Wheelchair Linkage

8/10/2019 Wheelchair Linkage

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FINAL DESIGN REPORTME350

SECTION 4

TEAM 43

James Butler

Gregory Caputo

Mary Molepske

Samuel Shrago

PREPARED FOR

Dr. Jeffrey SteinProfessor of Mechanical Engineering,

University of Michigan

Dr. Michael UmbriacAssistant Professor of Mechanical Engineering,


Mr. Yang XuGraduate Student of Mechanical Engineering


December 10, 2013


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Table of Contents

1 Introduction and Specifications.....................................................................................4-51.1Design Requirements.........................................................................................4

1.2Considerations....................................................................................................4

1.21 Torque and Transmission.....................................................................41.3 Final Report.......................................................................................................5

2 Functional Decomposition.............................................................................................5-6

3 Motion Generation.........................................................................................................7-93.1 Design Process...................................................................................................7

3.2 Design Matrix....................................................................................................83.3 Choosing the Final Design.................................................................................8

3.4 Test Results........................................................................................................93.4.1 Initial Test...........................................................................................9

3.4.2 Final Test............................................................................................93.5 Revisions to Final Design..................................................................................9

4 Energy Conversion and Transmission.........................................................................9-15

4.1 Down Selection: Belt vs. Gears....................................................................9-104.2 Summary of Values .........................................................................................10

4.3 Operating Speed ..............................................................................................104.4 Maximum Torque............................................................................................10

4.5 Gear Ratio........................................................................................................104.6 Torque Verification..........................................................................................11

4.7 Speed and Time................................................................................................124.7.1 Motor Low Speed.............................................................................12

4.7.2 Time of Low Speed Travel...............................................................124.7.3 Time of High Speed Travel...............................................................12

4.7.4 Angular Displacement at High Speed...............................................124.7.5 Angular Velocity at High Speed.......................................................12

4.7.6 Angular Velocity of Motor Shaft at High Speed..............................124.8 Remarks...........................................................................................................13

4.9 Input Power, Output Power Draw..............................................................14-154.10 Mounts and Joints..........................................................................................15

4.10.1 Motor and Transmission Mounts....................................................15

5 Safety and Motor Controls........................................................................................16-185.1 Sensor Capabilities...........................................................................................16

5.2 Threshold Values.............................................................................................165.3 Relevant Equations.....................................................................................16-17

5.3.1 Given and Measured Parameters......................................................165.3.2 Lower Count Threshold....................................................................17

5.3.3 Upper Count Threshold.....................................................................175.4 Changes to Arduino Code...........................................................................17-18


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5.6 Sensor Mounting..............................................................................................18

6 Design Critique..........................................................................................................18-216.1 The Good....................................................................................................18-19

6.2 The Bad............................................................................................................19

6.3 Linkage vs. Computer Model..........................................................................196.4 Load Considerations...................................................................................19-206.4.1 Loading of Backpack........................................................................19

6.4.2 Friction .............................................................................................206.5 Mechatronics....................................................................................................20

6.5.1 Control Algorithm.............................................................................206.5.2 Sensors..............................................................................................20

6.6 What We Could Have Done Differently..........................................................206.7 Mechanism Safety............................................................................................21

6.8 Final Remarks..................................................................................................21


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1 Introduction and Specifications

Our objective is to design a mechanism that pivots a backpack from the back of a

wheelchair to the chairs side, bringing a disabled persons possessions within reach. Sucha mechanism requires a safe and sturdy aluminum linkage driven by a robust transmission.

The specifications of the mechanism, both technical and abstract, will be discussed in this

section.

1.1Design Requirements

We successfully met the requirements for a linkage with an angle offset no greaterthan 15 (ours was 0), a horizontal offset no lesser than 2 inches and no greater than

10 inches (ours was 3.625 in), a forward offset no lesser than 6 inches and nogreater than 17 inches (ours was 8.5 in), a travel time of 9 seconds (ours was 9.2

seconds), a deceleration speed of 10/s (ours was 9.8/s), an operating torque of453.28 oz-in, a gear ratio of 6:1, an input motor power of 13.6 W and an output

motor power of 2.08 W. The mechanism volume is 1,202.91 in2. In terms of any

considerable figures obtained from mount and joint analysis, we determined that a

shear stress of 9234 ozf/in

2

acts on the hole through which a dowel is press-fitted,connecting the input gear to the input link. Upon investigation of the motor and its

mount, we found a bending moment, M of 1368.45 oz-in acting on the motor shaftby the motor mount. The motor shaft was found to undergo a deflection of 6.44x10-

4inches.

