University of Michigan
Final Report
ME 350 Winter 2013
$tAnCe WiLl MaKe HeR dAnCe
Dai Phuc Do, Mario Matanovic, Marcus Papadopoulos, Paarth
Shah, John Takacs
2013
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Table of Contents
1.
Introduction and Specifications ............................................................................................................. 4
2.
Motion Generator Description .............................................................................................................. 5
3.
4.
5.
2.1
Design Process ....................................................................................................................................... 5
2.2
Design Selection .................................................................................................................................... 6
2.3
Lincages .................................................................................................................................................... 7
2.4
CAD with Descriptive Pictures ......................................................................................................... 8
2.5
ADAMS and Loading Analysis ........................................................................................................ 13
2.6
Changes from Gate 1 to Final Design ........................................................................................... 18
2.7
Final Design Testing Results .......................................................................................................... 18
Energy Conversion and Transmission .................................................................................................. 19
3.1
Introduction ......................................................................................................................................... 19
3.2
Transmission Design ........................................................................................................................ 19
3.2.1
Transmission Ratio Selection ............................................................................................... 19
3.2.2
Power Discussion ................................................................................................................. 21
3.2.3
Transmission Type Selection ................................................................................................ 22
3.3
Mounting Design................................................................................................................................. 22
3.4
Transmission/Mount Loading....................................................................................................... 24
3.5
Final Energy Conversion Performance ...................................................................................... 25
Safety and Motor Controls .................................................................................................................. 26
4.1
Introduction ......................................................................................................................................... 26
4.2
Capabilities and Limitation of each sensor............................................................................... 26
4.3
Threshold value selection ............................................................................................................... 27
4.4
Changes made to Arduino Code .................................................................................................... 27
4.5
Sensor Mounting................................................................................................................................. 28
Design Critique and Evaluation ............................................................................................................ 28
Appendix A: Individual Design ..................................................................................................................... 31
A.1 Dai Phuc Do................................................................................................................................................ 31
A.2 Mario Mantanovic.................................................................................................................................... 32
A.3 Marcus Papadopoulos ............................................................................................................................ 34
A.4 Paarth Shah................................................................................................................................................ 35
A.5 John Takacs................................................................................................................................................ 37
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Appendix B: Motion Generator Section ...................................................................................................... 39
B.1 Detailed Design Drawings and Manufacturing Plans ................................................................. 39
B.2 Assembly Sequence................................................................................................................................. 39
B.3 Bill of Materials for Motion Generation........................................................................................... 44
Appendix C: Energy Conversion ................................................................................................................... 45
C.1 Detailed Design Drawings and Manufacturing Plans ................................................................. 45
C.2 Assembly Sequence ................................................................................................................................. 45
C.3 Bill of Materials for Energy Conversion ........................................................................................... 45
Appendix D: Safety and Motor Controls ...................................................................................................... 46
D.1 Wiring Diagram........................................................................................................................................ 46
D.2 Controller Code With comments ....................................................................................................... 46
D.3 Calculation for encoder count ............................................................................................................ 46
D.4 Drawings and Manufacturing Plans for Safety/Motor Controls ............................................. 46
D.5 Bill of Materials for Safety/Motor Controls ................................................................................... 46
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1. Introduction and Specifications
When confined to a wheelchair, even the most mundane tasks require an extraordinary amount of effort
to complete. Take, for example, the task of carrying and accessing a backpack around school. In order to
make this simple task easier, we were given the task of creating a linkage mechanism that can swing
around a wheelchair and allow someone to easily access the contents of their backpack. The mechanism
must be designed and using mostly given materials, and include a transmission system to most
efficiently transmit power from one linkage to another. In addition, the design should be safe to handle
and look respectable. In doing this, it is important to keep the volume low, while also minimizing power
and the time it takes to reach the user. The design should be compact while also bringing the backpack
as close and accessible to the user as possible. In the table below are the design requirements for our
project.
Table 1: Mobile Backpack Carrier device design specifications
Label
Description
Target
Min
Max
Measurement Method
Volume
Volume in the starting
position
Minimize
N/A
3000in3
Inch scale, used to
measure length,
height, and width
Angle Offset
Angle of the backpack
holder in the final
position, relative to
the armrest of the
wheelchair
0 degrees
-15
degrees
15
degrees
Machinist’s protractor
Horizontal Offset Horizontal distance
from the armrest
(outside edge) to
the farthest point on
the backpack holder
Minimize
2 in
10 in
Inch scale
Forward Offset
Maximize
6 in
17 in
Inch scale
Perpendicular
distance from the
centerline
(connecting the rear
posts of the
wheelchair) to the
farthest point on the
backpack holder
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Travel Time
Total travel time of the 9 sec
mechanism from the
starting position (rear)
to the ending position
(side)
Decelerated
Speed
Speed of input link
during the last 30
degrees of travel
N/A
Power
Power used by motor Minimize
6 sec
12 sec
Encoder and
LabVIEW (average of
3 measurements)
N/A
10
degrees
per sec
Encoder and
LabVIEW
(evaluating speed in
the last 10 degrees
of travel to allow
the speed to
stabilize after decel.)
N/A
N/A
Measurements
of
voltage and current
In this report we will discuss the design process that we used to design this linkage mechanism. First we
designed the motion generator using programs such as Lincages, Solidworks and ADAMS. We picked the
best design that our team came up with and began to consider energy conversion. This report outlines
the steps we took for energy conversion and transmission from torque measurements to transmission
type selection. Lastly we worked on motor controls and safety using sensors and the encoder included in
our motor set up. In the end we were able to design a successful linkage that met or exceeded all of the
design requirements.
Overall, our project came out to be a success. We met all the criteria given forth by the specifications.
Our forward offset reached 15.625 inches, which is very close to the maximum of 17. Our horizontal
offset was also at 6.75 inches, which is well within the 10 inch maximum. Our volume, which was down
to 884.36 inches^3, is less than 30% of the admissible value. In addition, the angular offset was very close
the 0 degree target. The mechatronics portions of our specifications were also met, and very close to
targeted values. Our travel time clocked in at 9.286 seconds in comparison to the 9-second target.
The decelerated speed was kept within 10 degrees/second and was measured at 9.1 deg/second.
Finally, our power draw was kept very low at 5.94309 Watts.
2. Motion Generator Description
2.1 Design Process
The design process required the use of three programs, LINCAGES, Solidworks, and ADAMS.
