1 ME350 Fall Semester FINAL DESIGN REPORT

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ME350

Fall Semester

FINAL DESIGN REPORT

Team 64

Nolan McPartlin

Yuzhou Zhuang

Zhentao Xu

Justin Lach

GSI: Steve Hwang

“We have fully abided by the University of Michigan College of Engineering Honor Code”

Nolan McPartlin

Yuzhou Zhuang

Zhentao Xu

Justin Lach

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Introduction

Audience

Table & Figure Formatting

Report Sections

Section 1: Project Introduction

Section 2: Design Processes

Section 3: Design Selection

Section 4: Final Linkage Design

Section 5: Final Team CAD

Section 6: Final Team ADAMS

Section 7: Motion Generator Revision

Section 8: Evaluation of Received Designs for Manufacturing

Section 9: Evaluation of Received Manufactured Parts

Section 10: Energy Conversion Introduction

Section 11: Transmission Ratio Determination

Section 12: Transmission Type Selection

Section 13: Final Transmission Design

Section 14: Power Analysis

Section 15: Torque Transfer Analysis

Section 16: Deflection Analysis

Section 17: Safety & Motor Controls Introduction

Section 18: Capabilities & Limitations of Sensors

Section 19: Mounting Considerations & Methods

Section 20: Encoder Counts, IR Sensor Threshold, and Controller Gains

Section 21: Arduino Code Changes

Section 22: Final Testing Results

Section 23: Design Critique & Evaluation

Appendix A: Individual Sketch Relations Design, 3D SolidWorks, and ADAMS Analysis

Appendix B: Drawings, Manufacturing Plans, Bill of Materials, and Assembly Plan for Final Design

Appendix C: Approval Packages, Bill of Materials, and Assembly Plan for Transmission Design

Appendix D: Wiring Diagram, Arduino Code, Calculations, and Bill of Materials for Safety &

Motor Controls

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Section 1: Project Introduction:

This project will focus on the construction of a mechanism that is capable of reflecting several different

lasers each emitted from opposite side of the playing field that the mechanism will be stationed. The

mechanism will reflect each laser onto a sensor in the middle of the field. The design of the device will

include a mirror for reflecting the incoming laser as well as a driven four bar linkage system that will

move the mirror into position. There are four lasers that will be firing automatically and randomly

throughout the duration of the game. The ultimate goal is to keep the laser on the target sensor for as

long as possible. To accomplish this, the mechanism will be designed to rotate the linkages quickly and

accurately.

Figure 1: A simplified explanation of the project statement

The mechanism will need to be able to interpret a signal sent from the laser battery which will tell the

mechanism which laser will be firing. It will then have to move into position as quickly as possible to

intercept and reflect the signal. This will be done automatically through the use of an Arduino

microcontroller. When the signal changes and a different laser fires, the mechanism will have to move

to a new position and begin reflecting the signal again. This will continue for two minutes and 40 laser

changes. The design will be restricted to a placement within the area of the mounting holes. It will also

need to fit within a specific volume given in the project description, and be able to use the supplied

voltage to perform its task.

The specifications for limits and metrics that the mechanism must adhere to are stated in the table on

the following page.

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Table 1 - Project Specifications, Taken from ME 350 Project Description:

Specification Description Target Min Max Measurement Methods

Volume Volume in the starting position

Minimize N/A 25,000cm² Meter scale, used to measure length, height, and width

Transmission Offset Angle

Defined as the largest absolute value of the transmission angle of the mechanism minus the ideal transmission angle of 90⁰

0⁰ -60⁰ 60⁰ Machinist’s protractor

Reflection Accuracy

The percentage of the 40 laser signals that the mirror is able to reflect onto the target and have detected by the sensor

Maximize 0% 100% Counting the total number of detections from LabVIEW and dividing by 40

Steady State Error

Average distance from the center of the reflected beam to the center of the target

Minimize 0mm N/A Meter scale measuring from center to center

Laser Detection Percentage

The amount of time that a laser is detected by a sensor divided by the total test time

Maximize 0% 100% Counting the total detection time from LabVIEW and dividing by test time

Craftsmanship will be very important for the proper functionality of the mechanism. Any extra material

or manufacturing flaws will inevitably slow down, hinder the range of motion, and/or affect the accuracy

of the mechanism.

Safety: The burs and edges will need to be ground and filled to ensure that no one is cut. Similarly, all

screws and fasteners will need to be fully seated, so that they do not catch on or cut anyone. Operators

also need to be aware of the pinch points so as not to cause harm to themselves or someone assembling

or maintaining the mechanism.

Alignment and Integrity: The mechanism will need to be constructed so that there is minimal slop

between parts. This will ensure accuracy and smooth operation. A mechanism that has integrity is also

important. If it is too delicate it will not survive transport and assembly; it may also be torn apart by its

own motor and transmission.

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Machining Quality: Well machined links and bearing surfaces will help to reduce friction and the force

required to move the mechanism as well as increase its response time.

Aesthetics and Design: The completed mechanism should look professionally done. There should be no

use of temporary fasteners (Duct Tape) and no stacking of spacers. If a washer larger than the ones

stocked is needed then it should be manufactured to specification. The design should account for ease

of assembly and of use common tools.

These are the measured dimensions for the playing field currently located in 1089 GG Brown. All

dimensions are in inches

Figure 2: Playing Field sketched in SolidWorks with measured dimensions from X50 room

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Section 2: Design Processes:

To generate individual design, SolidWorks was used to draw the simple version of the system setup and

get the design of the four bar links by taking advantage of geometric constraints. The condition is that

the target is fixed and the laser shooting device is fixed. The fixed position can be known by taking

measurements in the X50 assembly room. The measurements are given in Figure 1 above.

The four different positions of the four bar link can be found by drawing the routes of the laser light

from four different laser shooting device and make sure the light can be reflected towards the target.

Due to the basic reflection principle of the light, the incident angle is equal to the reflecting angle.

Therefore, the route of the light can be constrained by drawing a triangle whose sides are of equal

length to represent the incident and reflecting light.

A picture of this geometric setup has been included on the following page. The blue circle is the target

and the three vertical lines are the incoming lasers. The names of the links along with sample lengths

have been labeled. The transmission angles of the linkages for the first position and final position have

also been labelled. This process allows for easy manipulation of the initial design so that multiple

iterations can be accessed in a short time. By using SolidWorks to model the angles and linkage set up,

the solutions can be visualized and if there is any trouble with length, or angles they can be corrected.

ADAMS will be used to further assess the validity of the chosen design. ADAMS simulates the forces that

will be acting upon the linkage and can be used to analyze the motor requirements. This is useful

because many iterations can tested in a short amount of time, and different conditions can be set for

the input motion as well as friction, and material properties.

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Figure 3: Initial Linkage design using a sketch in SolidWorks

Lane 1 Lane 2 Lane 3

Target

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Section 3: Design Selection:

First, several important engineering specifications for a good design were selected and assigned a

weight percent (Wt. %) that represents the relative importance of each of the design specifications to

the final linkage design. AAA Pugh chart for these specifications can be seen on the next page in Table 2.

1. Reasonable link length

Link length should be short so that the system is more sensitive and easier to control by motor because

links of shorter length have smaller moment of inertia. This will also help the linkage to fit within the

maximum volume that is are allowed. Since this volume is relatively large this is not critically important

(Wt. % = 10).

2. Total Angle Change of the input

The link needs to move to the correct position as soon as possible. The total angle change from position

one to position two will need to be minimized, but the transmission angle is a far more important

measure then the overall angle (Wt.% = 10).

3. Manufacturability

The geometry of the design determines manufacturability. The input link and follower link are the same

part so it makes manufacturing the linkage more simple. Because the links are being produced by a

separate team, it is important to keep the design simple so as to minimize manufacturing issues (Wt. % =

25).

4. Mass

Mass of the link system should be small in order to minimize moment of inertia. The links should be

relatively small for every design and cutting mass from the links later in the design is not difficult (Wt. %

= 10).

5. Accurate Control of rotation

Only Zhentao’s design has a better control of rotation because he uses two pins for the joints to

constrain the motion in the horizontal plane. All the designs have good control and doubling the joints

adds more weight and inertia, so this specification is not as important (Wt. % = 10).

6. Transmission Angle

Transmission angle, which means the angle between the coupler and the follower link, should be within

30-150 degrees. A 90 degree transmission angle is ideal. This is very important because a transmission

angle closer to 90 degrees will maximize the amount of torque that is transferred. This allows for better

reaction to changing lasers and less power needed from the motor (Wt. % = 25).

7. Ease of assembly

Easiness of assembly depends on the free space surrounding each fastener. A design that is easy to

assemble will make it easy to make adjustment to later in the design if needed (Wt. % = 10).

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Table 2 - Pugh Chart for Design Specifications

Design Specifications Weight % Yuzhou Zhentao Justin Nolan

Reasonable link length 10 2 3 2 4

Total Angle change of the

input link

10 3 3 3 4

Manufacturability 25 4 3 4 3

Mass 10 3 2 3 4

Accurate Control of

rotation

10 3 4 3 3

Transmission angle 25 4 3 4 4

Easiness of assembly 10 3 3 3 4

Weighted Average 100 3.1 3 3.1 3.65

The data chart shown in Table 3 below holds the exact values for several important measurements of

the linkages and their behavior in the ADAMS simulation. This is offers a quick comparison between the

links and is used in the final design decision.

