared detector
where the ball will pass through the detector blocking the infrared light from entering the sensor and
signalling that the ball has been returned. This will be a cost effective solution and will be more than
adequate for this situation.
4.4.2. Arduino Controller ApplicationsThe control system for the ball thrower will operate on an Arduino controller. The components consist
of an infrared sensor, an ultrasonic sensor, two servo motors, a microphone and a sound board. These
components act together to control the training apparatus and the safety measures. A program that
encompasses all features of the design has not yet been created however code is readily available for
each individual part.
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4.5. Safety Considerations of the DesignA major consideration for any design project is the safety associated with its operation. Our design
project is no exception to the consideration of safety if anything our safety requirements should be
more stringent as we are dealing with the use of projectiles.
When dealing with a projectile the best safety mechanism that we could think of was stopping the act of
firing. To do this a sensor will be used to detect if there is any movement within the devices launching
direction. In the event that something could be within this area, the launcher is blocked by a flat plate
which is mounted on a servo motor attached to the end of the exit barrel. This would eliminate any
opportunity for a person or dog to be subject to being impacted by the projectile.
The ultrasonic sensor operates at 40 KHz which is in the hearing range of the dog. Ultrasonic sensors
outside this range are not available at a reasonable cost. The frequency of 40 KHz will not damage the
dogs hearing but could be irritating. For this reason the ultrasonic sensor will be activated by the
Arduino for a time period after the IR sensor is triggered. This should only irritate the dog enough to
move out of the path of the ball.
Another major safety concern is that there are moving parts associated with the system. These parts will
be subjected to fairly high rotational speeds so it is deemed necessary to remove any possible contact
with the contents of the launching mechanism. This requires that we actually completely incase the
launching mechanism assembly within a solid structure. This completely eliminates any possible
interaction between the moving parts and a human or dog.
The final foreseeable safety concern was the possibility of the dog jumping on or around the device. This
would mean that the dog could hit itself off of the casing. With the understanding that this is a
possibility the corners of the casing will be required to be foamed over so that there is no possibility of
harm to the dog if it becomes over excited within the devices vicinity.
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5. Progress Report
A prototype was constructed. The prototype was mounted on a plywood sheet base for easy
transportation and disassembly. Table 3 shows the proof of concept motor characteristics. The
prototype spun a small cart wheel as a flywheel using a small 1/5 Hp motor. The motor was run through
a dimmer switch so it could be turned on and off and so that we knew it was possible to vary the motor
speed using a dimmer switch. In the final design it is desired that a dimmer switch be included. This
motor did not have sufficient torque to rotate a two flywheel system so one was deemed sufficient to
proof the functionality of our launching mechanism. The single flywheel prototype showed very high
expectations for our proposed design. Through testing we were able to reach a distance of 51 ft at an
angle of approximately 20 degrees and the system was subject to large amounts of slip because the ball
was being fed through both wheels one of which had power transmission and was not rigidly connected.
This proof of concept at 3420 rpm with a flywheel size of 7” seemed an accurate representation for our
proposed design as the motor we have chosen has 1750 rpm but will be powering two 8” flywheels
which would give similar results as the prototype except there would be much less slip associated with
the final assembly. Our final design will require a high amount of precision to maintain a balanced
operation during flywheel rotation.