Firstly we used LINCAGES to generate our desired motion. Using 3 points, we defined a path for our
precision point, a point on the coupler. By moving the ground pivots and moving pivots, the shape of the
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path traced by the precision point changed. We did this until a desired path was achieved. LINCAGES
provided us with link and coupler lengths, which we then took into Solidworks.
Using Solidworks, we constructed our linkage mechanisms. The dimensions of our components were
defined by LINCAGES. Having a three dimensional representation of the mechanism assisted in
verification of the device. We were able to see if the linkage was capable of the range of motion, i.e.
no interferences, required and modify our designs accordingly. Once we were satisfied with our
design, we took the linkage into ADAMS for dynamical analysis.
With ADAMS, we simulated the forces and torques acting on our linkage. One point we were
concerned with was maximum forces and torques on the joints as these would affect bushings and
bearings. Another point of concern we had was the amount of deflection in each link. Deflection in the
link would create undesirable out of plane loads on the joint and so we wanted to minimize this.
2.2 Design Selection
Each team member designed a linkage mechanism. To choose our final design, we compared key
characteristics of each design. We strove to meet specifications defined by the project overview
document.
Firstly, we sought to minimize the volume of the mechanism in its collapsed position. The volume was
defined as the smallest rectangular box (length, width, and height), parallel to the connection points,
that encased the device including all elements such as the linkage, hard stops, sensors, mounts, motors,
etc. An upper volume limit of 3000 in3 was emplaced as the mechanism would be too large for effective
operation. Once we knew that the mechanism would fit into our specifications, we wanted to ensure the
accessibility of the backpack.
Ease of use was an essential concept in designing the mechanism. We wanted the backpack to be simply
reachable to the user. We quantified this by comparing the angle, horizontal, and forward offset, of each
device in its final position. The angle offset was defined as the angle of the backpack holder in the final
position, relative to the armrest of the wheelchair. We sought a horizontal offset of 0 degrees as this
would mean the backpack was parallel to the armrest, the most comfortable position for the user to
access the backpack. The lower limit for the angle offset was -15° and the upper limit was 15°. The
horizontal offset was defined as the horizontal distance from the armrest (outside edge) to the farthest
point on the backpack holder. Minimizing the horizontal offset was our aim, with an allowed minimum
offset of 2 inches and a maximum offset of 10 inches. The forward offset was defined as the
perpendicular distance from the centerline (connecting the rear posts of the wheelchair) to the farthest
point on the backpack holder. We aimed to maximize the forward offset to allow the user to reach more
comfortably forwards rather than backwards to use the backpack. We allowed a minimum forward offset
of 6 inches and a maximum of 17 inches. The accessibility of the linkage was important but we had to
also consider the forces and torques required to operate the mechanism.
Attention to the dynamics involved with each mechanism was crucial in our design selection. If the
torques and forces were unmanageable, the device would be unable to function. We sought to minimize
the torques and forces in each design.
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We have compiled the measurements and assigned scores to each design. We scaled the torque and
force points at half because we are unsure of the motors capabilities. Mario’s design accumulated the
most points meaning it excelled in our benchmark characteristics and so we chose it as our final
design. Table 2: Design Selection Pugh Chart
Criteria
Weight
Score
John
Score
Mario
Score
Paarth
Score
Marcus
Score
Phuc
Volume
(in^3)
2
382.44
0
293.33
3
212.64
3
327.87
1
286.86
2
Angle
Offset
2
0
0
0
3
17
1
0
3
0
3
Horizontal
Offset (in)
2
1.82
0
3.75
3
2.73
3
5
2
7.57
1
Forward
Offset (in)
2
7.21
0
13
3
8.18
1
15.3
3
11.01
2
Torque
(lbf)
1
13.87
0
16.72
1
8.4
3
16.72
1
10.92
3
Force (lb)
1
19.01
0
15.2
2
34.8
1
15.2
2
15.89
2
Total
Score
0
27
20
21
21
2.3 Lincages
As mentioned, the first step of the design process involved designing a workable linkage with lengths of
each link. Included in this is the length of the coupler joints, however, we are free to choose a coupler
shape as necessary. Another important usage of Lincages is the inclusion of the transmission angle graph.
A low transmission angle puts unnecessary stress on the motor which may often not have enough power
to overcome frictional forces acting between the linkages. By keeping our angle above the ‘magic
number,’ of 30 (as supplied to us by the GSI), we are able to stay in the safe zone and verify that our
linkage should have no issues going through the entire loop.
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Figure 1: Lincage of our final design model
2.4 CAD with Descriptive Pictures
In the final design the angle offset is 0 degrees, the forward offset is 13.32 inches, the horizontal offset is
4.47 inches and the box volume is 553.5 cubic inches.
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Figure 2: Top view of the linkage in collapsed position
Figure 3: Zoomed-in Isometric view of the linkage in collapsed position
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Figure 4: Isometric view of the linkage in collapsed position
Figure 5: Top View of the linkage during motion to ensure the backpack does not hit the tire
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Figure 6: Top View of the linkage during motion to ensure the backpack does not hit the tire
Figure 7: Top view of the linkage in extended position
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Figure 8: Isometric View of the Linkage in extended position
Figure 9: Front View of the Linkage in Extended Position
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Figure 10: Zoomed view of Input joint in Extended Position
Figure 11: Cross Section View of Input Joint in Extended Position
2.5 ADAMS and Loading Analysis
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Figure 12: Main Isometric View Showcasing Joint Types
Figure 13: Top Isometric View Showcasing the 5° adapter tilt as well as the 12 lbf point force Table
3: Final ADAMS forces analyzed without friction
Joint
Minimum Force in y Maximum Force
(lbf) (mag.)
in y (lbf) (mag.)
Minimum Torque
(lbf ft) (mag.)
Maximum Torque
(lbf ft) (mag.)
Input –Ground
0
31.7
0
27.08
Input –Coupler
Output –Ground
Output –Coupler
0.8
0
0.1
31.3
17.5
17.7
0
0
0
12.08
14.58
17.17
From max forces and torques, we can see that they are indeed manageable. Although we do not yet
have the correct information for frictional forces, they will be minimized by the use of bronze thrust
washers as well as bearings and bushings (explored later in this report). Using these forces, we can
analyze the links to check for deflection in the links. In addition, when using the stock bushings, we
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confirmed no force exceeds the ratings of the bushings (up to 2000 psi). This is key as the bushings will
not be put under abnormally high stress and will last the entire rated lifetime. In addition, the bolts can
take up to 84,000 psi, leaving room for error, even when adding the friction.
