This document describes the design of a cam and follower mechanism to pump peanut butter onto cookies. Three designs were considered and evaluated. The final design uses a cam with a prime radius of 70mm and follower displacement of 10mm over 180 degrees of cam rotation. Calculations were done to determine the required piston diameter and spring properties. Solidworks models were created of the nozzle and packaging for the mechanism. The design aims to meet specifications such as pumping 0.4cc of peanut butter per cookie at a rate of 600 cookies per minute.

1. 1
REPORT
as partial requirement
for
the course on
KINEMATICS OF MECHANISMS
ME 3310, A’16
DESIGN PROJECT TITLED:
DESIGN OF PEANUT BUTTER EXTRUDING CAM AND FOLLOWER PISTON
MECHANISM
Submitted by:
Group 19
Robert Boulanger - rdboulanger@wpi.edu
Constantine “Tino” Christelis - cschristelis@wpi.edu
Yuxin Gao - ygao3@wpi.edu
Nathaniel O’Connor - njoconnor@wpi.edu
Submitted to:
Prof. Onal Cagdas
DEPARTMENT OF MECHANICAL ENGINEERING
WORCESTER POLYTECHNIC INSTITUTE
WORCESTER, MA 01609-2280
10/9/2016
Project Score: TOTAL: _______ out of 100%

2. 2
Abstract
The goal of this project aims to design a cam and follower mechanism to pump 0.4 cc of
peanut butter onto cookies moving along a conveyor belt at a constant speed. Using our
understanding of mechanisms from our studies in ME 3310, discussions with Professor Onal,
and research on designs relevant to our purpose, we have developed a design that would satisfy
the necessary task specifications. Our final design utilized a kick period of 50 degrees, followed
by 180 degrees of constant velocity, a sniff period of 50 degrees, and finally 80 degrees of
constant velocity return.

3. 3
Table of Contents
Abstract 2
Table of Contents 3
Authorship Page 5
Introduction 6
Background 6
Goal Statement 8
Task Specifications 8
Ideation and Design 9
Design 1 9
Figure 1. Design 1 SVAJ Plot in Dynacam10 9
Design 2 9
Figure 2: Design 2 SVAJ Plot in Dynacam10 10
Design Comparison 10
Figure 3: Initial Design Comparison 11
Design 3 11
Figure 4: Velocity Calculations in Mathcad15 12
Figure 5: Design 3 SVAJ Plot in Dynacam10 12
Figure 6: Design 3 Displacement Plot in Dynacam10 13
Figure 7: Design 3 Velocity Plot in Dynacam10 13
Figure 8: Design 3 Acceleration Plot in Dynacam10 14
Figure 9: Design 3 Jerk Plot in Dynacam 10 14
Figure 10: Design 3 Cam Profile in Dynacam10 15
Package Design 16
Figure 11: Piston Diameter Calculation in Mathcad15 16
Figure 12: Final Design Kinetostatic Force in Dynacam10 16
Figure 13: Spring Calculations in Mathcad15 17
Figure 14: Design of Nozzle in SolidWorks2015 18
Figure 15: Design of Package in SolidWorks2015 18
Figure 16: Cross-Section View of Package in SolidWorks2015 19
Analysis of Final Design 20
Figure 17: Final Design Φ and ⍴ Plot in Dynacam10 20
Conclusion 21
Bibliography 22

4. 4
Appendices 23
Appendix 1: Design 1 Continuity Check, Boundary Conditions, and Segment Overview 23
Appendix 2: Design 1 Pressure Angle and Radius of Curvature 28
Appendix 3: Design 2 Continuity Check, Boundary Conditions, and Segment Overview 29
Appendix 4: Design 2 Pressure Angle and Radius of Curvature 31
Appendix 5: Design 3 Continuity Check, Boundary Conditions, and Segment Overview 32
Appendix 6: Design 3 Polynomial Functions 35
Appendix 7: Design 3 Pressure Angle and Radius of Curvature 37