Table 3 Proof of Concept Motor Characteristics
Characteristics Value Units
Power 0.20 Hp
speed 3420 rpm
Voltage 120.00 Volts
Current 3.80 Amps
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6. BibliographyS. Mish, M. Hubbard. (2001). Design of a Full Degree-of-Freedom Baseball Pitching Machine.California: DavisN. Basset, M. Bower, S. Michel, M. Shinew. (2005). Golf Ball Projectile Motion
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Appendix A Gantt Chart
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Appendix B Budget
Item Cost/Unit # Units Cost Vendor1hp treadmill motor 39.99 1 39.99 Princess Autoflywheel 30.00 2 60.00 Princess AutoV belt 3.99 2 7.98 Princess AutoFlange bearing 11.99 4 47.96 Princess AutoPulley 8.49 4 33.96 Princess AutoShaft 5/8" 16.99 1 16.99 Princess Auto3/8" bolt 0.43 24 10.32 Princess AutoMounting bolts 0.13 24 3.12 Princess AutoSpeakers 20.00 2 40.00 Princess AutoTennis Balls 3.50 2 7.00 Wal-martTreats 10.00 2 20.00 Wal-martArduino 35.00 1 35.00 Robotshop.caVoice Recording Chip 20.00 1 20.00 Robotshop.caMicrophone 8.00 1 8.00 Tigerdirect.caWiring 10.00 1 10.00 Princess AutoPower converter 50.00 1 50.00 Princess AutoMotor Bracketing 80.00 1 80.00 Princess AutoLexan Housing 126.00 1 126.00 Mcmaster-Carrultrasonic sensor 40.00 1 40.00 Robotshop.caTreat container 30.00 1 30.00 Mcmaster-CarrServo motor 55.00 2 110.00 Robotshop.ca1000 W dimmer 40 1 40 Mcmaster-CarrSteel frame 2"X2"X0.125"6ft 47.1 4 188.4 Mcmaster-CarrIR detector 15 1 15 Robotshop.ca
treat conveyor 50 1 50RapidPrototype
Ball Return Railing 23 1 23 Mcmaster-CarrTotal 1112.72Total after tax 1279.63Shipping Cost 191.94Budget Proposal 1471.57
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Appendix C MATLAB for Projectilei=1;t=[];t(i)=0;x=[];y=[];x(i)=0;y(i)=0;dt=.01;g=9.81;theta=pi/4;rpm=1750;omega=rpm*2*pi/60;r=.1016;Vo=r*omega;Vx=Vo*cos(theta);Vy=Vo*sin(theta);while ((y(i)>0)|(i==1))
i=i+1;t(i)=t(i-1)+dt;x(i)=Vx*t(i);y(i)=Vy*t(i) - .5*g*(t(i))^2;
endhold onplot(x,y)title('ball path with air drag')axis([0,160,0,30])xlabel('Distance (meters)')ylabel('Height (meters)')fprintf('Max Distance = %-5.1f m\n',max(x));fprintf('Max Height = %-5.1f m\n',max(y));i = 1;Cdh = 0.47;Cdl = 0.1;g = 9.81;dt = 0.01;d = .0635;p = 1.205;mu = .00001511;m = .057;tau = m/(3*mu*pi*d);y1max = 0;x1max = 0;theta=pi/4;rpm=1750;omega=rpm*2*pi/60;r=.1016;Vo=r*omega;Vx=Vo*cos(theta);Vy=Vo*sin(theta);x1 = [];y1 = [];u1 = [];v1 = [];t = [];x1(i) = eps;
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y1(i) = eps;u1(i) = Vx;v1(i) = Vy;Reu = eps;Rev = eps;t(i) = eps;while y1(i)>=epsi = i+1;Reu = (p*d*u1(i-1))/(mu);Rev = (p*d*v1(i-1))/(mu);
if Reu > (90000)u1(i)=((u1(i-1))*((48*tau)-(Cdl*Reu*dt)))/((48*tau)+(Cdl*Reu*dt));elseu1(i)=((u1(i-1))*((48*tau)-(Cdh*Reu*dt)))/((48*tau)+(Cdh*Reu*dt));endif Rev > (90000)v1(i)=((v1(i-1)*(48*tau-Cdl*Rev*dt))-(48*tau*g*dt))/(48*tau+Cdl*Rev*dt);elsev1(i)=((v1(i-1)*(48*tau-Cdh*Rev*dt))-(48*tau*g*dt))/(48*tau+Cdh*Rev*dt);end
x1(i) = x1(i-1)+(dt/2)*(u1(i-1)+u1(i));y1(i) = y1(i-1)+(dt/2)*(v1(i-1)+v1(i));t(i) =(i-1)*dt;
if y1(i)>y1maxy1max = y1(i);endif x1(i)>x1maxx1max = x1(i);endendfprintf('Max Distance with non-constant drag = %-5.2f m\n', x1max);fprintf('Max Height with non-constant drag = %-5.2f m\n', y1max);plot(x1,y1,'g');Title('Plot of Trajectory');axis([0,40,0,20]);xlabel('Horizontal Distance (m)');ylabel('Vertical Distance (m)');legend('no drag', 'variable drag');
Group #2 Fall Report Canine Ball Thrower
Dalhousie Univ.-Dept. of Mechanical Eng. 23 of 23
Appendix D CAD Drawings