Table 4: ADAMS forces on individual joints in only the y direction (gravity = negative y)
Joint
Maximum Force
(lbf) in y-direction
Input –Ground
31.9
Input –Coupler
Output –Ground
32.5
-17.25
Output –Coupler
17.7
Using these forces and free body diagrams, we can construct beam bending diagrams from normal free
body diagrams. For the input link, we have a force of 32.5 lbf downwards. If we assume the input is fixed
at the ground, we can compute the total dislocation of the input link.
Using this 32.5 lbf, we can use the formula for a beam bending with a point load:
Where P is the point load, l is the length from the fixed wall (in the input case, 10.25”), E is the Young’s
Modulus and I is the second moment of area. For a hollow tube, the second moment of area is given by:
E is also given by 1.015*10^7 psi. Plugging into the beam bending formula, we get a maximum deflection
of 0.0202”. This creates a moment of 333.1 lbf-inches in the ground plate joint.
For the output link, we use the same formulas (as the lengths are equivalent). However, this time, the
force is 17.7 lbf. Plugging into our formula, we see a deflection of 0.011”. This creates a moment of
181.4 lbf-inches in the ground plate joint.
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Unlike the input and ground joints, the coupler is not fixed. Deflection can be calculated by using a
combination of deflections from the input and output link. This gives us a value of 0.1524” deflection.
The overall deflection from input to backpack holder can also be calculated. Once again, using the beam
deflection formula
Using the point force of 12 lbf, and a length of 18.55” (full reach of backpack holder), our deflection
comes to 0.0441” of deflection.
This deflection can be quite high at times, almost nearing an entire inch. In order to alleviate these loads
and deflections, multiple steps have been taken. First, the input link is in between a clevis holder (or
sandwiched between two ground supports). By adding another ground support on top, the beam is fixed
in two places rather than just coming into contact with the ground in one place.
Figure 14: Ground Input Link
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In addition, the geometry of the links has been chosen as one that is favorable to deflection. Rather than
choosing a flat aluminum plate to make the links out of, the square tube gives a favorable geometry
proven by the second moment of area giving a higher number.
Minimizing friction and contact at the joints is good design option as it puts less stress on the bolts and
bearings. The addition of thrust washers addresses this issue and is available at every high stress point
of interest on the mechanism (most notably, the moving joints).
Figure 15: Input to Coupler
Figure 16: Coupler to Output
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Figure 17: Output to Ground
In addition to the joints having washers to minimize friction, the stacking or layering of linkages above
and below the base plate offers advantages in terms of compressive and tensile forces. By having these
counteract each other, we can alleviate some of the load off the joints.
2.6 Changes from Gate 1 to Final Design
After assembling our product post Gate 1, a few issues arose regarding our design. First, our torque
values were very high. Due to precision issues and just undervalued torque values, we hit very high
torques when testing our mechanism at the given 3 degree angle. We changed the angle at which our
base plate sits to alleviate the high torque. The base plate angle was changed by using screws through
the bottom of the wheelchair adapter. This allows the angle to be adjusted by screwing in the bolts
further if necessary.
In addition to this, some minor changes were made to the overall design. The dowel pin used previously
was removed in favor of an angle iron. Although the dowel pin was simple, it did not provide the
flexibility of an adjustable iron angle. In addition, spacers used to clamp the input link were made
shorter in order to accept larger sprockets (this is expanded upon later). Further additions were made to
the coupler in the form of the placement of the backpack holder location. The backpack adapter was
moved forward in order to provide enough clearance for the backpack and the sprockets. Finally, the
overall length of the baseplate changed slightly in order to save unneeded volume.
2.7 Final Design Testing Results
Listed here are the final designs testing results. These are the values for offset and volume of our final
linkage design. When compared to the requirements (Table 1. p4), we can see that we meet all the
requirements and excelled in angle offset, forward offset and volume. The reason these are different
between from what is discussed earlier (Section 2.4) is because of the addition of motor mounts and
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energy transformation. The horizontal offset was also altered by the coupler spacers we had to include
to make sure the backpack did not touch the chain and sprocket. The angle offset is adjustable via the
hard stops and we selected this location to optimize other values.
Table 5: Final Offset and Volume Values of the Final Design
Criteria
Value
Horizontal Offset
Forward Offset
Angle Offset
6.75 inches
15.625 inches
2 degrees
Volume
884.36 cubic inches
3. Energy Conversion and Transmission
3.1 Introduction
In order to transmit motion from the motor to the input link, a transmission system must be
implemented. A transmission allows the user to directly change the speed, direction, or amount of force
that the motor can output. Due to the constraints of the motor, such as the torque output, a
transmission is necessary to achieve the required torque to rotate our mechanism around. By measuring
the forces on the input link in lab, we were able to determine the maximum torque required by the
input link. In addition, our mechanism is required to slow down to below 10 degrees/second during the
final 30 degrees of travel. While in motion, the mechanism should also draw as little power as possible.
From these specifications, we were able to choose a suitable transmission system to implement in our
design.
3.2 Transmission Design
In this section we will discuss the process taken to design the transmission. This will include ratio
selection, power discussion and transmission type.
3.2.1 Transmission Ratio Selection
As mentioned before, the force measured in the lab led us to our torque calculations. Using the force
gauge, we determined our maximum force to be 52.9 ounces. Using the formula:
where distance, d, is the length between the holes of the input link (10.2 inches), we determined our
maximum torque to be 539.58 ounce-inches.
In order to properly use the torque-speed curve, the required speed is also necessary. This can be found
using the given specifications of the required time to be a total of 9 seconds. In addition, the final 30
degrees of travel must be at a speed of 10 degrees or slower. Using ADAMS to measure our total angular
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travel of the input link, we calculated a total of 213 degrees. From the formula of distance over time, we
can separate this into two components and find the maximum travel speed.