Furthermore, the top plate of the motor mount assembly was found to be

subject to a stress of 3899 ozf/in2, ultimately causing a vertical deflection of

2.67x10-4inches. Although these figures are not negligible, they are not significantenough to cause any serious deformation of our assembly.

1.2Considerations

Considerations included in the determination of a linkage to satisfy theserequirements are transmission design (down selection, gear ratio, DC motor

characteristics), mounts and joints (visual and written explanations of bothmotor/transmission mounts and torque transferring joints, discussion of gate 1

values) and transmission loading (stress analysis at torque transmitting joints,deflection analysis).

1.2.1 Torque and Transmission

In our design, the torque provided by the motor shaft (188 oz-in) is notenough to carry the torque required by our linkage (453.28 oz-in). The

preferred gear ratio is 6:1 (rounded up from 5.69:1, which was calculatedfrom our systems operating speed of 4.635 RPM and operating torque of

453.28 oz-in). A belt drive will be used because it has proven to be the mostadvantageous transmission in terms of design flexibility, maintenance, cost

and user safety.


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1.3 Final Report

This report provides a thorough explanation of the design process from the

formulation and choosing of individual designs to the final design. The functionaldecomposition breaks down the mechanism into its constituent components and

their basic functions, which provides clear reasoning for the inclusion of each part.

The design process is explained, starting with the formulation of a preliminarymodel in lincages as a confirmation that the link dimensions are within ratio, to amodel in Solidworks as a confirmation that the project materials can satisfy the

aforementioned design, to a model in Adams as a confirmation that the design willnot undergo significant deflection. Test results are discussed after the design

process. In the energy conversion section we discuss the down-selection processbetween belts and gears, gear ratio calculation, operating speed calculation,

maximum torque calculation, input and output power calculation, speed, time,mounts and joints. Included in these explanations are relevant equations used to

determine these vital design parameters. Afterwards we discuss the safety andmotor controls, weigh the capabilities and limitations of various mechatronic

sensors, determine the threshold values, changes to the Arduino code and theconsider the positioning of the sensors. At the end we critique the design process,

which serves to answer questions that address the project as a whole and developthe bigger, broader picture of the project.

2 Functional Decomposition

The following diagram on the next page is a functional decomposition of the linkagesystem. The functional decomposition helped us organize and simplify the function and

form of the project by determining what our design must accomplish and map out how itwould do so. This process allowed us to deeply understand the design problem and its

functional needs thus, allowing us to efficiently find our solution. This also helps simplifythe project by outlining the primary and auxiliary functions.


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3 Motion GenerationThe final plans for our design emerged from having chosen the most preferable preliminary

design in terms of the project requirements. This section breaks down the design process,includes a Pugh chart to illustrate the elimination process, discusses results from testing

trials with the finished linkage and mentions several revisions to the original chosen(not

sure could do either) design.

3.1 Design Process

The first step in our design process was to individually create a four bar linkagemodel using Lincages software. We each imported a picture of the wheelchair for

a reference frame and used the sketch function to create a design that would be ableto move the coupler link to the right side of the wheelchair. Each linkage was

designed for a transmission angle between 30 and 150 degrees. Once we foundeach links length by hand, we each created our own SolidWorks model and

imported it into ADAMS . In ADAMS we created joints and simulated the forcesacting on them creating a graph of the forces throughout the linkage movement.

Specific details on each individual design can be found in appendix A.

Next we analyzed each individuals design using the Pugh chart below. Weweighted our design criteria based the criterias importance for the final

design. . As a group we discussed how the four designs compared, and ranked themwith a 1 or -1, better or worse, for each category. After, we multiplied the criterias

weight by the designs ranks and summed all categories for each design. Theseresults contributed to the creation of our final design.


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3.2 Design MatrixBelow is a Pugh chart weighing the attributes of the project requirements and the

scores we assigned to them. In the far right column is the final design, whose valueswere obtained from the final testing.

Weight

(1-3)

Design 1

(Mary) Score

Design 2

(Greg) Score

Design 3

(Jimmy) Score

Design 4

(Sam) Score

FINAL

DESIGN

Volume (in^2), A 3 169.2 0 53.94 1 143.9 1 390 1 1202.906

Angle Offset, 3 ~0.0 0 0 0 0 0 5 -1 0

Horizontal Offset (in), B 3 5.85 0 5.67 0 3.14 1 5.49 0 3.625

Forward Offset (in), C 3 7.26 0 6.94 -1 1.36 -1 5.98 -1 8.5

Maximum Force (Lb) 3 -33 to 25 0-100 to

100 -1-169.07 to

157 -1 -13 to 13 1 2.6

Minimal (force graph from Adams)