Table 3 - Data Chart:

Individual design data Yuzhou Zhentao Justin Nolan

Maximum Power Output (N*mm/sec) 32.5 6.91 47.5 17.89

Volume Measurements(inch^3) 12.06 15.00 7.22 34.552

Transmission Angle Deviation

(degrees)

41.76 81.85 41 34.14

Based on the Pugh chart and the data chart, Nolan’s design of the link length, ground pivots, and

transmission angle was selected. The detailed design of the links, like the hollow part and the slot, were

discussed by the whole team and will be shown in the proceeding section.

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Section 4: Final Linkage Design:

Tables 4 and 5 show the specifications for team’s final linkage design.

Table 4 - Final Link Lengths (in inches):

Input Link Coupler Link Follower Link

5 3.5 5

Table 5 - Transmission Angles for all four Positions (in degrees):

Leftmost Middle-Left Middle-Right Rightmost

Transmission Angle 123.11 96.87 75.83 56.86

Deviation from Perpendicularity

33.11 6.87 14.17 34.14

Lane 1

Lane 2

Lane 1

Lane 3

Lane 4

Follower Link

Coupler Link

Input Link

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Figure 4: Final linkage design drawn in SolidWorks sketch

The maximum transmission angle deviation is 34.14 degrees and the limit is 60 degrees, which is well

within the boundaries of the project description. Due to the low angle deviations, during the game, the

perpendicular component of the force transmission between the coupler and the follower will always be

significantly greater than the force transferred along the length of the follower. This means that the

follower pivot will bear less load because the pivot only supports loads along the link. The positions of

the ground pivots are shown in Table 6.

Table 6 - Ground Pivot Locations Relative to Top Left Mounting Hole on Arena (in inches):

Pivot 1 Pivot 2

Relative X-axis Position 3.775 7.689

Relative Y-axis Position -2.754 -1.250

In the figure below, the top left hole is concentric with the top left mounting hole.

Pivot 1 is the hole with the smaller diameter that is closer to the left side of the plate.

Pivot 2 is the small diameter hole on the right side of the plate.

Figure 5: First revision of the Ground Link design as sketched in SolidWorks

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Section 5: Final Team CAD:

The linkage will be made entirely of aluminum. This decreased the weight and inertia of the linkage and

will make it easy to move. Lightening holes will also be used to further decrease the weight. The mass

lost to the lightening holes will be taken out of the middle of the links which will still give them the

necessary strength because the moment developed within the link is zero at the center and maximum at

the outside end.

Hardstops will be used to limit the range of motion of the linkage to the first and final positions. They

will also have the switches mounted to them that the linkage will trigger when initially positioning itself.

The hardstops will be adjustable through the use of slots in the ground plate. This will allow for fine

tuning of the linkage system later.

The mirror will be placed in the recessed space in the coupler link. It will be attached with two part

epoxy to ensure a strong and reliable fit.

The joints will be constructed around the 0.25” shoulder bolts. There will be a bushing pressed into each

link which will serve to decrease the friction between the link and shoulder bolt. Above the link and

below the head of the bolt there will be a bearing stack that consists of a needle bearing between two

washers. Below each of the links there will be another bearing stack. The end of the shoulder screws will

be fastened into the ground plate or another link.

The figures on the following page show the current CAD designs in SolidWorks.

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Figure 6: Mechanism in the position for reflecting the leftmost laser

Figure 7: Mechanism in the position for reflecting the leftmost laser

Figure 8: The whole setup for the four bar linkage system

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From the bottom up, the joints in the links stack up in the following manner:

Ground plate to Input / Follower

Threaded hole in ground plate (shoulder bolt is screwed in)

Washer

Bearing

Washer

Input / Follower

Washer

Head of shoulder bolt

The reasons of the design listed below:

1. With a washer bearing washer ‘sandwich’ between the input/follower link and the ground plate,

the links won’t rub with the ground plate directly and increase the friction as well as protect the

links.

2. Between the head of the shoulder bolt and the links, inserting a washer can also avoid the direct

rubbing the link and the bolt.

Input / Follower to Coupler

0.25’’ nut (shoulder bolt threaded inside)

Small washer

Input / Follower

Washer

Bearing

Washer

Coupler

Washer

Head of shoulder bolt

The reasons of the design listed below:

1. The 0.25’’ nut at the bottom prevent the parts of the joints slide in the axial direction.

2. A washer is placed between the link and the nut to avoid friction between links and the nuts.

3. With a washer bearing washer ‘sandwich’ between the coupler and input/follower link, the links

can move freely with smaller friction between each other.

4. Finally a washer is inserted between the head of the bolt and the link to prevent friction

between bolts and links.

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Figure 9: Design for joint between ground plate and the input/follower link and the joint between

coupler and links.

Figure 10: Section view of the input link to ground plate joint

Figure 11: Section view of the follower link ground plate joint

Washers

Shoulder Bolt

Bearing

Input Link

Ground Link

Bushing

Washers

Shoulder Bolt

Bearing

Follower Link

Ground Link

Bushing

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Figures 12: Sectioned view of the Figure 13: Design of the

input link - coupler joint coupler - follower joint

Figure 14: The overall design of the setup with size on it.

Figure 14 shows the current 3D model whose box dimensions are 1.59’’ in height, 10.00’’ in length and

6.51’’ in width. The total box volume, V, can be calculated in the following way

V=1.59’’ * 10.00’’ * 6.51’’=103.509 cubic inches.

The designs above are the original of the joint design, but now, the design of the joint between the

coupler and input/follower links has been improved by using dowel pins and snap rings.

Washers

Shoulder Bolt

Bearing

Input Link

Coupler Link

Follower Link

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Section 6: Final Team ADAMS:

For the Adams simulation model, a simple linearly increasing and decreasing acceleration curve for the

input motion was assumed because this type of acceleration curve would give good control and stable

operating conditions. The angle that it has to pass through was 56 degrees. This corresponded to an

angular acceleration of 224 deg/s². It was decided that the linkage should take one second to move from

the starting position to the ending position. This time would allow us to react quickly to the changing

lasers.

For the simulation, a frictional force was added at the joints. The frictional force was equal to the friction

that would be experienced from the bearings and washers. The angular position was expected; the

linkage moved 56 degrees throughout its motion. The angular velocity is reasonably high and at a

maximum at 125 deg/s. This velocity will allow us adequate speed to respond to the changes in laser

lanes. The power required from the motor produced a strange graph. This is likely a result of the

inclusion of friction at the joints. The maximum power does not exceed 0.09 W, which is in the range of

the motor. The torque curve also has a strange shape; again this is likely because of the added friction.

The curve is maximum at about 82 Nmm. This torque is well within the range of the motor which will

allow us to increase the response speed later on. The real mechanism will include fasteners which will

increase the weight of the linkage and the total inertia. The frictional force that was used could also

change depending on how the linkage is assembled.

The differences between the real mechanism and the Adams model are as follows:

1. Our Adams model neglect all the joints because it is easy for the simulation. However, in the real

situation, the forces in the joints will affect the motion.

2. The friction force might vary during the time and the motor torque can be not constant.

However, all the constant forces and torques in the simulation were constant. Because the link

will be rotating for a maximum of one second, it is okay to make this assumption.

Figure 15: ADAMS Model used for power calculations

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The following four plots are the ADAMS generated graphs for the angular position, angular velocity,

torque, and power of the mechanism. The simulation time was one second.

Figure 16: The angular position curve with respect to time for the linkage system

Figure 17: The angular velocity of input link with respect to time for the linkage system

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Figure 18: Input Torque curve for the linkage system

The first spike in the graph is the increase in torque required to overcome the static friction in the joints.

The small torque drop at time = 0.5 seconds occurs because the linkage begins to slow down and

angular momentum begins to contribute. The last spike in torque magnitude is the negative torque

required to balance the angular momentum and stop the mechanism at the final position.

Figure 19: Curve of power required by input link

Since power is the product of angular velocity and torque, the changes in the torque graph explain the

irregularities in the graph for power.

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Section 7: Motion Generator Revision:

The metrics and features that were used to evaluate the design in ADAMS are unchanged from the

original evaluation.

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Section 8: Evaluation of Received Designs for Manufacturing:

Ground Pivot Spacer - No Problem

Ring thickness dimension is redundant and unnecessary because ID and OD were already specified

Ground Plate - Problem

Which drawing they are using for their ground plate is unclear. Is it this drawing or link G?

Vertical features should be dimensioned horizontally. Right now they are annoying to read.

Resolution: this ground plate was from an earlier design review and was not manufactured

Hardstop - No Problem

Drawing is clear, but the purpose of the through hole is not clearly understood.

Link C - No Problem

It is not clear how the curved edges will be machined.

Link F - No Problem

Dimensioning space between features is redundant and unnecessary. The diameter of the hole for the

slot specifies that the hole diameter is repeated 8 times there are only 4 locations on the drawing. The

pivot holes are also specified to repeat 4 times but there are only two of them. This is confusing. It

would have also been nice to have a flat feature from which the x datum can easily be found, but there

are methods of getting the datum that the machine shop can help us with.