Solving for
gives us 30.5 degrees/sec or 5.083 rpm. From here, we can use the given values of the
motor such as the stall torque and no load speed to find an acceptable gear ratio. Scaling down the
Torque-Speed Curve from 12V to 9V gives us the following graph:
Torque-Speed Curves
300
250
200
150
12V
100
9V
50
0
0
10
20
30
40
50
60
70
80
90
Speed (rpm)
Figure 18: Torque-Speed Curve of the Motor at 12V and 9V
This graph can be calculated from Tnew = T0 * N and ωnew = ω0/N where N is the ratio 9/12. From here,
we can read off the graph (or do calculations) which give us a no load speed of 60RPM and a stall torque
of 187.5 oz-inch. By changing the gear ratio, we are then able to encapsulate the requirements of our
mechanism (5.083 RPM and 539.58 oz-inch) via changing the slope of the curve (and thus, the
transmission). A 1:6 gear ratio gives the following curve:
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Torque-Speed Curve with 1:6 transmission ratio
1200
1000
800
600
Torque Speed Curve with 1:6
transmission
400
Required Torque & Speed
200
0
0
2
4
6
8
10
12
Speed (rpm)
Figure 19: Torque-Speed Curve with 1:6 Transmission ratio and our target point
Although this value is just barely inside our torque speed curve (and thus, not giving us much of a safety
factor), we can remedy this by reducing our total travel distance or reducing our total torque necessary
at that point.
3.2.2 Power Discussion
In order to find power, we can use our motor constants to find the current required by the motor to
operate at the given torque:
Using the motor specifications given on the Pololu website, we are able to calculate the motor constant
Kt. Using the scaled no load torque of 187.5 oz-in. and no load current of 3.75 amps, we can calculate Kt
= 50. Given a T of 539.58 oz-inch (3.8103 Newton-meters), a Vb of 9V and an omega of 0.53229
radians/sec, we can calculate the current required: im = 539.58 / 6 / 50 = 1.7986 A. From here, we can
calculate the actual input power:
From the values above (Torque and speed), we can also calculate our maximum power output:
In order to minimize power, I * V must be reduced. Since the voltage is set, our only option is to reduce
current, I. From the motor constant equations, this can be minimized via minimizing our torque in a
multitude of options. Our main source of torque can come from lowering friction.
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3.2.3 Transmission Type Selection
Our design implements a chain and sprocket system. Several key factors played into this decision
including the availability of gear ratios, flexibility, manufacturing tolerances, and cost. As calculated
before, our design implements a 1:6 gear ratio. The available sprockets offered an acceptable reduction
ratio in our range, which the gears did not. Manufacturing tolerances also played into this decision:
gears require high manufacturing precision to keep gears meshed perfectly, whereas the chain and
sprockets do not. The chain and sprockets were chosen over the belt and pulleys due to the larger
torques that can be transmitted from one sprocket to the other. In addition, slippage of the mechanism
will not hinder our mechanism as it may with the belt and pulleys. Finally, the cost of purchasing the
chain and sprockets was significantly lower than the gears.
Despite all its pros, the sprockets do have a few setbacks. First of all, the mechanism can be very loud.
Due to the sprockets and chains both being made out of metal, any sort of interference will cause lots of
noise. The next problem is the speed transmitted from the chain drives, which are on average lower
than those of gears and belt and pulleys. This is an issue that can be addressed by changing the overall
travel of the input length.
The required gear ratio chosen is exactly 6, which was configured through a chain and sprocket system
of 48 gears to 8 gears. These parts were found using the SDP-SI online chain and sprocket catalogue. The
chosen chain is a #25 chain.
3.3 Mounting Design
In order for the transmission to actually transfer motion, specific mounts and joints must be fabricated.
The first torque transmission comes from the motor to the input sprocket. Due to the motor having a D
shaped shaft right out of the box, this interfaces well with a set screw. In addition, the input sprocket
contains a built-in hub allowing easy use of a set screw.
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Figure 20: View of driving sprocket attached to the motor
Figure 21: Cross Section view of the set screw attaching the driving sprocket to the motor
The second torque transfer comes from the output sprocket connected to the input link of the
mechanism. In order to provide a solid support, a ¼” off-axis dowel pin is attached to sprocket as well as
to the input link. In addition, the output sprocket freely rotates about the shoulder joint through the use
of a bushing and needle bearings. This allows the friction to be as close to negligible as possible. The
dowel pin is press fit into the sprocket in order for one mechanism to have a steady fit.
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Figure 22: View of driven sprocket attached to the input link
Figure 23: Cross section view of the driven sprocket attached to the motor via a key whole
These additions do very little to change our initial values measured in gate 1. At most, it will add a very
small amount of friction due to the interfaces between linkages. The motor mount adds height which
will increase our overall volume (height increase about 1.5 inches). This motor mount did not change
any of our offset or travel values from motion generation.
3.4 Transmission/Mount Loading
Transmission of power from the motor to the linkage was achieved through locking the sprockets to
both the motor shaft and then the output link. To lock the sprocket to the motor shaft, we utilized a set
screw through the hub of the sprocket that comes into contact with the motor shaft. Because the
prevalent mode of failure would be shearing, we looked to determine the stress across the set screw
face. The force, F, required to hold the sprocket to the motor shaft is given by
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where T is the torque output by the motor, and R is the distance between the center of the motor shaft
and the point of contact between the set screw and motor shaft. The shearing stress then is given by
where r is the radius of the set screw. Using a motor torque T of 5.615 pound inch, R of 0.39 inches, and
a set screw radius of 0.05 inches we determine the stress to be 1833 pounds per square inch.
To connect the motion of the output sprocket to our input link we utilized a dowel pin. A tight fit
clearance hole is drilled through the input link and through the face of the sprocket. We aligned the
clearance holes and then linked the two components together by sliding a dowel pin into each hole.
Because the dowel pin was offset from the center of the sprocket, the shear stress of the dowel was
given by
where T is the torque of the input link sprocket, r is the distance between the dowel and the center of
the sprocket, and J is second moment of inertia. Using a torque of 33.69 pound inches, a radius of 1.15
inches, and a second moment of inertia of 677.41 inches cubed we determined the shear stress to be
0.057 psi.
15.29 lb f
Figure 24: Loading on Motor Mount
Force translates to the motor mount assembly (68N) was determined by using the max torque needed to
move the assembly for preliminary testing. We determined deflection by using the deflection and
moment of inertia equations above and assuming the motor mount was beam being deflected. We
determine the deflection to be .0021 inches.
3.5 Final Energy Conversion Performance
Our final measurements were, as expected, not exactly as calculated in the report. Rather than the
calculated power draw of 16 watts, we were able to minimize this down to 5.94309 watts. This is due to
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us managing to alleviate the 3-5 degree angle offset of the wheelchair adapter. By doing so, we were
able to reduce friction between the components which allowed a smoother path of motion.