Ease of Manufacturing 1 0 1 1 1 1

Simple part design, easy toreproduce

Cost Effectivness 2 0 0 0 0 0

Effective use of kit, minimal

purchasing required

Safety 3 0 0 -1 1 -1

# of pinch points, minimizes user

injury, angular velcocity

Radius of Motion 1 0 1 1 1 1

maximum distance backpack is fromwheel chair (minimize)

Roubustness 2 0 -1 -1 -1 -1

ability to resist load while

minimizing deformation, lifspan

(ability to undergo maximumnumber of iterations)

TOTAL: 0 -3 -3 3 -3

3.3 Choosing the Final DesignWe based our final design on Sams preliminary design because it had the highest

score of all the mechanisms and therefore the most desirable characteristics and

least potential for failure. The dimensions of the individual links in Sams designwere the most preferable because the mechanism had the most compact range ofmotion while also satisfying the project requirements. Other attributes of Sams

design were altered at a later point in time (such as the ground plate, addition ofsandwich plates, addition of transmission and mechatronics, etc.).

Figure 3.2Preliminary Design Pugh Chart


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3.4 Linkage Specifications

Input: 9.8336

Output: 11.3607

Coupler: 12.2479

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An ideal transmission angle is between 30 degrees and 150 degrees. Throughout themovement process of the linkage our transmission angle stays within those limits. This

means our linkage has an ideal transmission angle.

3.5 Final Design Description

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This 3-D isometric view shows our linkage design including ground link, input link,coupler link, follower link, and the backpack holder. The input link is on top of the

ground and is supported between the ground and the transmission triangular platewhich will be used later to hold the transmission. The ground link has a large area

in this model because we have not yet designed our transmission and mechatronic

systems for the wheelchair design.

This 3-D isometric view shows our linkage design including ground link, input link,coupler link, follower link, and the backpack holder. The input link is on top of the

ground and is supported between the ground and the transmission triangular platewhich will be used later to hold the transmission. The ground link has a large area

in this model because we have not yet designed our transmission and mechatronicsystems for the wheelchair design.

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In the ending position the Backpack is parallel to the side of the wheelchair whichgives the user easy access to their backpack. The forward offset, angle offset, and

horizontal offset are all within the required values in the end position.

3.6 Loading Analysis

Max Forces at Pin-Joints:Input-Coupler: FIC= -14 lb

Follower-Coupler: FFC = 16.5 lbFollower-Ground: FFG = 17.5 lbCoupler-Holder: FCH = 12 lb

In our loading analysis we calculated our total deflection by summing the deflection

from each individual link. We assumed that one end of the link was fixed, startingat the ground-input link. This allowed us to use the equation for a cantilevered

beam with a force at the end. We had to modify the equation for the coupler linkbecause it has a force in the center and on the end due to the coupler supporting

both the backpack holder and the follower link. (See Appendix A for detailedcalculations and Free Body Diagrams)

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Our total deflection is .04134 inches. This is a realistic number because the squarealuminum stock we used is very strong and aluminum has a high Youngs Modulus.

In addition, our downward force is very small in comparison to the materialstrength, causing only a small deflection. This deflection is totaled from three

different links and will not be noticeable to the naked eye.

This deflection will affect the joints because it will cause slight misalignment inthem. This causes out of plane loading (off-axis loading) creating friction at each of

the joints. To counteract this large friction force, caused by the deformation in eachlink, we made sure to use bushings in pairs. We also used the shortest links

possible (that still achieve our desired forward offset) in order to reduce the momentthat the force at each joint creates, thus reducing defection and reducing friction.

We compared our max forces and the pin-joints, taken from our ADAMS loading

analysis graph and we compare with the Bearing/Bushing rates below; we foundthat all our forces were smaller than our Bearing/Bushing ratings which means that

we are not at risk of causing damage to any of our bearings or bushings. The forcecapacity for our shoulder screws is not listed. However, after talking with a GSI hetold us that, The shoulder bolt can withstand a much larger load than you would

apply in this project. Using this knowledge we can assume the shoulder bolts willnot be damaged by deflection. This makes sense because the material in the screws

is Alloy Steel, which has a large Youngs Modulus and the bolts have a thick radiuswhich provides large support against outside loads.

Bearing/Bushing load ratings:

Steel Thrust Ball Bearing

Steel Washers, for 3/8" Shaft Diameter, 13/16" OD

Dynamic Load Capacity: 31 lb (From McMaster-CarrSAE 841 Solid Bronze Thrust Bearing

for 3/8" Shaft Diameter, 3/4" OD, 1/16" Thick

Pressure max: 2,000 lb/in2(From McMaster-Carr)

Area: 1.32536 in2

Load Capacity: 2650.71 lb (See Appendix A)

SAE 841 Bronze Sleeve Bearing

for 3/8" Shaft Diameter, 1/2" OD, 1" Length

Pressure max: 2,000 lb/in2(From McMaster-Carr)

Area: .323611 in2

Load Capacity: 687.22 lb (See Appendix A)

The Dynamic Load Capacity of the Steel Thrust Ball Bearings are given directly onthe McMaster-Carr website and can be immediately compared to the forces at the

pin-joints.