Link G - Problem

Which drawing they are using for their ground plate is unclear. Is it this drawing or Ground Plate?

Again, all dimensions should be horizontal. Only one of the 0.249’’ diameter holes are dimensioned. The

diameter for the 0.249’’ hole needs to have “x2” next to it.

It would be more accurate to center drill, pre drill, and ream or tap all for each hole before moving onto

the next hole. This would take a lot more time, however, so this manufacturing plan is good if the

accuracy of the readout on the mill is enough.

Resolution: This was the plate that was manufactured instead of “Ground Plate”

Link I - No Problem

Link I is identical to Link F in everything except length. See Link F analysis.

Ground Plate Spacer - No Problem

Since ID and OD are both dimensioned, the wall thickness dimension is unnecessary.

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Section 9: Evaluation of Received Manufactured Parts:

1. None of the parts had been deburred or files clean. The team deburred and filed the parts.

2. The spacers are not of equal height and the surfaces are not flat. There is a clear slope and they

appear to have only been cut to length with a band saw. Team 65 faced and cleaned up each

spacer.

3. The holes in the ground plate that were to be tapped to 10-24 were instead tapped to 10-32.

The team re-tapped the holes with a 10-24 tap over the 10-32 threads.

4. The bushings that were press fit into the coupler are too tight. The holes in the coupler were too

small and the resulting compression in the bushing shrunk its inner diameter too much

5. The steel pins were not finished because the groove specified in the drawing was smaller than

the smallest groove tool in the machine shop. The design was changed to fit the tooling in the

shop and the pins were finished later.

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Section 10: Energy Conversion Introduction:

A transmission allows a motor’s speed and torque to be modified to suit the use of the mechanism that

it will be used for. The motor used will affect the usefulness of the transmission. It is therefore

important to select an adequate motor for the application and apply a transmission to it that will

optimize output speed and torque. An electrical motor has a very high speed and a relatively low torque.

In order to make an electric motor more useful and controllable, a transmission is implemented to

increase the output torque by decreasing the output speed. A transmission decreases the efficiency of

the motor due to friction caused by gears, belts, or chains. Efficiency measures how much of the power

put into the motor is transferred into the linkage. Any transmission is limited by its size and material.

Size is important for vehicles and structures. Cars operate more efficiently with less weight and there

are physical limitations on how large any vehicle can be if it is to perform on the road. A material that

cannot support the torques that it is required to transfer would cause the transmission will fail. The

transmission for the design cannot be larger than the spacing between the links because it could

interfere with the function of the links or make the mechanism too large to fit within the prescribed

dimensions. Materials are not as important to the design because there will not be any large torques.

This design will attempt to optimize output speed and accuracy of angular displacement.

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Section 11: Transmission Ratio Determination:

The inertia matching method was used to determine the transmission ratio for our mechanism. This

method was chosen because it was immediately applicable to our design and allowed for a physical

interpretation of what was being done. All the values could be obtained through the SolidWorks model

and the measurements for R1 through R5 were found by adding in the necessary lines. This method was

also supported through the course with the inclusion of an Excel chart that automatically calculated all

applicable values.

Step 1: The moment of inertia can be found looking from the motor side by the formula:

Where 𝐼𝑚 is the moment of inertia of the motor.

𝐼𝐿 is the moment of inertia of the load.

N is the transmission ratio.

𝐼𝐿/𝑁2 is the reflected load inertia

Step 2: Using N, the motor’s angular acceleration can be found in the following manner:

Where ALPHA_M is the angular acceleration of the motor

ALPHA_L is the angular acceleration of the load, the input link

Step 3: Since the startup torque is the torque provided by the motor to accelerate the linkage which is

larger than the operational torque. To satisfy the power requirement, the first thing to consider is the

startup torque, 𝑇𝑆, which has the following formula:

Given the motor, the gear transmission ratio must be designed to minimize start-up torque. To find the

minimum, take the derivative of the Torque with respect to the independent variable, N - the

transmission ratio. Then set the derivative equal to zero because when the slope of the Torque vs.

Transmission Ratio graph is zero there must be a either a maximum or minimum.

𝛼𝐿 won’t be equal to zero while the motor is operating, so,

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Solve the previous equation for N to find the value needed to reach minimum start up torque

If then T is decreasing. If then T is increasing. Therefore,

is a minimum and not a maximum.

The benefits of this method

This method is simplified, but still useful. It neglects the friction between gears, friction inside the

motor, and friction at the joints. The moment of inertia was found using geometry and material as

inputs into SolidWorks. The SolidWorks model doesn’t consider all the details. It is merely a quick

method to gain a big picture of the whole transmission design. From the transmission calculation, the

theoretical transmission ratio is 0.628. To achieve this ratio, a 32 tooth gear was selected to be used on

the shaft of the motor and a 20 tooth gear that will drive the input link. This gives a transmission ratio of

0.625 for the transmission, which is not exactly 0.628, but the difference won’t substantially affect the

functionality of the links.

Table 7 - Parameters at the five positions:

Position 1 Position 2 Position 3 Position 4 Position 5

Transmission angle (deg)

57.64 73.22 87.92 77.01 56.94

R1 (cm) 12.70 12.70 12.70 12.70 12.70

R2 (cm) 49.10 59.79 64.24 60.37 44.63

R3 (cm) 53.28 61.90 63.94 57.74 39.16

R4 (cm) 12.70 12.70 12.70 12.70 12.70

R5 (cm) 51.04 60.69 63.94 58.90 241.75

Total Inertia (gram*cm^2)

9828.11723 9326.519 8938.146 8568.09 7853.227

The total angle the input link can rotate is 62 degrees. So, in the calculation of transmission ratio, the

angle was equally divided into four parts, which created five positions, as is shown above. The data

obtained included R1 to R5, transmission angle, moment of inertia about the center of mass of each link.

Then the input moment of inertia was found using parallel axis theorem. Eventually, using this and

motor inertia, a transmission ratio of 0.628 is finally found.

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The following figures show the inertia length dimensions for the linkage in the five positions.

Figure 20: Position 1

R1

R4

R5

R3

R2

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R1

R4

R5

R3

R2

R4

R5

R3

R2

R1

28



R4

R2 R3

R1

R5

R4

R2 R3

R1

R5

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Section 12: Transmission Type Selection:

The following Pugh chart was used to determine which transmission type would be chosen to drive the

linkage. Efficiency, reliability, volume, and ease of assembly were the most important specifications for

deciding which transmission to choose. Volume and ease of assembly were the most important because

the transmission had to fit within the existing linkage. Any increase in volume could increase the box

volume and cause the team to lose points. The transmission must be easy to assemble and disassemble

to allow for many changes and design revisions that the team will almost certainly be making. For these

reasons, Volume and Ease of Assembly were both assigned weights of 30%.

Reliability is also important because the linkage will be making many changes of position and it is

important to ensure that there will be no failure or slipping. Slipping would cause catastrophic failure in

performance because the motor is controlled by angular displacement. Reliability was therefore

assigned a weight of 25%.

Efficiency was also important though not as much as the other specifications. All of these transmissions

would be relatively efficient and would not have much energy loss due to their small size. However, it is

still important to minimize these losses.

Table 8 - Pugh Chart for Selection of Transmission Type

Design Specification Weight % Gears Belts Chains Cam

Efficiency 15 5 3 4 3

Reliability 25 4 3 4 4

Volume 30 5 2 2 3

Ease of Assembly 30 4 3 3 2

Weighted Average 100 4.45 2.7 3.1 2.95

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This linkage will use gears for its transmission. This type of transmission will have good efficiency and

will be easy to install. Chains and pulleys would require more space and an idler to ensure proper

tension. The transmission ratio generated by the calculations was 0.628. The closest transmission ratio

that can be achieved with the gears in Stock at McMaster-Carr is 0.625. The 32 tooth and 20 tooth gears

will yield this ratio. These will be the gears that are used to determine the all the forces and torques that

will be present in the design. 48 pitch gears are too small so 32 pitch gears were used instead.

The other gears listed will provide gear ratios of 0.643 (18:28), 0.75 (24:32), and 1 (28:28). If it is later

found that the mechanism will operate better with a different ratio, then the team will be able to

quickly change gears instead of waiting for McMaster to deliver the parts.

Table 9 - List of Ordered Transmission Gears:

32 Pitch Gears Manufacturer Part Number

32 teeth (implemented) McMaster-Carr 57655K42

20 teeth (implemented) McMaster-Carr 57655K36

28 teeth McMaster-Carr 57655K41



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Section 13: Final Transmission Design:

The transmission will use nylon gears to transfer torque from the motor to the linkage. Using nylon

gears will reduce the weight and inertia of the transmission while still maintaining strength and

reliability. A 20 tooth gear will be mounted to the input link through the use of a steel shaft. This shaft

will be press fit into the gear and press fit into the link. This will ensure that the gear and shaft move at

the same angle and stay rigidly connected. The free end of the shaft will pivot in the ground plate and be

fixed by a nut from the bottom. The motor will be mounted upside down and held in place by angle

stock. The aluminum angle stock will be constructed in an F shape that will support the motor and the

shaft that protrudes from the gear.