Our travel time also did not meet the exact 9.0 specifications. Due to factors such as inconsistent friction
amounts, the reaction of the encoder to the Arduino code (in regards to slowing down at the 30 degree
mark), and our path of travel not exactly what we measured in ADAMS/Solidworks, we were not able to
reach exactly 9 seconds. The deceleration speed was also not exactly 10 degrees/second. Due to the
previously mentioned factors (friction, etc.), this value needed to be adjusted in our code in order to
more accurately meet the 9 second mark.
4. Safety and Motor Controls
4.1 Introduction
Although the linkage may work by turning on the motor and running it, our project was not ‘smart’ in
any way. It would not stop unless the power was cut, and it would not detect anything in the way of its
path. In order to achieve these goals and keep our mechanism safe for real world use, a multitude of
sensors and accompanying computer code were used. In addition, in order for these to interact with the
encoder attached to the motor, an Arduino microcontroller, along with accompanying code, was used
which allowed the mechanism to stop and react to real world interferences. The sensors chosen, the
rocker switch, limit switch, and IR sensors, all served different purposes in our design, but each had a
common use; to keep the design safe.
4.2 Capabilities and Limitation of each sensor
For this design project we were given three different types of sensors to control the motor and ensure
the safe use of the linkage.
The first type of sensor was a single pole, double throw rocker switch (35-695: Jameco). This switch can
be pressed into two directions (forward and backward) but returns to rest neutral position when it is not
being pressed. This switch would be used by the user to control the entire mechanism. If the forward
switch is being held the linkage moves into the extended position. If the backward position is being
pressed the linkage returns to the collapsed position. The linkage will only be moved while one of the
positions is being pressed on the rocker switch. This switch acts a user control of the linkage but it does
have some limitations. The user has to hold the switch the entire time of travel instead of just tapping
the button and allowing the linkage to swing around.
The second type of sensor was a limit switch (187733: Jameco). This switch is only activated when
something is hitting it. As soon and the object is removed the switch is turned off. We used these
switches to determine the extended and collapsed positions. One switch would be pressed in each
position. This would ensure that the motor could not keep running past the desired location. This is good
to prevent damage to a motor trying to drive past a hard stop. This switch worked very well for our
project but also had some limitations. Due to its size this switch was very hard to mount and it also only
was on when something was hitting it. This means that the motor only turned off right when it hit the
P a g e | 27
hard stops. This sometimes allowed the motor to run for too long and the linkage was strongly driven
into the hard stops.
The third type of sensor was an infrared proximity sensor (GP2D120XJ00F: Sparkfun). This was used for
the safe use of the mechanism. These were put in positions where it would we unsafe to have an object
while the mechanism was moving. The proximity sensors can detect objects and how far away they are.
We put one sensor and the front of the mechanism to ensure that the linkage does not hit anything
while extending. Using varying threshold the motor will stop if something gets within a few inches of the
front of the linkage. The other point we used was in between the input and output link. We considered
this a pinch point and did not want object to get stuck in there. These sensors were great to ensure a
clear path for the linkage as it moved through its path but they were not flawless. The proximity sensors
are not very accurate at a far range so the linkage is only stopped when something gets very close to it
(i.e. within a couple of inches). The proximity sensors also send out the infrared signal in a cone
formation so it is hard to pin point one location to test. At further ranges the proximity sensor will pick
up more than just the pinch or danger point.
4.3 Threshold value selection
In order for the sensors to work with our specific design, the encoder and each sensor had to be
calibrated in a different manner. Due to the simplistic nature of the limit switch, these did not need any
sort of calibration, as they were either turned on or off depending on the physical position of the switch.
In addition, the rocker switch did not require any calibration as it served to move the mechanism
forwards and backwards. However, the IR sensors and encoder used changing values that were specific
to our mechanism. The IR sensors used a “threshold” value in order to determine whether or not to
send a signal to the motor to stop running. The values output by the sensor were determined based on
how far away an object was to the sensor, and thus, were chosen based on a guess and check method.
Depending on the placement of the sensor relative to the mechanism, these were given differing values.
The encoder values on the other hand, were calculated using a specific formula which was dependent on
our transmission ratios of both the motor and our chosen transmission. In addition, the formula also
takes into account the total travel distance in degrees to calculate the point at which the mechanism
must slow down. Calculations and final values can be seen in Appendix D.
4.4 Changes made to Arduino Code
Rather than use the given stock Arduino ME 350 code, the optional code was chosen for our project.
Although the original code works, the speed at which the code responded to the sensors did not work
well with our mechanism. Thus, the optional code allowed more flexibility. In addition, the values given
to the motor were given in rpm and did not have to be converted to some sort of percentage of the
current. In order to meet the 9 second requirement, the code had to be further altered; specifically the
lowerLimitThreshold, upperLimitTreshold, as well as the integration constant. As mentioned before, the
upper/lowerLimitThreshold were determined via a formula, however, the integration constants were
determined through extensive guess and check testing. In addition to the change in the ‘main’ code,
P a g e | 28
smaller changes such as which pin referred to which sensor were changed to match our wiring diagram.
Refer to Appendix D for full code with comments.
4.5 Sensor Mounting
We wanted to mount our sensors in the logical spots, the hard stops, but our hard stops did not offer
adequate surface area for mounting via double sided tape. Instead we mounted our limit switches to the
input plate and to the motor mount holder. The input plate worked well because it had enough area to
mount the switch and because the travel of the output link ends at a location that can easily actuate the
switch. We mounted the other limit switch on the motor mount holder because it is located above the
hard stop, had enough area to mount, and the path of travel of the input link was in-line with the motor
mount holder.
We mounted our proximity sensors with double sided tape in the first two places where we saw it was
obviously needed: at the end of the backpack holder and in the middle of the input link facing outwards.
These were obvious locations because the backpack holder travels the furthest away from the original
position and the middle of the input link is always facing the pinch point in the middle of the four-bar
linkage. None of the switches or sensors affected the volume of the mechanism.
Figure 25: Linkage mechanism with limit switches in red and proximity switches in yellow
5. Design Critique and Evaluation
Looking back on our design process, we can see that there were things that we did correctly and things
that we could’ve done differently.