5. 5
Authorship Page
Section Author Editor
Abstract Rob Boulanger Nathaniel O’Connor
Introduction Yuxin Gao Nathaniel O’Connor
Rob Boulanger
Background All All
Goal Statement Rob Boulanger All
Task Specifications Rob Boulanger
Yuxin Gao
All
Design 1 Nathaniel O’Connor Tino Christelis
Design 2 Tino Christelis All
Design Comparison All All
Design 3 Tino Christelis Nathaniel O’Connor
Package Design Tino Christelis
Yuxin Gao
Nathaniel O’Connor
Analysis of Final Design Tino Christelis All
Conclusion Nathaniel O’Connor Rob Boulanger
Bibliography Rob Boulanger N/A
SolidWorks Modeling Tino Christelis N/A

6. 6
Introduction
One of the most advanced cookie manufacturers in the world provided fresh cookies to
the local people for several years. To offer better service to their customers, this company plans
to make a new flavored cookie by spreading peanut butter on it. The company does not want the
rate of cookie production reduced by this additional process. Therefore, 600 cookies should
receive a coating of peanut butter per minute. The cookies’ centers are spaced 40-mm apart on a
constant-velocity conveyor. 0.4 cc of peanut butter will be applied to each cookie as a 1-mm
thick square patch when the cookie passes by a nozzle. The factory doesn’t want to change the
previous production line, so this mechanism should be able to fit around the existing conveyor
belt. We need to design a simple cam and follower-piston mechanism to work as a pump to
finish the task.
Background
The product that this project design surrounds is peanut butter. Peanut butter is a food
paste and spread made primarily from ground dry roasted peanuts (Wiki, 2016). The peanuts are
crushed down and added into a mixer with powdered sugar. After the mixture is stirred into a
sticky and smooth paste, peanut oil is added and mixed until the viscosity is just right (Baidu
Encyclopedia, 2016). The normal viscosity of peanut butter under room temperature (70F) is
250,000 cps (Viscosity Table, vp-scientific.com). In this project, the CAM mechanism will pump
peanut butter onto the cookies as they pass by the nozzle on the conveyor belt.
One design on the market that performs a function similar to what we are looking for is
used for spread sauce on sandwiches. The cycle functions similarly to our project problem in that
the product is moving at a constant rate along the conveyor belt and needs to be applied the sauce
on each of product fast and continuously and maintain constant distance between each piece of
product before and after getting sauce. The amount of sauce output can be controlled and
changed (GS Italia - Linea Panini, https://youtu.be/uqBpNBV3-pw). But this design uses
computer-controlling system, not CAM mechanism as asked of us.

7. 7
During our research, we found a patent for a piston on a cam follower used for a
hydrostatic pump (Cunningham, 1974). It describes using a low friction material for the bearing
for the cam follower. It is shaped in such a way that the low friction bearing locks around the
piston. This patent is essentially one of the first designs for a similar application to our project.
In order to gain a better understanding of cam analysis, we referenced a brief paper
detailing optimal cam and follower designs which analyzed polynomial curves using F.E.M. in
ANSYS 10 to determine the best way to minimize the effects of impact and high contact loads
(Al-Shamma, 2010). For the purposes of this project, we did not need to perform such in depth
analysis, but it gave us a general idea about conditions to avoid and how to properly size our cam
relative to the follower to reduce stress and deflection.
Before we began drafting our first designs, we performed preliminary calculations that
would help us later on in the design and analysis process. Given the number of cookies being
produced per unit of time (600 cookies/min), we can divide this by 60 to get cookies per second
(10 cookies/sec), which then gives us one cookie every 0.1 second. This means that the entire
cycle must be completed and repeated every 0.1 second. With the cam performing one cycle
every 0.1 second, we found the necessary angular velocity of the cam by dividing 2π by 0.1
second. This gave us an angular velocity of 62.832 rad/s.
In talking with Professor Onal, we were able to better understand the principles of
mechanism which would be completing this task. One such principle being the principle of
maximizing mechanical advantage by increasing eccentricity of the cam-follower, and that
regulations regarding maximum Φ angles are actually a bit looser than we originally thought.