To allow for adjustability, the second piece of angle that attaches to the ground plate will be wider than

the one used to mount the motor. This L bracket will include slots to allow for a change in the gears

center to center distance. It will also have a bearing press fit into it so that it can support the steel drive

shaft. This will allow the shaft from the motor to be supported and the distance between the motor and

input to be adjusted to maximize gear contact. The vertical adjustability will be given by the placement

of the set screw on the motor shaft. This will maximize the face contact of the gears, ensure maximum

torque transfer, and prevent the development of any destructive forces.

The volume of the transmission and motor assembly is approximately 35 cubic inches. This brings the

total volume to 138.509 cubic inches. This increase will not affect the overall design because the

transmission and motor mount are placed within the perimeter of the ground link.

The 3D models for the transmission design with the motor are shown on the following pages.

32

Figure 25: Isometric view of the entire transmission with all fasteners.

Figure 26: The 6 slots in the ground plate provide horizontal adjustability for the hardstops and motor

mount assembly. Two slots were incorrectly designed after design review 1 and now serve no function.

33

Figure 27: There is a 1/8’’ gap between the motor shaft and the ground plate that allows for slight

vertical adjustability of the vertical location of the motor gear.

Gap

Motor Drive Shaft

Ground Plate

34

Section 14: Power Analysis:

The Power analysis is being performed because in order to determine whether the motor is powerful

enough to drive the linkage system and reach a quick system response. It basically ensures that the

linkage system can move. It also help us modify a better operation status for the motor.

Table 10 - Variables used for Power Analysis

Variable Value of the variable in the analysis

Angular Acceleration 𝛼 11.1rad/s^2

Startup torque 𝑇𝑆 41.25ozin

Inertia of the motor 𝐼𝑚 250000 grams*cm^2

Inertia of the load 𝐼𝐿 9861.86477 grams*cm^2

Inertia of the gear 1 1.0747g*cm^2

Inertia of the gear 2 0.1835g*cm^2

Transmission ratio N 0.628071212

Rotation angle of the input link 𝜃 1.15628 radians

Maximum Angular Velocity 𝜔𝑚 2.31256 rad/sec

The time of motion 𝑇𝑚𝑜𝑡𝑖𝑜𝑛 1 second

Total Inertia of the linkage system 𝐼𝑡𝑜𝑡𝑎𝑙 256114 grams*cm^2

For the above table, Rotation angle of the input link 𝜃is the Angular displacement from leftmost position

to rightmost position known from the SolidWorks design.

In the power analysis of the motor, the following assumptions were made:

1. The motor was accelerating in a constant angular acceleration and reached the maximum at the

time current cut off from the motor.

2. When the current is cut, the motor will decelerate at the same constant angular acceleration

until it stops.

Based on the assumptions above, the maximum angular velocity is

𝜔𝑚𝑎𝑥 = 2*𝜃/t rad/sec

35

The total inertia of the system is

The gear is Nylon with the density of 1.15g/𝑐𝑚3 , the estimated 48 pitch, 32 teeth gear‘s moment of

inertia is

which is negligible considering the inertia of load and motor.

In the same way, the 48 pitch, 20 teeth gear’s moment of inertia can be estimated:

And therefore the inertia of the gears can be neglected to simplify the method and doesn’t influence the

outcome at all. And the total inertia is:

Alpha was substituted for 4*theta/t^2 because theta, angular displacement, can be controlled using the

motor.

Here, given the motor specs, it is easy to calculate the time of motion to see how fast the system

responds.

So,

36

Section 15: Torque Transfer Analysis:

The two joints where torque is being transferred is basically the motor shaft and the shaft connecting

input links and the output gear. Torque transfer is performed to make sure that the input torque from

the motor after transmission will still be able to drive the linkage system. The analysis will be performed

into two parts, one is the free body diagram analysis for the gear system. Another is to compare the slip

rotation torque of the press fit and the output torque so that the torque on the gear doesn’t make it slip

on the shaft.

Figure 28: The free body diagram of the gears

As the free body diagram shown above:

Assume the torque is positive counterclockwise then,

where pitch diameter 𝑝1is obtained from the McMaster-Carr, and the stall torque 𝑇𝑆 is estimated by the

average stall torque between 6V and 12V based on linear estimation.

And then based on the force balance in vertical axis,

And also from McMaster-Carr, the pressure angle is 14.5 degree and therefore,

37

Next, analyze the output gear free body diagram:

From the balance of the force both in x and y axis:

Assume counterclockwise as the positive direction, apply the equilibrium of torque:

The torque transfer ratio is

which means because of the transmission only 62 percent of the torque remains.

The assumption in the analysis is the following:

1. Friction between gears and friction between the gear and the shaft is neglected.

2. The torque during rotation is in equilibrium.

3. Stall torque is used in the analysis because it is worst case for the motor.

The failure of the torque transfer is defined when the torque is larger than the resistance torque due to

press fit which makes the gear slip on the shaft. The analysis is based on the formulas in Fundamentals

of Machine Elements by Hamrock, etal McGraw-Hill, 1999. The book was found at the following URL:

http://www.engr.colostate.edu/~dga/mech325/handouts/press_fit.pdf

The most important assumption for the following analysis is that since the hardness of steel is much

larger than nylon, deformation of steel is negligible compared to nylon.

The constants regarding the property of materials are as below:

where v gives the Poisson ratio of nylon, E is the Young’s modulus, is the radius of the gear and is

the radius of the shaft.

Given the constants known, solve for 𝑝𝑓

38

Now solve for the press fit force between shaft and gear:

T is the torque provided by the friction of the press fit, which is larger than the torque driven by the

gear:

This proves that the transmitted torque won’t exceed the resisting torque from the press fit. Therefore,

the design is feasible. Stress failure on the press fit won’t be a problem.

The two press fits that were used in the design are shown in cross section in Figures 29 and 30 on the

following page.

39

Figure 29: The cross section of the motor shaft coupler press fit into the Output gear

Figure 30: The cross section of the output gear, input link, and hat all press fit onto the input drive shaft.

The motor shaft coupler has been suppressed in this figure to better display the press fits on the input

drive shaft.

Output Gear

Motor Shaft

Input Gear

Output Gear

Input Drive Shaft

40

Section 16: Deflection Analysis:

Figure 31: Free Body Diagrams for beam deflection - Gears 1 and 2

Constant list:

Sign Convention:

All positive directions of force and torque are shown in figure above.

First consider the Input gear, once again assuming equilibrium case. So the total torque acting on gear 2

is zero. In this way the tangent force can be found:

Now apply balance condition to gear 2 in y direction, the force provide by gear 1 and by pivot balance

with each other, which yields:

After getting the tangent force, use the pressure angle to calculate force between two gears and the

normal force.

So the force of the shaft on gear 1 is:

First, calculate the force of the shaft on gear 1. Using balance condition in both x and y direction,

41

Now, calculate the torque provided by gear 1 using the balance conditions. Assume that in equilibrium

condition, the total moment on gear 1 equals zero

Now analyze the axis:

Here, the model of a bar with one end fixed in a wall with an applied perpendicular force was used. The

relation between end-deflection and force is:

In reality, the pivot consists of two parts: the upper one with length ⅜ [in] and radius 1/16[in] and lower

one with length 0.43[in] and radius ⅛ [in]. But for the upper one, since force is acting at a distanced 1/16

[in] from top, so 3

8−

1

16can be used as the length. So, the deflections of two parts are separately:

So the total deflection is:

Since this deflection is so small, it can be said with confidence that failure will not happen. The diameter

of the shaft that fit into the gear was changed from 1/8” to 3/16”. This will decrease the total deflection

of the shaft and it will still be negligible.

Now, calculate the deflection of motor axis.

42

The force acting on the pivot:

Since the pivot in the design consist of two parts, one with diameter 0.88’’ and the other with diameter

0.995’’. To simplify the analysis process.

Using these, calculate the area moment of two part:

Assume force x is acting on upper part and F-x is acting on the lower part. Use the condition that the

deflection of two parts are the same to find the relation between force F and deflection, delta, so as to

calculate the deflection at the point where F acts.

Figure 32: Free Body Diagrams for beam deflection - Motor Coupler and Input Shaft

43

The three beam deflections, 𝛿1, 𝛿2, 𝛿3 are

Now use the condition that

Result:

The deflection can be calculated in the following manner:

This is obviously negligible. So, the deflection will not be a problem.

44

Section 17: Safety & Motor Controls Introduction:

Safety features are needed for the motor to prevent damaging the linkage and motor and to prevent

injury to nearby operators. Mistakes in coding or wiring can cause malfunction which, in the worst case,

can cause the motor to spin at maximum speed and smash the linkage into the nearest obstacle. These

obstacles could be the stand for the motor or someone’s finger. If the motor doesn’t have enough

torque to drive the linkages or becomes stuck the motor will run at high voltage. High voltages and

currents in the motor circuit might burn and destroy the motor. Therefore, safety features need to be

included. The parameters in both software (motor controls) and hardware (safety features) must be

adjusted in order to prevent events like this from happening.