P a g e | 29
Our final design had several issues arise that we did not foresee during the initial design process. One
issue we encountered was finding a space to mount our motor. During the initial design process we
knew that space had to be reserved for the drive system but did not know exact specifications of the
motor at the time. This presented a problem when we had to implement our drive train as we had
removed too much material from our baseplate to make our design more compact. Fortunately we were
able to come up with a solution that worked in our limited space. This issue could’ve been avoided by
being more thoughtful of potential changes that would be need made in subsequent phases of design.
Despite these issues a number of things worked very well for us. For example, we obtained strong
performance against the angle offset, forward offset, and horizontal offset benchmarks.
Despite the fact that the final linkage design was born from several theoretical models, the performance
of the mechanism varied from those representations. In several aspects it performed better than we had
thought based on models and in other aspects it underperformed relative to the model. One factor that
may have created this discrepancy was exclusion of friction from our ADAMs model. This required our
motor to work harder than expected to produce the torque required to overcome the friction at the
joints. Because of this, the actual power required of the motor was greater than we had originally in our
models. In addition to frictional effects, loading caused further issues as well.
The real test of our mechanism was whether the performance would be greatly affected by the inclusion
of the backpack load. Operation of the linkage was markedly different when loaded with the backpack
compared to no loading. Inclusion of the load increased out of plane stresses at joints causing the motor
to have to work harder to overcome these additional stresses. Because of limits placed on supply
voltage, the motor saturates and is unable to provide the power for operation similar to the unloaded
case and so the device moves much slower.
The control algorithm could be improved to make better use of the available equipment. One way the
speed could be more precisely controlled is by creating several process intervals using the
EncoderCount. We could assign each interval its own speed so that while the linkage is operating within
a certain interval it would have a unique velocity. This will allow more precise control of the linkage.
During the development of our design, there were many variables to be considered. Allowing flexibility
and room for alterations was paramount throughout the design process. Constant changes took place,
parts were remanufactured, and problems were reengineered along the way. Allowing for these
modifications was essential in producing the best possible resulting product from the initial design
phase. Looking back at the overall process which took place in implementing our final product, there is
no need to alter any aspect of the procedure we used to reach our goal. Trial and error is one of the best
methods for this type of product development because it allows for constant improvements to be made.
In regards to the sensors applied to our mechanism, the provided sensors were adequate for the
purpose they served as safety features. Proper location and sensitivity settings were taken into
consideration when determining the best application of the proximity sensors. The limit switches also
served their purpose well when properly located to achieve desired stoppage at beginning and end
positions. Any possible interference with path of travel was addressed when placing proximity sensors
and setting threshold values. With these sensors, the safety design of our mechanism would be rated a 5
out of 5. The only additional safety option that could have been added was an enclosure housing the
P a g e | 30
transmission system. This would protect the transmission components from any possible debris or
foreign object impedance.
With our present design being a prototype, we would advise against allowing our current product to be
used for everyday application. During testing, we were able to meet or exceed all benchmarks
confirming that we designed a properly manufactured device that could achieve the specifications
provided. However, we never performed any test to verify longevity of use and possibility of misuse or
potential failure rate. Since a design in theory may not allow be produce identical results in application,
we would advised for additional long-term performance testing before allowing actual application by a
consumer.
When considering the materials and supplies used in manufacturing our design, a few alternative
components could have contributed to a more ideal final product. Allowing the use of steel over
aluminum would have provided the ability to design thinner linkages and cause for a sleeker, more
compact design. During the initial phases of the design process, having a better program to determine
our linkage placement and transmission angle could have led to a more precise travel path. The provided
Lincages program seemed limited in its ability to provide accurate or consistent results and did not allow
for minor adjustments to be made. Other than these minor factors, we were able to meet all design
specifications with the materials supplied.
In conclusion, this project was challenging and valuable experience. Many factors influenced the design
process, some we accounted for and others that surprised us. The important thing was that we were
able to confront issues quickly and effectively. Throughout the design process we were given more
details such as motor specifications that changed our initial design. This could be similar to a real life
engineering project in which the clients’ needs change. We learned that to be successful it’s important
to expect bumps in the road and to prepare for them accordingly by being flexible.
P a g e | 31
Appendix A: Individual Design
A.1 Dai Phuc Do
Figure A 1: Phuc Do Lincages
Table A 1: Phuc Do Loading Analysis
Joint
Minimum Force in
y (lbf)
Maximum Force
in y (lbf)
Minimum Torque
(lbf ft)
Maximum Torque
(lbf ft)
Input –Ground
0
5.3
0
0
Input –Coupler
Output –Ground
Output –Coupler
0
15.4
14.9
5.31
16.3
15.89
0
3.6
10.5
0
20.95
10.92
The forces on this design are quite small on the input link while the output link bears much of the load.
This is due to the very acute transmission angle that the linkage endures during its motion. This causes
unnecessary extra stress on the motor. Despite these flaws the linkage does quite well in terms of
accessibility.
P a g e | 32
Figure A 2: Phuc Do CAD
A.2 Mario Mantanovic
Figure A 3: Mario Mantanovic Lincages
My initial design was very similar to the final design. The things changed for the final version were the
shape of the base plate to accommodate mounting to the wheelchair and the shape of the coupler to
allow proper mounting of the backpack as well as adding spacers, a brace for the input to baseplate
connection, and hardware. All basic design as well as the geometry of motion stayed the same. Pictures
and a table of pin forces can be seen below.
Table A 2: Mario Mantanovic Loading Analysis
Joint
Minimum Force in y Maximum Force
(lbf) (mag.)
in y (lbf) (mag.)
Minimum Torque
(lbf ft) (mag.)
Maximum Torque
(lbf ft) (mag.)
Input –Ground
0
31.7
0
27.08
Input –Coupler
Output –Ground
0.8
0
31.3
17.5
0
0
12.08
14.58
P a g e | 33
Output –Coupler
0.1
17.7
0
Figure A 4: Mario Mantanovic CAD
17.17
P a g e | 34
A.3 Marcus Papadopoulos
Figure A 5: Marcus Papadopoulos Lincages
In my design the loads a fairly manageable but the torque values are rather high. It is natural for a 4 bar
to have high torque and it extends. It is important to use very strong and stiff materials in the design to
manage these loads and torques. This would prevent any sort of deflection in the parts of links.