The Load Capacity of the Bronze Thrust Bearing was calculated by using the MaxPressure from McMaster-Carr of 2,000 lb/in

2and the Area of 1.32536(See

Appendix A). Applying the formula P=F x A to solve for force we obtained a LoadCapacity of 2650.71 lb which was the compared to the forces at the pin-joints


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The Load Capacity of the Bronze Sleeve Bearing was calculated by using the Max

Pressure from McMaster-Carr of 2,000 lb/in2and the Area of .323611 in2(SeeAppendix A). Applying the same P = F x A formula we obtained a Load Capacity

of 687.22 lb and then compared it to the forces at the pin-joints.

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3.7 Test ResultsSeveral tests were performed on the final linkage in order to determine the force on

the linkage and therefore the required transmission ratio for a given DC motor.Several weeks after these trials came the final testing results, which provided vital

information about the mechanisms motion.

3.7.1 Initial Test

During the link force analysis, which was performed with an electronic

force meter, we registered a maximum force of 2.6 lbs (41.6 oz), which afterbeing multiplied by the length of the input link, Linput(9.08 in) and the safety

factor, SF (1.2), yielded a maximum torque, Tmaxof 453.28 oz-in.

3.7.2 Final Test

In the final testing, our mechanism registered an angle offset of 0, a

horizontal offset of 3.625 inches, forward offset of 8.5 inches, travel time of9.2 seconds, deceleration speed of 9.8/s and total volume of 1,202.91

square inches.

3.8 Revisions to Final DesignAlterations to the final design included the insertion of a dowel through the output

gear and input link, lengthening of the transmission sandwich spacers, and themotor mount. We added a dowel, connecting the output gear and input link, offset

from the input joint so the gear and the input link rotated together throughout thelinkage motion. Our original input joint design did not leave enough room for the

height of the gear. We thus had to increase the length of the transmission sandwichspacers to account this. We also had to decrease the radius of a transmission

sandwich spacer to make a path for the timing belt. Lastly we decided to design ourown motor mount, because we believed that the mount provided would not

adequately support the motor and forces acting on it. This also gave us flexibility onchoosing the location and direction of the motor.


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4 Energy Conversion and Transmission

This section discusses the advantages of a belt-driven transmission and how it satisfies the

requirements of our design. The purpose of our transmission is to transfer the torqueoutput from the motor to the input link. Additionally, the transmission transforms the

torque through a gear ratio to allow the motor to operate under controlled conditions while

driving the linkage. Included in this discussion are calculations relating torque and speedto determine the appropriate gear ratio for our design.

4.1 Down Selection: Belt vs. Gears

We prefer a belt-driven transmission because of its added flexibility to the designer

(center distance), lower cost compared to gears, shock absorption, and in the eventof a disruption in the loading (such as the mechanism striking the hard stop at a

high speed), the slipping of the belt ensures a safety overload mechanism, whereas agear-driven transmission may undergo internal damage. Lastly, in the event of a

design flaw that requires an unexpected modification to our linkage, the gear-driventransmission may restrict our options for such a modification, whereas a belt

transmission provides the designer with flexibility.

4.2 Summary of ValuesCombining the DC motor specifications provided by Pololu (Tstall(187.5 oz-in),

!no-load @ 9V(60 RPM)) and the maximum torque required to move our linkage(Tmax= 453.28 oz-in) derived from the link force test, we were able to calculate a

gear ratio of 5.59:1, which for the sake of safety we rounded to 6:1. Using free-runcurrent of 225 mA and stall current of 3750 mA of the DC motor at 9V, we

calculated the input power of the motor to be 13.60 W and using the previouslymentioned mechanical data, we measured the output power to be 2.08 W.

4.3 Operating Speed

The execution angle of our design is 176, the first 146 ("1) of which is operated ata speed !opand the last 30 ("2) at a speed of 8 /s (!2). Also specified in the

project statement was the required runtime, trunof 9 seconds. Combining theseparameters into the following equation yields an operating speed !opof 4.635 RPM:

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4.4 Maximum TorqueDuring the link force analysis, which was performed with an electronic force

meter, we registered a maximum force of 2.6 lbs (41.6 oz), which after beingmultiplied by the length of the input link, Linput(9.08 in) and the safety factor, SF(1.2), yielded a maximum torque, Tmaxof 453.28 oz-in.