The safety control is achieved through the use of a proximity sensor which detects object in the way of

the linkage and stop the linkage when there are obstacles. The motor control is achieved by the encoder

and the limit switches. The encoder detects the angular position and reads how much the gear rotates

and allows the motor to move to the correct position. The limit switches reset the first and fourth

positions so that the linkage can be accurately controlled during repeated forward and backward

movement. These switches also allow for the linkage to be calibrated during initial startup and

determine its position in space and where the zero point is.

45

Section 18: Capabilities & Limitations of Sensors:

The sensors which will be used are an infrared proximity sensor, two limit switches, an encoder, and a

toggle switch. The Infrared sensor is capable of detecting how close an object is to the sensor and shuts

down the system when the object gets too close. It uses an infrared signal that is reflected off an object

and picked up by the sensor. The time that it takes for the signal pulse to return is read and interpreted

as the distance to the object. There is a limited range for the sensor and a limited field over which it can

sense objects. This means that it must be conveniently positioned so that it has good visibility and can

oversee the entire area that needs to be monitored. Noise in the signal for the infrared sensor can

increase or decrease the distance value that is obtained. This can vary by about ten to fifteen units, but

the signal change from an incoming object will change the signal by more than 100 units. In order to not

generate false positives this must be taken into account and the difference in signal between a positive

and negative should not be too close to the noise threshold.

The encoder is the most important sensor as it controls the position of the motor. It works by counting

the rising and falling edges of the encoder wheel and then producing a signal at 16 counts per

revolution. The minimum angular change that the encoder can measure (using a transmission ratio of

0.625) is

𝐶𝑜𝑢𝑛𝑡𝑠

1 𝑙𝑖𝑛𝑘 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛=

64 𝑐𝑜𝑢𝑛𝑡𝑠

1 𝑒𝑛𝑐𝑜𝑑𝑒𝑟 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛∗29 𝑒𝑛𝑐𝑜𝑑𝑒𝑟 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠

1 𝑚𝑜𝑡𝑜𝑟 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛∗ 𝑇𝑟𝑎𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑅𝑎𝑡𝑖𝑜 =

1160 𝑐𝑜𝑢𝑛𝑡𝑠

360𝑜 =1 𝑐𝑜𝑢𝑛𝑡

0.31𝑜

The minimum measurable change in angle of the input link is 0.31 degrees. This is also the minimum

error of the encoder itself. The transmission system can also cause error in the angular position

measurement. The largest problem found in the prototype testing is that the backlash of both the motor

and the transmission system can cause error in excess of 0.31 degrees. If the motor shaft is slipping on

the gear, the measurement of the position can vary greatly

The switches produce a simple on/off signal that is the same for both limit switch and the toggle switch.

This signal is created by the collapsing or opening of the switch between two nodes. The switch is

immobile and in order to be useful it must be placed in a precise location within the system to ensure

that it is not triggered early or late. There is also some bending that occurs along the arm that

closes/opens the limit switches that can cause a slight error when the switch is triggered. There is no

noise in the switches since it is either on/off or 1/0. The limit switch can cause error if it is not correctly

mounted. For example, the linkage can touch the limit switch when it has not reached the exact position

required and if the limit switch resets at this time it will create error and the linkage could miss the

following positions.

46

Section 19: Mounting Considerations & Methods:

The sensors should be mounted in a relatively open space without any obstacles disrupt the information

they receive. It should be also mounted without wasting the volume of the setup and can be easily

assembled.

1. Mounting of the proximity Sensor

The proximity sensor should be mounted so that it is facing the linkage. In this way, anything moving

between or into the linkages while it is moving will be detected and thus stop the motor to avoid injury

or damage.

2. Mounting of the limit switch

Limit switches should be mounted on the hard stops so that when the linkage gets to the first position

(hard stop 1) and the fourth position (hard stop 2) it will reset the encoder count to the lower bound

and upper bound respectively. This thus corrects the error of backlash within the motor and allows the

linkage to be calibrated and find the zero point from any initial starting position. It should be mounted

without obstructing the motor’s movement and preventing the linkage from reaching the hard stop

position.

3. Mounting of the toggle switch

There is much flexibility to mount the toggle switch and the only requirement is that it is easy to reach

and operate.

47

Section 20: Encoder Counts, IR Sensor Threshold, and Controller Gains:

1. Method of choosing desPositions

First the number of counts per degree of rotation of the input link was calculated. desPosition is the

theoretical encoder count for the motor and is calculated using the following derivation:

𝐶𝑜𝑢𝑛𝑡𝑠 =64 𝑐𝑜𝑢𝑛𝑡𝑠

1 𝐸𝑛𝑐𝑜𝑑𝑒𝑟 𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛∗ 𝑀𝑜𝑡𝑜𝑟 𝑅𝑎𝑡𝑖𝑜 ∗ 𝑇𝑟𝑎𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑅𝑎𝑡𝑖𝑜 ∗

𝜃𝑙𝑖𝑛𝑘

360𝑜

𝐶𝑜𝑢𝑛𝑡𝑠 = 64 ∗ 29 ∗ 0.625 ∗𝜃𝑙𝑖𝑛𝑘

360𝑜

𝐶𝑜𝑢𝑛𝑡𝑠 = 1160 ∗𝜃𝑙𝑖𝑛𝑘

360𝑜

Because the encoder count increments whenever it detects a rising edge or a falling edge on A or B

channel the resolution of encoder is 4. The gear ratio of the motor is already given by 29:1, and our

linkage gear ratio is 0.625.

And therefore the encoder counts for the four positions are:

𝜃1 = 0𝑜 , 𝜃2 = 14𝑜 , 𝜃3 = 40𝑜 , 𝜃4 = 55𝑜

𝑑𝑒𝑠𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛1 = 1160 ∗𝜃1

360𝑜= 0 𝑐𝑜𝑢𝑛𝑡𝑠







There are many factors influencing the encoder counts like backlash, the mirror thickness, the width of

the linkage, the mounting position of the mirror, etc. The actual encoder counter when the links get to

those positions should be different from the calculation. The exact value of encoder counts at the four

different positions was found using the encoder test and the serial monitor. These values are listed in

Table 11.

2. Method of choosing Base Voltage

Base Voltage is the minimum voltage needed to drive the linkage. After testing from 1.5 and increasing

by about 0.1 or 0.2 points at a time, a final setting of Base_CMD=2.4*2.15 was selected.

48

3. Method of choosing controller gains

For choosing controller gains Kp, KI, Kd , since these three parameters interact with each other, the

methodology of choosing these values was to select values and test them. Based on the results the

values were changed until the desired performance was achieved.

First, the integral gain and differential gain were set at 0 and only change Kp, if Kp is too small, the

linkage is not powerful enough to drive to the desired position; if Kp is too large, it would cause

vibrations because the motor resists movement of the linkage. The final Kp was set at 0.072, which

needed further adjustment after setting the remaining values.

Second, even after lowering Kp, there is still some oscillation when moving the linkage, and so Kd was

set slightly above 0 and incremented to a final setting of 0.003 to avoid vibration.

Third, since only having Kp to drive the linkage doesn’t avoid steady-state error, KI was added as 0.002

to increase the accuracy of the linkage as it changed position.

4. Method of choosing controller error range

In the code, the error range was set by Dr. Remy at 4 which stops the motor count 4 units short of the

desired value to account for the momentum of the linkage and any additional travel that it creates. After

testing, the parameter, CTRL_DEAD_BAND, was set to 3 as 4 was too large and induced vibrations.

5. Method of choosing proximity sensor threshold

In order to select a suitable proximity threshold several values were tested between 100 and 500. It was

found that a threshold value of 260 gave the best results, and allowed the sensor to detect objects at a

reasonable distance and stop the linkage.

49

Table 11 shows all the important variables and their values in Arduino Code which determine the

mechatronic system’s behavior.

Table 11 - Summary of Variables in Arduino Code:

Variable Name in

Arduino Sketch File

Purpose of Variable Device Calculated

Value

Actual Value Used

During Testing

desPosition1 Laser Position #1 Motor 0 0




Kp Proportional Gain Motor N/A .072

KI Integral Gain Motor N/A .002

Kd Differential Gain Motor N/A .003

CTRL_DEAD_BAND The error range of the

motor encoder count

Motor N/A 3

proxSwitchThreshold

Threshold value for

proximity sensor

before stopping the

motor

Proximity

Sensor

N/A 260

50

Section 21: Arduino Code Changes:

Parameters including proportional gain Kp, integral gain KI, differential gain Kd, and base_command

voltage

Here the values of DES_POSITION_1, DES_POSITION_2, DES_POSITION_3, DES_POSITION_4 and K_I,

K_P, K_D were all adjusted. The value of the DES_POSITOINs were measured using the serial monitors.

After affixing the mechanism to the table, the linkage was moved to the corresponding positions and the

count value was recorded. These values were then used in the code.

The value of K_D, K_I, and K_P were also changed according to the behavior of the design.