Deflections can drastically increase friction in joints because the bearing will no longer be in line. A
design that does not manage the loads will also fail due to fatigue earlier. Although this design does well
in the offset and transmission angle parameters, the fact that the loads and torques are so high makes
this design undesirable. The high loads would be too difficult and expensive to manage. Table A 3:
Marcus Papadopoulos Loading Analysis
Joint
Minimum Force in
y (lbf)
Maximum Force
in y (lbf)
Minimum Torque
(lbf ft)
Maximum Torque
(lbf ft)
Input –Ground
Input –Coupler
13.9
13.3
15.2
14.7
13.83
3.49
16.72
3.6
2.6
2.5
6.5
6.5
8.01
8.53
9.3
8.95
Output –Ground
Output –Coupler
P a g e | 35
Figure A 6: Marcus Papadopoulos CAD
A.4 Paarth Shah
Figure A 7: Paarth Shah Lincages
P a g e | 36
Figure A 8: Paarth Shah CAD
Table A 4: Paarth Shah Loading Analysis
Joint
Minimum Force in
y (lbf)
Maximum Force
in y (lbf)
Minimum Torque
(lbf ft)
Maximum Torque
(lbf ft)
Input –Ground
Input –Coupler
Output –Ground
2.3
1.2
1.1
34.8
33.8
22.2
.2167
.2834
.3958
2.583
8.4
.9227
Output –Coupler
0.8
22.1
0
7.3
The forces on this linkage are about average; however, this design excels at carrying the torque load.
Due to the geometry of the part, the coupler at times creates a sandwich between the input and output
link which at times may offset some of the moment on the joints. In addition, the lengths of the links are
small, allowing the torque to reach smaller values. Although this design manages loads fairly well, the
main issues arise with the geometry of the part. The forward offset is not very high, forcing the user to
reach backwards to access their backpack. In addition, the angle offset from the wheelchair arm is very
high, once again, forcing the user into an awkward position to reach the backpack. In addition to this,
the transmission angle dips to a very low number (~10°) as seen by the transmission angle graph.
P a g e | 37
A.5 John Takacs
Figure A 9: John Takacs Lincages
Table A 5: John Takacs Loading Analysis
Joint
Minimum Force in
y (lbf)
Maximum Force
in y (lbf)
Minimum Torque
(lbf ft)
Maximum Torque
(lbf ft)
Input –Ground
Input –Coupler
Output –Ground
1.48
1.48
13.44
7.01
7.01
19.01
1.34
0.01
8.94
6.88
5.18
11.43
Output –Coupler
13.44
19.01
4.42
10.65
The linkage I designed seemed to manage both the force and torque loads fairly well. However, the
coupler and output link travel over the same path sandwiching the backpack straps before reaching a
fully closed position. Based on the values for maximum force and torque loads, deflection could become
an issue if proper materials are not considered with adequate strengths and stiffness to manage these
loads. Taking these factors into consideration with also prevent early failure due to fatigue. The
transmission angle of this design is more than adequate, as seen above by the graph, with a minimum
value greater than 30o. Overall, this particular design produces acceptable parameters capable of
managing the tasks desired. Due to the path of travel, adjustments would be needed for clearance issues
and to prevent pinching of foreign objects within this path.
P a g e | 38
Figure A 10: John Takacs
P a g e | 39
Appendix B: Motion Generator Section
B.1 Detailed Design Drawings and Manufacturing Plans
See attached.
B.2 Assembly Sequence
Step 1: Press 0.5” height bushing (McMaster-Carr part number: 6391K173) into all 0.5” diameter holes of
the following parts: base plate, coupler, input plate, and all spacers
Step 2: Press 1” height bushing (McMaster-Carr part number: 6391K178) into all .05” diameter holes of
input link and output link
Step 3: Mount base plate onto wheel chair. Fasten baseplate with 1 bolts (McMaster-Carr part number:
91259A633), 1 nut (McMaster-Carr part number: 97149A200), and 2 washers (McMaster-Carr part
number: 5906K511) as pictured below.
Step 4: Place motor mount holder on baseplate. Secure with 1 bolts (McMaster-Carr part number:
91259A633), 1 nut (McMaster-Carr part number: 97149A200), and 2 washers (McMaster-Carr part
number: 5906K511) via through hole. Secure with additional bolt (part number: 90201A111) and
washer (McMaster-Carr part number: 5906K511) via threaded blind hole as pictured below.
P a g e | 40
Step 5: Mount hard stop to baseplate using 1 bolt (McMaster-Carr part number: 90201A109) and 1
washer (McMaster-Carr part number: 5906K511). Second hard stop is bolt (McMaster-Carr part number:
90201A113) bolted into threaded blind hole in baseplate. Both are pictured below.
Step 6: Mount motor mount to motor mount holder using 2 bolts (McMaster-Carr part number:
90201A111), and 2 washers (McMaster-Carr part number: 5906K511), bolted into the motor mount via
threaded holes, through the motor mount holder, as pictured below
Step 7: Attach motor (Pololu part number: 1447) using 6 screws (McMaster-Carr part number:
92005A006 ). Attach Driving Sproket (SDP/SI part number: A 6C 7-25B48) using sprocket setscrew.
Step 8: Sandwich 6 washers (McMaster-Carr part number: 5906K511) and 3 input plate spacers as
pictured below.
P a g e | 41
Step 9: Mount input plate on top of input plate spacers. Bolt together using 2 bolts (McMaster-Carr part
number: 91251A554), 2 nuts (McMaster-Carr part number: 97149A100), 4 washers (McMaster-Carr part
number: 91083A029) as pictured below
Step 10: Attach input link to assembly as pictured below with Driven Sprocket (SDP/SI part number: A 6C
7-25B48), 1 input dowel (McMaster-Carr part number: 98380A546), 1 bolt (McMaster-Carr part number:
91259A635), 1 nut (McMaster-Carr part number: 97149A200), and 6 thrust washers (McMaster-Carr
part number: 5906K511), as pictured in the cross section picture below
Step 11: Attach output link to assembly as pictured below using spacer, 1 bolt (McMaster-Carr part
number: 91259A633), 1 nut (McMaster-Carr part number: 97149A200), and 4 washers (McMaster-Carr
part number: 5906K511) as pictured in the cross section picture below
P a g e | 42
Step 12: Attach coupler to input and output links as pictured below using spacer, 2 bolts (McMaster-Carr
part number: 91259A633), 2 nuts (McMaster-Carr part number: 97149A200), and 8 washers
(McMasterCarr part number: 5906K511) as pictured in the cross section pictures below.