Equation 4.3


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4.5 Gear Ratio

Knowing Tstall, !no-load @ 9V, !opand Tmaxallows us to use the following relationship

in point-slope form ([y-y1] = m[x-x1]) to solve for the desired gear ratio, N:

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on the following page.

Equation 4.5


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4.6 Torque Verification

Below is verification that the motor satisfies the torque/speed requirements for the

high, medium and low torques (1050 oz-in, 560 oz-in, 290 oz-in, respectively)given to us in the Gate 2 Review.

Figure 4.6A

Figure 4.6 B


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4.7 Speed and TimeOur low speed was first calculated by multiplying the desired motor velocity by the

transmission ratio. We then found the estimated time of low speed travel assuming30 degrees of low speed travel. Next we subtracted this time from our total travel

time (nine seconds) to give us the time of high speed travel. We found the degrees

traveled during high speed travel by subtracting thirty degrees from the totaldegrees traveled (176.2 deg, from report 2). Next, we divided the degrees traveledduring high speed travel by the time of high speed travel to get the high link speed.

Finally we multiplied this by our transmission ratio (N=6) to get the high motorspeed.

Given:

!link,low= 8/secN = 6

4.7.1 Motor Low Speed

!motor,low= !link,low* N

!motor,low= (8/s)*(6) = 48/s

4.7.2 Time of Low Speed Travel

Timelow= Distancelow/ !link,low

Timelow= (30) / (8/s) = 3.75 s

4.7.3 Time of High Speed Travel

Timehigh

= Timetotal

TimelowTimehigh= 9 s - 3.75 s = 5.25 s

4.7.4 Angular Displacement at High Speed

Distancehigh= Distancetotal- DistancelowDistancehigh= 176.2-30 = 146.2

4.7.5 Angular Velocity at High Speed

!high= Distancehigh/ Timehigh

!high= 146.2 / 5.25 s = 27.85 /s

4.7.6 Angular Velocity of Motor Shaft at High Speed

!motor,high= !link,high* N!motor,high= 27.85 /s * 6 = 167.09/s

Equation 4.7.1

Equation 4.7.2

Equation 4.7.3

Equation 4.7.4

Equation 4.7.5

Equation 4.7.6


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4.8 Remarks

After obtaining these values for Motor High and Low Speed we converted the

Distance Traveled at High and Low Speed (deg) to counts in order for the code toread the encoder of the motor. These counts were thresholds for when the code

switched from low to high or high to low speeds. These count thresholds

corresponded to distances measured in degrees, not time.

In order to calculate the time we used a stopwatch to measure the time it took to

move from start to finish. It turned out that our time was too short (the linkagemoved too fast) so we adjusted the speed, in small increments, until the 9 second

goal was reached.


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4.9 Input Power, Output Power Draw

Figure 4.8 B

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4.9 Input Power, Output Power

The motors input power is 13.60 W and the output power is 2.08 W, yielding apower loss of 11.52 W. The power quantity we can control is the mechanical

output power. We manipulate this output power with the 6:1 gear ratio. We aredesigning the links and joints so that the power provided from the motor is directly

delivered to the input link by designing against friction and slip. The radial ballbearings, thrust bearings, and thrust washers reduce the power loss, thereby

minimizing the power needed at the operating point. Although the consideration ofpower minimization may be marginal in this case, it is a crucial theme because

minimal power consumption is a characteristic of intelligent design.

4.10 Mounts and JointsThis section discusses various mounts and joints used in our system. Torque

transfer and joint stress are considered, and included in the discussion are how theyrelate to both deflection analysis and gate 1 parameters (volume,

horizontal/vertical/angle offset, safety, etc.).

4.10.1 Motor and Transmission Mounts

Whether for a motor or transmission, a mount is an important design theme

because it creates reaction forces, torques and bending moments that are notnegligible when considering other aspects of the design. As a precursor to

the next section on transmission loading, this section is comprised of bothexplanations and images of mounts and torque-transferring joints. The

volume was somewhat affected by the addition of these mounts, since theyare located at the top of the linkage. We estimate that these mounts

contribute to 15% of the linkages total volume. We are unable to find anyeffects of the mounting assemblies on the motion generation.

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4.10.2 Torque Transferring Joints

This 3-D isometric view shows our linkage design and focuses on our

transmission. The input to ground joint is supported by the transmissionsandwich plate, transmission sandwich spacers, and ground plate assembly,

which minimizes moments occurring at the input to ground joint.

The motor is mounted by a custom made motor mount assembly. Webelieve that the bracket included with the motor is not strong enough to

counter any deflection caused by the transmission, and we decided to mountthe motor vertically so we would not need to transfer the direction of torque.