If the design oscillated about its balance position, then the K_P value was decreased since K_P will make

the backing_force too large. If the mechanism had a steady_error for the position, then K_I was

increased, since K_I was the error accumulate with the operation of the linkage. If the linkage didn’t

move quickly enough, then the value of BASE_CMD was increased to speed up the response.

51

Section 22: Final Testing Results:

Testing Equipment Needed For Setup:

1. Mechatronics system including linkages, the motor and circuit.

2. Four laser pointers.

3. Laser Controlling Circuit and corresponding LabVIEW Files.

4. Field where laser pointers and our mechanism are mounted.

Process:

1. Fix all mechanisms and connect circuits

Three screws and spacers are used to connect the mechanism to the Arduino table. Also, the four signal-

input-wires are connected into the breadboard. The voltage for the H-Bridge is also measured to be

exactly nine volts.

2. Get the exact locations of four position.

Before testing, the input link is rotated to its initial position first, then to the second, third and

fourth position in order to measure the value of sensor counts. These values can be measured from the

left and right directions of rotation. The average of these two values will be used as the corresponding

DES_POSITION value for each of the four positions. This can guarantee this value is exactly of its balance

position.

3. Test Laser Detection Percentage

Using the LabVIEW controlling circuit, four laser beams are turned on randomly. The reflected

laser signal is caught by the target sensor and sends information to LabVIEW. After certain processing,

the laser detection percentage is calculated.

4. Test State Error

The input signal changes from position 1 to 2, 2 to 3, 3 to 4, and 4 to 1. The light signal is read

from the control panel in LabVIEW. During final testing, position 1 was not consistently reflecting the

incoming laser. All other positions worked well. The maximum steady state error is 1 ring when moving

from position 4 to position 1.

5. Test Safety

Safety was tested by covering the proximity sensor with a finger. If the code was written

correctly and the sensor was placed in a smart location, the mechanism should stop

immediately after the finger is detected.

52

Final Testing Results:

Table 12 - Volume and Transmission Angles:

Max Transmission Angle 132o

Min Transmission Angle 56o

Worst Transmission Angle Deviation 42o

Length 225mm

Width 155mm

Height 145mm

Volume 5056.875cm^3

Table 13 - Mechatronics Testing:

Reflection Accuracy Trial #1 29/40

Laser Detection Percentage Trial #1 38%





Chosen Trial for RA/LDP 2

Table 14 - Units for steady state error = # of concentric

Steady state error (1 to 2) 0 Rings




Worst Steady State Error 1 Rings

Safety (Out of 5 trials) 0/5

Craftsmanship (see Rubric) 0/10

53

Section 23: Design Critique & Evaluation:

1. What worked well? What didn’t work well? Most importantly, explain why.

The mechanism responds quickly to the input signal. The length of the links in the design are

short and the weight of links are relatively light so the moment of inertia is very small. In terms

of manufacturing, the dimension of connections was strictly controlled. This reduced the friction

a lot. In terms of electrical controlling, by testing the Arduino code, the optimum values of

parameters were found: K_I, K_P, K_D, and BASE_CMD.

The accuracy of the system didn’t work well for two major reasons. The first case is related to

backlash. When our linkage moved into one position from different directions, the final position

was not consistent. There was always a small range of error. The second reason is that the input

link would not return to its initial position. Possible explanations for this is that the

CTRL_DEAD_BAND was set to 3, which allows a minimum error in position three. Minimizing it

causes oscillation, so the error was maintained at 3.

2. How well did your design perform relative to your models? Explain what you think the

difference was.

The performance of the design was good. It matched the model well. In the model, the

acceleration time is about 1 second, which closely matched the performance. Other parameters

such as speed, after calculation and comparison, also matched well.

3. How did friction influence your built device?

Initially, friction was a big problem for the mechanism, but later the friction on the system was

reduced. Friction comes from the connection between two gears, the connection between the

linkages, and connection between linkage and grounds.

Initially, the motor gear was placed too close to the gear on the input link. This caused the

normal force between two gears to become large, which in term increased the friction. Later,

after reducing the relative positions between these two gears, this problem was resolved.

The friction between links and between the links and ground plate are small due to the tight

tolerances on the dimensions of holes and pins.

54

4. How could the control algorithm (Arduino code) be improved to make better use of the

available equipment? For example, could the position be more precisely controlled? Could you

make use of a feedforward signal? How?

The first possible improvement on the mechanism would be reducing the position error of the

input link. In the Arduino code, a minimum position error was allowed. This error creates a

difference between locations of the input link. The value in the final code is 3, but the angular

position can be more accurate by reducing the value of CTRL_DEAD_BAND. The problem with

this method is that it causes the mechanism to oscillate around its balance position. The

oscillations can be suppressed by adjusting other parameters like K_D, K_I and K_P. Reducing

K_P a little could decrease the time constant of the mechanical mechanism so that the vibration

can come stable as soon as possible.

Another possible improvement that can be made is reducing the effect of backlash.

The backlash is caused by the mechanical structure. But it can be compensated for using

software.

The method is shown in the following flow-diagram.

Figure 33: Summary of proposed Arduino sketch

Determine direction of rotation:

Determine the direction the input linkage is rotating by comparing the current position and the

next position. In order to save the position signal, two groups of variables are used.

Position_Now is used to store the current active position and Position_Previous stores the

previous position. After an input signal is obtained, it is stored in Position_Now and the value

that it replaced is stored in Position_Previous. Then the two values are compared. If

Position_Now is less than Position_Previous, the motor is turning leftward. However, if

Position_Now is greater than Position_Previous, the motor is turning rightward.

Modify the angle:

The angle of the linkage can be modified to make up for the backlash. After taking

measurements, the count of the sensor corresponding to the backlash was found to be about 5

due to the mechanism and algorithm. This discrepancy was taken into account in the program.

Wait for next input

signal

Determine direction

of rotation

Add motor

counts

Back lash is

compensated

55

5. Would there be a better way to use the sensors that were provided, or to use different sensors,

to accomplish the same objectives?

Another sensor can be used to have feedback control to have a better control of the position,

and the speed as well.

Figure 34: Proposed change of feedback sensors

The sensor is located exactly at the position that the input bar will be rotated. If the linkage is

not at the correct position, the input link will continue to rotate until the desired position is got.

In this method, since the signal feedback is set at exactly the position where the input link would

have to be, using encoder counts would no longer be necessary. Teams would also no longer

have consider backlash. The position control would be extremely accurate.

6. What other lessons or unique observations did you make about your device and the process

that you follow to develop it? Having completed it, would you do anything different – what and

why?

The team made a few large mistakes toward the completion of our device. First, the team never

set the system to calibrate itself or use the limit switches, so a significant amount of points will

be taken away for that. The team should have read the instructions more carefully and gone

through all of them before submitting the mechanism. Then, code could have been written to

calibrate the linkage

56

7. On a scale of 1-5, how would you rate the safety of your mechanism? Were the provided

sensors adequate or would additional sensors and guards be necessary?

During the testing of the mechanism, the infrared sensor had not been properly set-up and was

inoperable during the test. Even if someone put his/her hand into the mechanism, it would not

stop. If the infrared sensor had been properly installed the presence of an object would stop the

machine. Despite this mistake in design, one could not hurt themselves in our mechanism even

if he/she put a finger directly into the gears so on a scale of 1-5, the mechanism earns a 4 in

safety. The only reason it didn’t earn a 5 is because the proximity sensor did not work.

As an improvement, a different, more advanced sensor can be used. For example, the human-

movement sensor, which is shown below, can detect movement in a spherical radius. This would

be safer because the linkage could be stopped no matter which direction the movement came

from.

Figure 35: Spherical Proximity sensor that could possibly be used in the future

8. Would you recommend that we give your device to someone else right now to use and operate?

Why or why not?

The mechanism can only satisfy the basic requirements. It has a laser reflecting rate of 64% at

best during the three tests. There are several small changes the team needs to make on the

mechanism before it can be handed off to another team. A calibration routine must be

implemented, the threshold for the proximity sensor needs to be decreased and the proximity

sensor itself needs to be placed in a more effective spot on the mechanism. In addition to these

big changes, more testing is necessary to determine why our reflection rate was so low.

9. What other parts and materials would have been useful to have in your design, if you had been

given them?

A belt system could have been used to transfer power from the motor. In this case, power can

transmitted over a longer distance, which will replace the complex supporting mechanism and

power transmission mechanism that is currently employed. This kind of transmission can also

eliminate the gap between gears in our current mechanism, which can improve accuracy.

57

10. What would you do for a project next year in ME350?

A mechanism that can collect Ping-Pong balls would be very interesting.

Figure 35: Proposed change for project using ping pong balls instead of lasers and a net instead of a

mirror.

This mechanism can change to the correct position so that the ping pong ball can be collected into a bag

which is attached to the coupler linkage.

58

Appendix A: Individual Sketch Relations Design, 3D SolidWorks, and ADAMS

Analysis:

Nolan’s Individual Design

Nolan’s first design for the linkages were not intended to be used in the final design. For this reason, his

initial design in the sketch relations was very simple. All of the Links are rectangles with no rounded

edges, the transmission angle deviations aren’t as small as they could have been, and the link lengths

are not nice numbers that would be easy to manufacture in the ME machine shop. In his sketch relations

design, the pivots in the ground plate are actually located outside of the plane of the through and

tapped holes in the arena. For this reason, Nolan designed his ground plate to extend beyond the plane

of the holes, but still within the boundary of the table.