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Goal Statement
Design a cam and follower mechanism to pump peanut butter onto cookies moving along
a conveyor belt.
Task Specifications
● The motion of pump will be achieved by machine composed of cam, follower, spring and
piston.
● The roller follower has diameter of 20mm and mass of 0.5kg.
● The nozzle is a 1mm*20mm rectangle.
● Peanut butter should be pumped on 600 cookies per minute.
● Peanut butter pumped on per cookie is 1mm thick square.
● Peanut butter pumped on per cookie is 0.4cc.
● Cam undergoes a constant angular velocity of 62.832 rad/s.
● Cycle of operation is performed in 0.1 sec
● Pumping the peanut butter onto the cookie occurs within 0.05 sec of the cycle
● Cam design reflects that the kick velocity is 3 times the steady state velocity, and the
sniff velocity is -4 times the steady state
● Cookies must maintain a separation of 40-mm between the center of each piece, both
before and after receiving peanut butter.
● All designs and peanut butter pump must be OSHA and FDA compliant
● Cam operates on a forced-closed system
● Functions for displacement, velocity, and acceleration are continuous, jerk is finite
● The spring has a negligible mass and is continuously under some magnitude of
compression
● Spring should have infinite life under fatigue
● Peanut butter is only assumed compressible under constant velocity
● Peanut butter undergoes no displacement during “kick” and “sniff” periods

9. 9
Ideation and Design
Design 1
Our first design was created in such a way that both the kick and sniff were to be short
durations of constant velocity. The longer constant-velocity portions of the piston movement
were for 140 degrees of cam rotation, while the constant-velocity kick and sniff were 20 degrees
each. The four constant velocity segments were each connected with 10 degree segments of
acceleration. This was done under the initial assumption that the kick and sniff were required to
have a certain constant-velocity duration. Polynomials were chosen for all 8 segments of this
design in order to make sure all boundary conditions were met. Polynomials we required for the
constant velocity segments, so the acceleration portions had to have the same boundary
conditions as the beginning and end of those segments.
Figure 1. Design 1 SVAJ Plot in Dynacam10
Design 2
Our second design approached the kick and sniff steps from a different angle. Instead of
assuming the kick and sniff velocities to be constant for a long duration, the assumption was

10. 10
made that the kick and sniff velocities were speed minimums that the follower should surpass for
a short amount of time. This assumption allowed us to treat the kick and sniff periods as
polynomials, with boundary conditions at their ends and mid-beta. Halfway through the
kick/sniff (mid-beta), a velocity condition was set to be at least 3 times or four times great for the
kick and sniff respectively. The “extrusion” of peanut butter for this design was assumed to be
proportional to total displacement, resulting in having the first two and last two beta segments
each adding to 180 degrees of cam rotation.
Figure 2: Design 2 SVAJ Plot in Dynacam10
Design Comparison
To fairly compare the two designs, each of the design’s maximum values that we wanted
to compare was divided by that designs maximum displacement. This allowed us to compare the
designs regardless of the fact that each design called for the follower to move different lengths.
The calculations, considerations, and results from this process are shown below (note that in the
figure, “Design 3” actually refers to “Design 1”).

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Figure 3: Initial Design Comparison
Design 1 ended up minimizing velocity relative to our other designs, but had a
significantly higher acceleration. This higher acceleration was due to the kick and sniff requiring
a much shorter duration to reach their constant velocity, rather than just peaking at a high
velocity during the entire kick duration. The velocity was lower, but not nearly as significantly
lower because it still needed to cover a similar displacement over the kick and sniff periods.
Regardless of the design, this mechanism would be required to operate for millions of
cycles without experiencing wear and fatigue. Since we wanted to focus on the long term life of
this mechanism, we decided that a lower acceleration would be better suited for this kind of
application.
And so, we decided that Design 2 would be the best approach to this problem, and used
the designs beta values, function type, and boundary conditions as a template for the next
iteration of design.
Design 3
The first design change that would have to be made for the next iteration would be a
correction of the beta values, as it was learned late into the design process that peanut butter is
NOT displaced during the kick and sniff periods. This meant that the follower’s constant velocity
movement had to be recalculated, as it went from being done in 120 degrees to having a cycle

12. 12
length of 180 degrees. Assuming a 10mm displacement of peanut butter was desired, the new
velocity required for this movement was calculated using the below functions.
Figure 4: Velocity Calculations in Mathcad15
With the velocity conditions calculated, the boundary conditions for all the polynomials
were determined and entered into Dynacam10. Below are screenshots of the resulting SVAJ
plots. Full details on boundary conditions and polynomial coefficients are available in the
Appendix.
Figure 5: Design 3 SVAJ Plot in Dynacam10

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Figure 6: Design 3 Displacement Plot in Dynacam10
Figure 7: Design 3 Velocity Plot in Dynacam10