Our motor mount is made up of a plate and two rectangular spacers. It ismounted to slots in the ground to allow adjustment of the mount and thus

the tension put on the belt.

Figure 4.10.2A

Transmission

(Isometric)


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4.10.2 Torque Transferring Joints (continued)

This top view shows our linkage design focusing on our transmissiondesign. The ground link has a large area in this model because we have not

yet designed our mechatronic system for the wheelchair design.

Figure 4.10.2B

Transmission

(Top)


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(for more detail on part callouts see Assembly Plan in Appendix C)

This cut-away image shows the components of our input to ground joint.The input link and 3.8OD gear are attached by a press fitted pin offset from

the joint, as shown in the image above. The input link and 3.8OD gearrotate with respect to the shoulder bolt.

Figure 4.10.2C

Transmission

(Isometric #2)


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This cut-away image shows the input gear to motor connection. The inputgear has a snug fit to the motors shaft. The gears set screw is tightened

against the flat keyway on the motor shaft to keep the input gear in placewith respect to the motor shaft.

Figure 4.10.2D

Transmission

(Isometric #2)


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4.10.3 Transmission Loading

When designing a mount, important considerations have to do with the

reactionary physics of such a mount and the effects on the transmission andsurrounding componentry (in this case, joints). Included in this section are

discussions and calculations relating to such considerations.

4.10.31 Stress Analysis

A shear stress of 9234 ozf/in2was found to be acting on the hole,

through which the dowel is press-fitted, connecting the input link tothe input gear. Although not negligible, this shear stress is not

significant enough to cause any deformation to the assembly,especially because the use of thrust bearings reduces any reactionary

forces and friction.

Sandwich Plate

Gear

Input Link

Sandwich Plate

Dow

el

Bolt/

Bushi

ng

Figure 4.10.31A

Side View of Assembly Under Stress

! ! ! ! !

!"#!!"!"! !" ! ! ! !!"

! ! !"#!!"!"#

! !

!

!

! ! !"#!!"!"# !! ! !!!"! !!!!

! ! !"#$!"#!!!!

Figure 4.10.31B

Shear Stress Equation

!

r

InputGear

Input Link

Gear Center

Dowel Hole

Figure 4.10.31C

Ariel View of Assembly Under Stress


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4.10.4 Deflection Analysis

A net horizontal force of 1954.94 oz was found to act on the motor shaft,

while a 1368.45 oz-in bending moment was found to be acting on the motoritself by the top plate of the motor mount. The reaction forces of the

mounting plate were +/- 570.19 oz. A shear stress of 9234.14 ozf/in2was

found to act on the joint through which a dowel was press-fitted toaccommodate the input gear and input link. Due to a normal stress of3898.65 ozf/in

2, the top plate of the mounting plate was found to deflect by

0.000267 vertically downwards. Although not negligible, these figures arenot significant enough to deform the assembly or cause any internal motor

or transmission damage.

4.10.41 Gear-Shaft Assembly

Figure 4.10.4A

Ariel View of Motor Gear Shaft Assembly

Figure 4.10.4B

Force Analysis:Relevant Equations

"

"

Fnet

F1

F2

MotorGear

Shaft

!! ! !!!

!! ! !!!"# ! !"#

!! ! !!"!!"#!"#

!! ! !""#!!"!"

!! ! !! ! !" !!

!! ! ! !!"#!!"# !!!"#!

!! ! !"#!!"!"

! ! !! ! !" !"#$%&!!!

!"

! ! !!!!"!

!!"#

! !! !"# !! !! !"#!

!!"#

! !"#$!!"!"

Where d = diameter f gear above motorD = diameter of gear over input li#= angle between forces acting o

gear and horizontal


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5 Safety and Motor ControlsThe purpose of this section is to introduce the capabilities and limitations of the proximity

sensors, how threshold values were chosen for the IR sensors and the encoder, changesmade to Arduino code, and the mounting of the proximity sensors. This section covers the

mechatronic decisions made by our team in order to successfully meet goals for mechanism

movement and improve safety for the user.

5.1 Sensor Capabilities

The proximity sensors have the capability to sense an obstruction in the view range.The output can then be interpreted by code to stop or start the desired motion. One

of the limitations of the sensors is that the range of view is a cylinder facing outfrom the sensor which does not allow the proximity sensors to see objects that

approach from the side until they break the plane of the cylinder. Anotherlimitation is that the sensors do not take perfect readings and output ranges of

numbers at certain distances. These sensors also have a maximum range and canhave a false positive if readings are taken further out.