Input Link Cross Section
Output Link Cross Section
Step 13: Step 13: Attach 2 backpack holder tabs to coupler using 2 bolts (McMaster-Carr part number:
91251A546), 2 nuts (McMaster-Carr part number: 97149A100), and 4 washers (McMaster-Carr part
number: 91083A029) as pictured below
P a g e | 43
Step 14: Attach backpack holder to backpack holder tabs using 2 bolts (McMaster-Carr part number:
91251A546), 2 nuts (McMaster-Carr part number: 97149A100), and 4 washers (McMaster-Carr part
number: 91083A029) as pictured below
Step 15: Connect Driven (SDP/SI part number: A 6C 7MHK2508) and Driving (SDP/SI part number: A 6C 725B48 ) Sprocket with roller chain (SDP/SI part number: A 6Q 7-25) and Chain Connecting Link (SDP/SI
part number: A 6Q 7-25SCCL).
Step 16: Attach Snap Action Switches (Jameco part number: 187733) to mechanism in the location
marked by red circles in the picture below. Attach Infrared Proximity Sensors (Jameco part number:
35695) to mechanism in the location marked by orange boxed circled with orange circles in the picture
below.
P a g e | 44
B.3 Bill of Materials for Motion Generation
Material
In Kit or
Shop? Quantity
Purchase Price
(each)
Part #
Supplier
Square Aluminum Tubing
(1” x 1” x 6’ long, 1/8” wall)
88875K33
McMaster-Carr
Yes
1
N/A
Aluminum Plate
(1/2” x 12” x 12”)
9246K33
McMaster-Carr
Yes
1
N/A
Sleeve Bearing
(3/8” dia. shaft, 1” long)
6391K178
McMaster-Carr
Yes
4
N/A
Sleeve Bearing
(3/8” dia. shaft, 1/2” long)
6391K173
McMaster-Carr
Yes
6
N/A
Shoulder Screw
(3/8” shoulder dia., 2 ¼” long,
5/16”-18 thread)
91259A633
McMaster-Carr
Yes
3
N/A
Shoulder Screw
(3/8” shoulder dia., 2 ¾” long,
5/16”-18 thread)
91259A635
McMaster-Carr
Yes
1
N/A
Nylon Lock Nut (3/8”-16)
97135A230
McMaster-Carr
Yes
4
N/A
Thrust Washer
(3/8” dia. shaft, 1/16” thick)
5906K511
McMaster-Carr
Yes
28
N/A
P a g e | 45
Socket Head Cap Screw (1/4”20 x ½” long)
90201A109
McMaster-Carr
Yes
1
N/A
Socket Head Cap Screw (1/4”20 x ¾” long)
90201A111
McMaster-Carr
Yes
4
N/A
Socket Head Cap Screw (1/4”20 x 1” long)
90201A113
McMaster-Carr
Yes
1
N/A
Socket Head Cap Screw (1/4”20 x 1 ½” long)
91251A546
McMaster-Carr
Yes
7
N/A
Socket Head Cap Screw (1/4”20 x 2” long)
91251A546
McMaster-Carr
Yes
4
N/A
Socket Head Cap Screw (1/4”20 x 3” long)
91251A554
McMaster-Carr
Yes
2
N/A
Black Oxide Nut (1/4”-20)
97149A100
McMaster-Carr
Yes
10
N/A
General Purpose Washer
(1/4” dia. shaft, 1/16” thick)
91083A029
McMaster-Carr
Yes
20
N/A
TOTAL:
$0
Appendix C: Energy Conversion
C.1 Detailed Design Drawings and Manufacturing Plans
See attached.
C.2 Assembly Sequence
Refer to Appendix B.2 for complete assembly manual of Motion Generation, Energy Conversion and
Safety.
C.3 Bill of Materials for Energy Conversion
Material
In Kit or
Shop? Quantity
Purchase Price
(each)
Part #
Supplier
Dowel Pin
(1/4” dia., 1” long)
98380A546
McMaster-Carr
Yes
1
N/A
#25 Hardened Steel Chain (2 ft)
A 6Q 7-25
SDP/SI
No
2
7.58
Chain Connecting Link
A 6Q 725SCCL
SDP/SI
Driven Sprocket with 48 teeth
and pitch diameter of 3.823”
and a bore of 0.5”
A 6C 725B48
SDP/SI
No
1
9.79
Driving Sprocket: with 8 teeth
and pitch diameter of 0.653”
and a bore of 6mm.
A 6C
7MHK2508
SDP/SI
No
1
25.42
P a g e | 46
Aluminum Angle, 2.5” x 2” X ¼”
thick, 6” long
8982K33
McMaster
Yes
2
N/A
Polulu 131:1 Metal Gear motor
1447
Pololu
Yes
1
N/A
92005A006
McMaster
Yes
6
N/A
M3 x 8mm Motor Screws
TOTAL:
$50.37
Appendix D: Safety and Motor Controls
D.1 Wiring Diagram
See attached.
D.2 Controller Code With comments
See attached.
D.3 Calculation for encoder count
Calculations: Lower Count Threshold:
Calculations: Upper Count Threshold:
D.4 Drawings and Manufacturing Plans for Safety/Motor Controls
No addition materials need to be manufactured for Safety and Motor Controls. All of the sensors were
mounted onto existing structures.
D.5 Bill of Materials for Safety/Motor Controls
Material
Part #
Supplier
In Kit
or
Shop?
Quantity
Purchase Price
(each)
Arduino Uno microcontroller
board
DEV-09950
Sparkfun
Yes
1
N/A
P a g e | 47
H-bridge (L298 Motor Driver –
preassembled)
K CMD
Solarbotics
Yes
1
N/A
351
Pololu
Yes
1
N/A
Custom
ME 350
Professors
Yes
1
N/A
Infrared Proximity Sensor,
short Range
GP2D120XJ00F
Sparkfun
Yes
1
N/A
Snap Action Switch (a.k.a.
limit switch)
187733
Jameco
Yes
1
N/A
Rocker switch, single-pole,
Double-throw
35-695
Jameco
Yes
1
N/A
22 Gauge Stranded Electronic
Wire
7587K931
McMaster
Yes
10 ft
N/A
22 Gauge Solid Core
Electronic Wire
8073K631
McMaster
Yes
10 ft
N/A
400-point Breadboard
Mounting Board for Arduino,
H-bridge and breadboard
TOTAL:
$0