Nolan’s SolidWorks model is also very simple. For the purpose of lab, he did not include fasteners or

assign materials to his parts. Because the SolidWorks model was transported into ADAMS, the ADAMS

model is just as simple. For his simulation, Nolan assigned a constant 5 N-mm torque to take place over

0.5 seconds. He chose the torque because he thought it was a realistic value for the given motor, but he

did not verify the value with the motor specifications. He chose a 0.5 second simulation time with 200

frames because it made the simulation run smoothly.

Shown below are the details of the first revision of Nolan’s design

Linkage Sketch

Table A1 - Nolan’s Link Lengths (in inches):


4.07 3.03 3.85

Table A2 - Transmission Angles for all four Positions (in degrees)




25.40 2.09 26.74 64.03

59

Figure A1: Nolan’s Initial Transmission Angle Sketch

Lane 1 Lane 2

Lane 3

Lane 4

60

SolidWorks Model

Figure A2: Nolan’s Initial Design in Leftmost Position (the object attached to coupler is the mirror)

The four bars attached to the bottom of the ground plate were initially designed to fit into the four

corner holes in the arena.

Figure A3: Nolan’s Initial Design in Rightmost Position

61

Nolan’s ADAMS Model

Figure A4: ADAMS Model with Constraints and Input Torque

62

Nolan’s ADAMS Simulation Graphs: Angular Position and Angular Velocity

Figure A5: Angular Position of Links

Figure A6: Angular Velocity of All Three Links

63

Nolan’s ADAMS Simulation Graphs: Input Torque and Power in Input Link

Figure A7: Input Torque

Figure A8: Power in Input Link

64

Yuzhou’s Individual Design

Yuzhou’s design is easy to be manufactured and the length of the links are small, averaging 5 inches.

However, the coupler and the follower don’t have the same length and therefore, it increases the effort

of manufacturing. That’s why the team decided use Nolan’s linkage design. Nolan’s design gave the

input and follower having the same length, which decreases the amount of working and manufacturing.

The transmission angles are reasonable and only hard to drive the follower link when in the fourth

position. The linkage design method is exactly the same as others by 2D SolidWorks drawing, it just

about pulling the ground pivots to a reasonable position. Besides, the location of ground pivots are

reasonable close within the area of the ground plate.

Yuzhou doesn’t draw any bots or joint design in the SolidWorks model because it is easier to analyze

when exported to the Adams. Yuzhou plots the power output, input angle displacement, and the

angular velocity, which is a very good estimate of the system dynamics when the parts and components

are not been produced. The power output is big and the angular velocity is good.

Linkage Sketch

Below are the details of Yuzhou’s design.

Table A3 - Yuzhou’s Link Lengths (in inches):


6.63 3.37 5.00

Table A4 - Yuzhou’s Transmission Angles for all four Positions (in degrees)




13.63 20.00 29.35 48.24

65

Figure A9: Yuzhou’s Initial Transmission Angle Sketch:

Lane 2 Lane 3

Lane 1 Lane 4

Target

Input Link

Coupler Link

Follower Link

66

SolidWorks Model

Figure A10: Yuzhou’s Initial Design in Leftmost Position

Figure A11: Yuzhou’s Initial Design in Rightmost Position

67

Yuzhou’s ADAMS Model

Figure A12: ADAMS Model with Constraints and Input Torque

68

Figure A13: Input Angular Displacement

Figure A14: Velocity Profile

69

Figure A15: Power Output

Figure A16: Torque Input

70

Zhentao’s Individual Design

Zhentao’s design is use plates instead of single bars to serve as links, which can increase the

stability of the structure when links are moving. But on the other hand, this design might

increase the weight, which makes the acceleration of links slower.

Also, in the revised design, the length of links are shorten in a large extend, on the one hand,

weight is no longer the short board, on the other hand, the angle the input link need to rotate

increases greatly.

Table A5 - Zhentao’s Link Lengths

Link Length [in]

Input Link 8.00

Coupler Link 3.00

Follower Link 8.00

Table A6 - Zhentao’s Transmission Angle and Deviation

Position Transmission Angle[degree] Angle Deviation [degree]

Position 1 (Left Most) 55.23 34.77

Position 2 72.20 17.80

Position 3 86.66 3.34

Position 4 (Right Most) 79.88 10.12

71

Figure A17: The Overview of Mechanism

Lane 2

Lane 1 Lane 4

Lane 1

Lane 1

Lane 1

Lane 1

Lane 3

Target

Lane 4 Lane 1

Lane 1

Lane 1

Lane 1

Lane 1

Lane 1

Lane 1

Lane 1

Coupler Link

Follower Link Input Link

72

Figure A18: Label of Links and Positions

Figure A19: Dimension of Mechanism

73

SolidWorks Model

Figure A20: Zhentao’s Initial Design in Leftmost Position

Figure A21: Zhentao’s Initial Design in Rightmost Position

74

Figure A22: Angular Velocity:

Figure A23: Angular Position:

75

Figure A24: Torque Input:

Figure A25: Power Output:

76

Justin’s Individual Design

Justin’s design was built with the intent to be easy to manufacture. The Links are set at lengths that have

an exact value and can be milled to exact dimension. The rounded corners allow the links to rotate

smoothly without needing to worry about running into other parts on the base plate. The linkages are

not hollowed out which makes them heavier than needed. The thought was that if this design was

picked modifications could be made to decrease the weight. In the sketch relations diagram, Justin

attempted to keep the pivots of the linkage within the confines of the mounting holes.

This would allow the linkage to be easily attached to a relatively small base plate.

The SolidWorks model does not include the fasteners or bearings that would need to be present in the

final design. This was intended to keep the model simple and allow it to be easily modified. The ADAMS

model is the same as the SolidWorks model. Because ADAMS is a new simulation tool that has not been

previously used by the team, it was best to keep the model simple so that the desired results were

obtained without too many errors. The motion used to govern the movement of this design was chosen

to reflect the one done in the tutorials. 1 second was chosen as the movement time because this

seemed fast enough to respond to the laser changes.

Below are the details of Justin’s design.

Table A7 - Justin’s Link Lengths (in inches):


8.00 2.50 6.35

Table A8 - Justin’s Transmission Angles for all four Positions (in degrees)




10.02 9.22 25.83 41.00

77

Figure A25: Justin’s Initial Transmission Angle Sketch

Lane 4

Lane 1

Lane 2

Lane 3

78

SolidWorks Model

Figure A26: Justin’s Initial Design in Leftmost Position

Figure A27: Justin’s Initial Design in Rightmost Position

79

Justin’s ADAMS Model

Figure A28: ADAMS Model with joints, friction, and input movement based on acceleration.

80

Justin’s ADAMS Simulation Graphs: Angular Position and Angular Velocity

Figure A29: Angular Position

Figure A30: Angular Velocity

81

Justin’s ADAMS Simulation Graphs: Input Torque and Power in Input Link

Figure A31: Input Torque

Figure A32: Power in Input Link

82

Appendix B: Drawings, Manufacturing Plans, Bill of Materials, and Assembly

Plan for Final Design

Coupler Link

Figure B1: Drawing for coupler link

83

Table B1 – Coupler Link Manufacturing Plan

Manufacturing Plan

Part Number: ME350 - 001 Revision Date: 9/27/2014

Part Name: Coupler

Team Name: Team 64

Raw Material Stock: Stock 0.25 x 12 x 18 Aluminum Plate

Step # Process Description Machine Fixtures Tool(s) Speed

(RPM)

1 Cut on Waterjet Waterjet standard standard n/a

2 Find x and y datums Mill vice, parallels

0.25'' edge finder

800

3 center drill pivot hole Mill vice, parallels

center drill 800 or less

4 Drill pivot hole Mill vice, parallels

5/16 drill bit* 800

5 Ream pivot hole Mill vice, parallels

5/16 reamer* 150

6 repeat step 3-5 for other pivot hole

n/a n/a n/a n/a

11 Remove part, return all tools and fixtures to crib

n/a n/a n/a n/a

84

Ground Plate:

Figure B2: Drawing for Ground Link

85

Table B2 – Manufacturing Plan for Ground Link

Manufacturing Plan


Part Name: Ground link / Ground Plate

Team Name: Team 64

Raw Material Stock:

Stock 0.25 x 12 x 18 Aluminum Plate

Step # Process Description Machine Fixtures Tool(s) RPM


2 find x and y datums Mill vice, parallels 0.25'' edge finder 800

3 Center drill one corner hole

Mill vice, parallels center drill 800

4 Drill one corner hole Mill vice, parallels 3/8 drill bit 800

5 repeat step 3 and 4 for other two corners

n/a n/a n/a n/a

7 Center drill one pivot hole


8 Drill one pivot hole Mill vice, parallels 10-24 drill bit 800

9 tap pivot hole Mill vice, parallels #25 tap drill 150

10 repeat steps 6-8 for other pivot hole

n/a n/a n/a n/a

11 Center drill one stop hole Mill vice, parallels center drill 800

12 Drill one stop hole Mill vice, parallels 10-24 drill bit 800

13 Tap the stop hole Mill vice, parallels 0.25'' tap hand

14 repeat steps 11-13 n/a n/a n/a n/a

15 file sharp edges n/a n/a file n/a


n/a n/a n/a n/a

86

Input / Follower Link:

Figure B3: Drawing for input/follower link

87

Table B3 – Manufacturing plan for Input / Follower Link

Manufacturing Plan


Part Name: Input / Follower Link

Team Name: Team 64

Raw Material Stock:

Stock 0.25 x 12 x 18 Aluminum Plate

Step # Process Description Machine Fixtures Tool(s) Speed

(RPM)


2 Find x and y datums Mill vice, parallels 0.25'' edge finder

800

3 center drill pivot hole Mill vice, parallels center drill 800 or less

4 Drill pivot hole Mill vice, parallels 5/16 drill bit* 800

5 Ream pivot hole Mill vice, parallels 5/16 reamer* 150

6 repeat step 3-5 for other pivot hole

n/a n/a n/a n/a

7 Center Drill one hole for end of slot


8 Drill one for end of slot Mill vice, parallels 1/4'' Drill Bit**

800

9 Repeat steps 8 & 9 for each end of each slot

n/a n/a n/a n/a

10 Mill Slots Mill vice, parallels 1/4'' end mill* 800

11 (INPUT LINK ONLY) Ream slot

Mill vice, parallels 1/4'' reamer* 150


n/a n/a n/a n/a

88

Bill of Materials:

Part Name Part Number Quantity Supplier Cost Notes

Aluminum Plate, 1/4" x 12" x 18"

9246K45 1 McMaster-Carr Supp.

SAE 841 Sleeve Bearing for 1/4" Shaft Diameter


Needle Thrust Bearing, Bore .250

4XFL8 6 Grainger Supp.

Shoulder Screw, 1/4" Diameter x 1/2" Shoulder, 10-24 Thread

91259A537 4 McMaster-Carr Supp.

SAE 841 Washer for 1/4" Shaft Diameter, 5/8" OD, 1/16" Thick


Socket Head Cap Screw, 3/8"-16 Thread, 2-1/2" Length


Washers, 3/8" 91083A031 2 McMaster-Carr Supp.

Nuts, 3/8-16 97149A200 2 McMaster-Carr Supp.

1/4" ground and polished steel dowel pins

Various 2 McMaster-Carr Supp.

*Supp. (Supplied in kit) Purchased parts total cost: $0.00

89

Assembly Manual:

Materials are listed above in the part table with graphs. First, connect the coupler with the input and

output links, and then fix the links to the ground plate. At last after fixing the hard stops, fix the whole

ground plate to the table. The whole process is exactly shown below.

Table B-4 List of Components in the assembly manual

1 Shoulder Screw, 1/4" 2 SAE 841 Washer for 1/4" Shaft Diameter 3 SAE 841 Sleeve Bearing

4 Needle Thrust Bearing

5 Nuts, 3/8-16

6 Washers, 3/8"

7 Hard Stop

Input link

Coupler link

Follower link

1

2

3

2

4

2 5

90

1. Assemble input and coupler links. Shoulder bolt and accompanying washers

2. Install the shoulder bolt through the hole and fix the input link and the coupler together.

3. Repeat 1, 2 to connect the output link and the coupler.

2

3

1

2 4

6

5

91

4. Glue the mirror onto the middle of the coupler.

5. Align a SAE 841 washer, a 1/4’’ needle thrust bearing, a SAE 841 washer, the rectangular end of

the input link outside the sleeve bearing, a SAE 841 washer in order from the bottom to the top.

Meanwhile, do the same to connect the rectangular end of the output link and the ground plate

together.

5

Mirror

Coupler Link

Follower

link

Coupler link

6 3

4

2

2

1

92

6. Install the shoulder bolt through the hole and fix the input link to the ground.

7. Fix two hard stops by installing a 1/4’’ screw at the bottom.

Input link

Input link

1

4

2

2

3

93

8. Align the three corner holes of the ground plate with the given table setup.

9. Install three socket head cap screws to fix the ground plate to the table.

10. The Assembly is completed. Test the stability of the linkages and screw tightly the bolts if

necessary.

7

94

Appendix C: Approval Packages, Bill of Materials, and Assembly Plan for

Transmission Design:

Ground Bracket:

Figure C1: Drawing for Ground Bracket

95

Table C1 – Manufacturing Plan for Ground Bracket

96

Connecting Bracket

Figure C2: Drawing for Connecting Bracket

Table C2 – Manufacturing Plan for Connecting Bracket

97

Motor Bracket:

Figure C3: Drawing for Motor Bracket

Table C3 – Manufacturing Plan for Motor Bracket

98

Input Link Shaft:

Figure C4: Drawing for Input Link Shaft

Table C4 – Manufacturing Plan for Input Link Shaft

99

Motor Shaft Coupler:

Figure C5: Drawing for Motor Shaft Coupler

Table C5 – Manufacturing Plan for Motor Shaft Coupler

100

Hat:

Figure C6: Drawing for Hat

Table C6 – Manufacturing plan for Hat

101

Table C7 - Bill of Materials:


32 Tooth Gear 57655K42 1 McMaster-Carr 7.74

20 Tooth Gear 57655K36 1 McMaster-Carr 6.51

29:1 Metal Gearmotor 37Dx52L mm with 64 CPR Encoder

1443 1 Pololu Supp.

L-Bracket Pair for 37D mm Metal Gearmotors

1084 1 Pololu Supp.

Aluminum Angle, 2.5" x 2" x 1/4" thick, 6" long

Custom 1 McMaster-Carr Supp.

1/4" ground and polished steel dowel pins

Various 2 McMaster-Carr Supp.

Washers (3/8" hi-collar spring lock)


Screws 4-40 for motor Various 4 McMaster-Carr Supp.

10-32 Screws Various 6 McMaster-Carr Supp.


102

Assembly Manual:

Table C-8 List of Components in the assembly manual

3 SAE 841 Sleeve Bearing

8 Input Link

9 10-32 Screws

10 10-32 Nuts

11 Motor

12 Shaft Head

13 Rotating Shaft

1. Press fit the bronze bushing into the hole of the input link.

2. Pass the shaft through the hole and press fit the 20 teeth gear onto the shaft.

3

13

103

3. Press fit the 20 teeth gear onto the shaft and press fit the head onto the shaft above the gear.

4. Slip fit the washer bearing washer onto the shaft.

8

104

5. Assemble the linkages to the ground plate

6. Assemble the two screws to combine the one right angle stand with the vertical stand together.

Linkage

Ground Plate

9 10

105

7. Assemble the motor shaft into the right angle stand. Assemble the gear and the motor together

by both press fitting into the dowel pin.

8. Assemble the right angle stand onto the vertical stand and the lower right angle stand

Vertical stand

Right angle stand

Lower stand

11

12

106

9. Assemble the screws onto the stand and thus finishing assembly the whole stand for motor.

10. Assemble the two screws to fix the stand on the ground plate.

Stand

Ground

plates

9

9

10

9

12

9

107

Appendix D: Wiring Diagram, Arduino Code, Calculations, and Bill of Materials

for Safety & Motor Controls:

Wiring Diagram:

Figure D1: Wiring diagram for controlling circuit

The symbol legend for the wiring diagram has been provided on the following page.

108

Figure D2: Legend for circuit diagram

109

Arduino Code:

110

111

112

113

Calculations:

𝐶𝑜𝑢𝑛𝑡𝑠 =64 𝑐𝑜𝑢𝑛𝑡𝑠

1 𝐸𝑛𝑐𝑜𝑑𝑒𝑟 𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛∗ 𝑀𝑜𝑡𝑜𝑟 𝑅𝑎𝑡𝑖𝑜 ∗ 𝑇𝑟𝑎𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑅𝑎𝑡𝑖𝑜 ∗

𝜃𝑙𝑖𝑛𝑘

360𝑜

𝐶𝑜𝑢𝑛𝑡𝑠 = 64 ∗ 29 ∗ 0.625 ∗𝜃𝑙𝑖𝑛𝑘

360𝑜

𝐶𝑜𝑢𝑛𝑡𝑠 = 1160 ∗𝜃𝑙𝑖𝑛𝑘

360𝑜

𝜃1 = 0𝑜 , 𝜃2 = 14𝑜 , 𝜃3 = 40𝑜 , 𝜃4 = 55𝑜









Bill of Materials:


Infrared Proximity Sensor, short range

GP2D120XJ00F 1 Sparkfun Supp.

Snap Action Switch 187733 2 Jameco Supp.

Toggle Switch Single Pole Single Throw

76523 1 Jameco Supp.

400-point Breadboard 351 1 Pololu Supp.

Arduino Uno Microcontroller board

DEV-09950 1 Sparkfun Supp.

H-bridge (L298 Motor Driver)

K CMD 1 Solarbotics Supp.

Mounting Board Custom 1 N/A Supp.

Wire Various N/A N/A Supp.


1 ME350 Fall Semester FINAL DESIGN REPORT

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