5.2 Threshold Values

The threshold values of the proximity sensors were chosen based on a guess andcheck method. We did tests using a binder (large flat surface, gives consisting

blocking of sensor) to find the distance where the sensors needed to be triggered.After each test we adjusted the code so the value of each sensors range would be

closer to the desired range. The final values of the proximity sensors values were:500 and 140.

The threshold values of the encoder count were chosen using calculations based on

a total travel distance of 176.2 degrees (from report 2) and 30 degrees of low speedtravel. However, we ended up using 40 degrees for low speed travel because we

wanted to give a safety period of ten degrees for the mechanism to change speedsand slow down to the lower speed. The total counts were measured by running the

mechanism in the forward direction and recording the max value of the encodercount.

The calculations are shown in the next section and can be found in Appendix D.

5.3 Relevant Equations

The calculations required include the lower and upper count threshold.

5.3.1 Given and Measured ParametersGivens and Measured:

Total Counts = 12963 counts6 rev. gearbox

131 rev. encoder32 counts/rev


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5.3.2 Lower Count Threshold40 deg of encoder rev. = 40deg(1 rev. input/360deg)(6 rev. gearbox/1 rev. input)

(131 rev. encoder/1 rev. gearbox)= 87.333 revolutions of encoder

LowerCountThreshold = (87.3 rev. encoder)(32 counts/1 rev.) = 2794.667 counts

5.3.3 Upper Count Threshold

UpperCountThreshold = TotalCount - LowerCountThresholdUpperCountThreshold =12,963 counts - 2794.667 counts = 10,169 counts

5.4 Changes to Arduino Code

We made four changes to the Arduino code. The first change we made was in thevoid doEncoder. The change was made because the program was adding a

negative number, one for each count, to the encoderCount value when going in theforward direction. This gave us a large negative value when we needed to switch to

low speed, however the code was written expecting a positive value. Therefore, inthe if( digitalRead(encoderPinA) == digitalRead(encoderPinB) ) we switched

encoderCount++ to encoderCount--. The code was counting the numbers in anopposite fashion when the mechanism was moving backwards so, in the else we

changed the encoderCount-- to encoderCount++. These changes allowed thehigh and low speeds to enable at the right time and the were determined based on an

understanding of how the encoder counts and talking with the GSIs.

The second change we made to the code was adjusting the values for the High andLow speed. This was done using a guess and check method. We changed the high

and low speed because our calculated values were not reaching the desired time ofnine seconds. We used a stopwatch to record the time it took the mechanism tomove in the forward direction. Our time was under nine seconds so we lowered the

high speed and the low speed until we reached the desired time. The high speed

was lowered more, from our calculated values, in order to decrease the amount ofpower needed to move the backpack. The final value for high speed was: 60deg/sec and the low speed was: 14 deg/sec.

The third change we made to the code was adjusting the proximity switch values.

These are the values that determine if an object is in a pinch point of themechanism. It is important that these values are precise because they are integral to

the safety of the mechanism. Again, we utilized a guess and check method. Abinder was used to trigger the sensors and then the values were adjusted in the code

based upon whether the sensor needed to reach further or closer. We repeated thisprocess until the sensors were triggered at the proper distances in order to protect

outside objects from getting pinched in the moving mechanism.

The fourth change we made to the code was changing the upper and lower thresholdcount values. These needed to be changed in order for the high and low speed to be

used at the right angles in the mechanisms motion. These values were determinedusing calculations similar to those provided in the mechatronics lab tutorial.


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The final change we made to the code was to the float Ki integration controlconstant. We lowered this value to zero in order to eliminate the steady state error

and it was determined to lower it based on the suggestion from a GSI.

5.5 Sensor Mounting

Our Proximity Sensors are attached to the ground plate and are calibrated to sense

an obstruction near a pinch point. We chose to attach them to the ground plate sothe wires connecting the proximity sensors to the Arduino board would not get

tangled and would not have to move with every rotation of the mechanism. Thistakes away a large possibility of failure from the wires breaking or failing under

heavy use.

We attached the proximity sensors by using the double sided tape. This held theproximity sensor in place securely because the proximity sensor is light and does

not create that large of a torque on the tape.

A hand or object moving from above will be caught in the pinch point when themechanism is moving in the reverse direction; therefore, the first sensor is

positioned to sense any obstructions in the position above the linkage. This sensorwas calibrated at a value of 140.

A hand or object moving from below can also fit into a pinch point when the

mechanism is moving backwards, Therefore, the second proximity sensor ispositioned to sense any obstruction in the position below the linkage.

The sensors placement did not affect the previous volume or offset because they

were placed on the ground plate and did not extend out of the previous height,length, or width.


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6 Design CritiqueAs with every design, ours had its features and flaws. This section will clarify these

positive and negative attributes of the design process and derive meaning from theexperience as a whole.