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Figure 8: Design 3 Acceleration Plot in Dynacam10
Figure 9: Design 3 Jerk Plot in Dynacam10

15. 15
The next step was to physically size the cam. With a total piston displacement of 15mm,
a cam prime radius of at least 4 times this displacement is ideal. To be safe, a prime radius of
70mm was chosen (10mm longer than the minimum requirement). While increasing the
eccentricity of the follower-cam system produces a greater mechanical advantage, and thus
lowers motor torque requirements, we decided not to add such a feature to the system. The
rationale behind this decision was that the small increase in mechanical advantage would not be
worth the trouble of an added layer of tolerance and thus possibility for error in the machining
and assembly of the package. The visual representation of the cam-follower system showing
these final design parameters is shown below.
Figure 10: Design 3 Cam Profile in Dynacam10

16. 16
Package Design
With the cam design finalized, the other aspects of the mechanism could be determined.
Given the volume of peanut butter that must be displaced, and given that the follower moves
(and displaces peanut butter) 10 mm, we were able to calculate the piston diameter.
Figure 11: Piston Diameter Calculation in Mathcad15
The most important part of the mechanism, second to the cam itself, is the spring. The
spring is placed between a grounded surface and the follower, ensuring that the cam-follower
system is “force closed”. First, the preload the spring exerts on the follower had to be
determined. This was estimated by changing the preload value in the “dynamics” tab of
Dynacam10 until all forces present on the follower throughout the cam cycle were greater than
zero. What this means, is that the follower is constantly forced into contact with the cam,
regardless of how much force the cam is exerting on the follower as it is equalized by the spring.
Figure 12: Final Design Kinetostatic Force in Dynacam10

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For our chosen cam design, the required preload force was approximately 150 Newtons.
This means that a spring must apply 150 Newtons of force on the follower, keeping it tangent
with the cam, when the system is static. To do this, said spring must not be at its free length, but
rather be compressed a small, arbitrary amount. We chose a deflection of 5mm. From here, we
could calculate the required spring constant, and choose a spring from the tables in Appendix D
of Norton’s “Design of Machinery”. It should be noted that the spring constant was not the only
constraint, as springs have other parameters that must be taken into consideration. These
parameters include maximum deflection, maximum load, and under what deflection the spring
will work free. As a general design precaution, higher wire diameters were more appealing, as
springs will generally have longer life spans the thicker the wire diameter.
Figure 13: Spring Calculations in Mathcad15

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0.4cc of peanut butter will be pumped by a cylinder-shaped piston, and come out through
the rectangle-shaped outlet. According to calculation, an outlet of 1mm*20mm is best to meet
the demand. We designed a nozzle that adapts the cylinder-shaped input port to the rectangle-
shaped outlet.
Figure 14: Design of Nozzle in SolidWorks2015
With the cam, follower, piston, spring, and nozzle all fully defined, we have a complete
system of parts ready for packaging. In an ideal design, linear bearings would be positioned
along the length of the piston-follower, supporting its weight, taking all shear forces delivered
from the cam, and generally keeping it concentric with the peanut butter cylinder. However, due
to the scale of the system, these components were not modeled, but their presence should be
assumed. Below is a model of the complete package for the system, as well as a cross-section
labeled diagram.
Figure 15: Design of Package in SolidWorks2015

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Figure 16: Cross-Section View of Package in SolidWorks2015

20. 20
Analysis of Final Design
With the cam completely defined, analysis was required to check for acceptable pressure
angles and curvature radii. Large pressure angles are unideal, as a large pressure angle means the
cam surface is starting to put force on the follower at an angle non-collinear with the followers
allowed axis of motion. The smaller the pressure angles, the less force is “wasted”, and the less
torque is required by the motor driving the cam. As calculated by Dynacam10 and shown below,
pressure angles never exceed +/- 10 degrees, which is more than substantial.
Radius of curvature is another important aspect of cam analysis. If the radius of curvature
is ever smaller than the radius of the follower and concave, then the follower is unable to follow
the cam surface through the rotation, as it physically could not be tangent to such a surface. If
radius of curvature is smaller than follower radius and is convex, then the follower will move
unpredictably over the cusp, and possibly damage the cam surface. The Dynacam10 screenshot
from below shows that we have minimum concave and convex radius of curvature values of
~933mm and ~46mm respectively. Both of these values are over four times greater than the
follower radius, which makes our design not only functional, but also highly optimal since ρ
values are recommended to be at least 3 times greater than the follower radius (Norton, pg.459).
Figure 17: Final Design Φ and ⍴ Plot in Dynacam10