6.1 The GoodThe most positive aspects of the design process were the benefits of having a meticulouslyplanned model. For example, we cut no corners in the determination of each joint assembly

and the necessary bolts and bearings, which left us with no unpleasant surprises during themanufacturing process. This sort of meticulousness ultimately played to our benefit.

Another benefit was the division of labor between the group. Mary and James were very

experienced with the lathe, whereas Greg and Sam were experienced with the mill. Giventhat we had a variety of parts that required both machines, the group was able to divide the

labor based on the different skills of its members. Added to this division of labor wasMarys expertise with SolidWorks a skill she honed during an internship. Marys

expertise allowed the group to quickly update changes to the CAD model in the case of adesign alteration.

In addition to being meticulous and varied in skillsets, the group was always diligent,

punctual and mindful of deadlines. The group always opted to contact Mr. Xu or ProfessorUmbriac to avoid confusion that would have otherwise led to mistakes. We met often and

had the habit of planning our next meeting ahead of time. This ensured that we stayed onschedule and met each requirement in a timely manner.

6.2 The Bad

The group is pleased to report that the occurrence of error was minimal. Despite very minor

errors made during manufacturing, we encountered no situations that required us toremanufacture any vital components. These small, almost negligible errors included a

misinterpretation of a dimension on a motor mount drawing and consequently led to anerror in the hole locations. The error was resolved.

The most significant error was our failure to predict the effects of the belt tension on our

mechanism. Our transmission was designed in such a way that the belt would fit perfectly in other words, the belt tension was extremely high and caused stripping in the threaded

holes of the motor, consequently destroying the mechanism that kept the motor in place andthus rendering our transmission useless. This failure inconveniently occurred during the

final testing and could have been avoided if we separated the belt from the transmissionduring the overnight storage.

Prediction of these situations is a subtle, yet crucial theme of engineering and we became

more mindful and careful with these situations.


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6.3 Linkage vs. Computer Model

Our mechanism behaved exactly like the computer models. The computer models were

designed in such a way to limit the forces on the joints to the maximum possible degree.Because our linkage minimized friction at joints and its deflection analysis yielded

favorable values, we are pleased to report that our linkage behaves like the computer

model.

6.4 Load Considerations

Conditions for load are crucial considerations in the design, even if the mechanism operateswell with no load. The two major areas for load consideration are the loading of the

backpack and friction.

6.4.1 Loading of Backpack

The device moved slower when loaded with the backpack than under no load. The

added vertical force increases friction between joints therefore increasing the torquerequired for motion. The added weight also increases the linkages moment of

inertia and greatly affects its start up speed and ability to decelerate.6.4.2 Friction

We realize that friction greatly affected the required torque for motion. Wecompensated for this by using thrust bearings at interfaces between moving links.

There were also instances where we used friction to our advantage. For instance, inaddition to a set screw, we relied on a press fit to attach the gear to the motor. We

also relied on a tight fit for an off axis pin to fit into the input link.

6.5 Mechatronics

When implementing a mechatronic system, one must consider the many tradeoffs and

effects involved in his options. The two major areas of consideration for mechatronics arethe control algorithm and the choice and placement of sensors.

6.5.1 Control Algorithm

One goal of the control algorithm is to maintain certain operating speeds. Thetorque is not constant throughout operation, and when the linkage is loaded with the

backpack, these changes in torque are amplified. Therefore the control algorithmcan be adjusted to expect these changes in torque and therefore vary motor speed to

maintain a constant speed of the input link. Also, the control algorithm can beimproved by varying sensitivity of the proximity sensors throughout motion. This

would allow the proximity sensors to be mounted on moving links and moreaccurately patrol pinch points while not being triggered by the linkage itself.

6.5.2 Sensors

The proximity sensors could have been used as limit switches. The presence of thelinkage would trigger sensor to stop the mechanism.


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6.6 What We Could Have Done Differently

Although we had access to different aluminum stock, we decided on using the square

tubing for our links immediately without even considering the other materials. Using theflat aluminum plate instead of the tubing would have allowed for a more compact design

and would have reduced the final volume of our linkage.

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6.7 Mechanism Safety

On a scale from 1-5 (1 = very unsafe, 5 = very safe), our mechanism scores a 3.The proximity sensors do a great job of protecting pinch points, however there are othersafety concerns that should be addressed. For instance, the motor and belt transmission are

exposed and it is possible for the users hair to get caught while sitting in the chair duringoperation. Also, there is no sensor that prevents the linkage from hitting a casual onlooker.

A possible suggestion is a sensor that detects added stress to the motor that will turn off themotor instead of allowing it to stall upon hitting an object.

6.8 Final Remarks

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