21. 21
Conclusion
Our final design consists of a cam and follower characterized by four polynomial
sections, two of which are constant velocity, and two of which are a kick and sniff that accelerate
the follower. The extending and retracting constant velocities are not equal and opposite, due to
the need to have peanut butter extruded for exactly half of the cycle. The displacement, velocity,
and acceleration functions are all continuous, with a total peanut butter displacement of 10mm.
This cam and follower design satisfies the kick, sniff, and constant velocity requirements
to extrude peanut butter onto cookies at the proper rate and timing. The design meets all of our
task specifications, but there are other ways in which it could be improved and optimized. The
places which are a concern are with the sniff portion, as well as potentially the tolerances of the
cam radius.
An undesired effect that occurred while reiterating design 2 into design 3 is that the sniff
segment became slightly distorted, with the velocity actually falling below the constant retraction
velocity briefly. This should not have any real effect on the outcome of the process, as during the
kick and sniff the peanut butter undergoes no displacement. It does however introduce
unnecessary acceleration to the cam and follower, which in turn will cause fatigue sooner in its
life cycle. In a further iteration of this design, a better polynomial function could be selected in
order to minimize the acceleration during this segment.
An additional concern is with how the design will wear after use and with tolerances
while manufacturing the cam. Since the total displacement is only 10mm, if the cam wears down
enough over thousands of cycles, the device will no longer extrude enough peanut butter onto the
cookies. Also, after many cycles, the spring will begin to fatigue and will no longer hold the
follower to the cam as strongly. If this system were to be manufactured, very strict tolerances
would be required to make sure the cam functions as intended. A future design could fix this
issue by using a larger displacement with a smaller piston. In addition, by increasing the cam
prime radius to a greater value, more control can be had over accurate machining of the cam
surface, resulting in actual follower motion that more accurately fits with what we
mathematically designed.
Besides the minor secondary concerns as described above, this design fulfills all task
specifications and accomplishes the company’s project goal with a highly optimized cam and
follower system.

22. 22
Bibliography
Al-Shamma F. Mustafa F. Salimann S. An Optimum Design of Cam Mechanisms with Roller
Follower for Combined Effect of Impact and High Contact Loads. Al-Khwarizmi
Engineering Journal, Vol6, No. 4, PP 62-71. 2010. Retrieved from
http://www.iasj.net/iasj?func=fulltext&aId=2181
Cunningham, S,Firth, D,Wells,J. "Cam Follower Piston". Patented 1974: US3783749
[Michele Scandroglio]. (2011, April, 14). GS Italia - Linea Panini. [Video File] Retrieved from
https://www.youtube.com/watch?v=uqBpNBV3-pw&feature=youtu.be
Norton, R. L. (2012). Design of Machinery – An Introduction to the Synthesis and Analysis of
Mechanisms and Machines. New York, NY: McGraw-Hill.
Peanut Butter. (2016, Oct 7). Retrieved from https://en.wikipedia.org/wiki/Peanut_butter
Viscosity Tables. (n.d.). Retrieved October, 2016, from http://www.vp-
scientific.com/Viscosity_Tables.htm
花生酱. (n.d.). Retrieved October, 2016, from http://baike.baidu.com/item/花生酱
/8544484?fr=aladdin
Programs and Software Used
Mathcad15 - for calculation presentation
Dynacam10 - for cam design and analysis
SolidWorks2015 - for package design and product visualization

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Appendices
Appendix 1: Design 1 Continuity Check, Boundary Conditions, and Segment Overview

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25. 25

26. 26

27. 27

28. 28
Appendix 2: Design 1 Pressure Angle and Radius of Curvature

29. 29
Appendix 3: Design 2 Continuity Check, Boundary Conditions, and Segment Overview

30. 30

31. 31
Appendix 4: Design 2 Pressure Angle and Radius of Curvature

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Appendix 5: Design 3 Continuity Check, Boundary Conditions, and Segment Overview

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34. 34

35. 35
Appendix 6: Design 3 Polynomial Functions

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37. 37
Appendix 7: Design 3 Pressure Angle and Radius of Curvature