me 340 final report cycloid race exhibit...similar to the cycloid race, which helped us visualize a...
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ME 340 Final Report
Cycloid Race Exhibit Discovery Space Museum, State College, PA
Team 1D: QuaShawn Rosario Ed Gill Eric Levi Matt Jablonski 12/13/2011
Executive Summary
This document presents Team 1D’s detailed design of the Cycloid Race Exhibit for the
Discovery Space Museum. The team was tasked with producing an interactive exhibit aimed at
children from ages 9-12. The product was required to fit in the limited amount of space available
at the museum and stay within a budget of $50. This detailed design report explains background
information, project planning, concept development, and design methods. Concept generation
and selection were driven by recognizing customer needs and developing target specifications
after extensive external research was completed. The design process was completed through the
collaborative efforts of the project team and continuous communication with the Discovery
Space Museum staff.
The beta prototype of the Cycloid Race Exhibit included two curves, a cycloid curve and
a straight curve. Children will roll spherical masses down each track to demonstrate that the
quickest path is not a straight line, but rather a cycloid. Educational concepts relating velocity,
acceleration, and trajectory paths are displayed through the concept in an interactive and
engaging manner. Upon completion of the Cycloid Race Exhibit it will be presented to the
customer for display at the Discovery Space Museum.
Table of Contents 1. Introduction ............................................................................................................................................. 1
1.1 Problem Statement .............................................................................................................................. 1
1.2 Background Information ..................................................................................................................... 1
1.3 Project Planning ................................................................................................................................. 1
2. Customer Needs and Specifications ....................................................................................................... 2
2.1 Identification of Customer Needs ........................................................................................................ 2
2.2 Design Specifications .......................................................................................................................... 2
3. Concept Development ............................................................................................................................. 3
3.1 External Search ................................................................................................................................... 3
3.2 Concept Generation ............................................................................................................................ 3
3.3 Design Concepts ................................................................................................................................. 4
3.3.1 Magnet/Levitation Concept .......................................................................................................... 4
3.3.2 Mechanical Sundial System Design Concept ............................................................................... 4
3.3.3 Cycloid Race Concept .................................................................................................................. 5
3.4 Concept Selection ................................................................................................................................ 6
4. System Level Design ............................................................................................................................... 6
4.1 Overall description ............................................................................................................................. 6
5. Detailed Design ........................................................................................................................................ 7
5.1 Modifications to Proposal Sections .................................................................................................... 7
5.2 Theoretical Analysis ............................................................................................................................ 8
5.3 Component and Material Selection Process ....................................................................................... 8
5.4 Fabrication Process ............................................................................................................................ 9
5.5 Industrial Design ................................................................................................................................ 9
5.6 Detail Design Drawings.................................................................................................................... 10
5.7 Economic Analysis ............................................................................................................................ 10
5.7.1 Unit Production Cost ................................................................................................................. 10
5.7.2 Business Case Justification ........................................................................................................ 11
5.8 Safety ................................................................................................................................................. 11
6. Construction Instructions..................................................................................................................... 11
7. Test Results and Discussion of Results ................................................................................................ 13
8. Conclusion and Recommendations ...................................................................................................... 14
9. References .............................................................................................................................................. 15
Appendix A – Gantt Chart ....................................................................................................................... 17
Appendix B – QFD Chart ......................................................................................................................... 18
Appendix C – AHP Chart ........................................................................................................................ 19
Appendix D - List of Concepts ................................................................................................................. 20
Appendix E - Concept Selection Matrix ................................................................................................ 21
Appendix F - Theoretical Analysis .......................................................................................................... 22
Appendix G - Detail Design Drawings .................................................................................................... 26
Appendix H – Bill of Materials ................................................................................................................ 31
Appendix I – NPV Chart .......................................................................................................................... 32
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1. Introduction
1.1 Problem Statement
Team 1D was tasked with developing an interactive exhibit for the Discovery Space
Museum located in State College, PA. The exhibit was to meet identified customer needs,
targeting ages 2-12, with a focus on science education. The team acknowledged the importance
of attracting younger generations to science, technology, engineering, and mathematics, also
known as STEM careers. According to a paper published by Purdue University, statistics on
education in the United States indicate decreasing trend in the number of students entering and
completing academic programs rooted in STEM disciplines [1]. In order to succeed in an
increasingly global economy, the United States must continue to place emphasis on STEM
careers [2]. There are many problems in today’s world that can only be solved by intelligent and
diligent individuals, and exposing the youth to these subjects helps them develop into effective
problem solvers and productive members of society. In its final form, this project will peak the
curiosity of children toward STEM related topics.
1.2 Background Information
External research identified customer needs through the following actions: meeting with the
customer, researching existing exhibits at museums such as the Exploratorium [3], and accessing
the knowledge-base of the specified age group. This provided the team with a platform for
concept generation. After a comprehensive list of concepts was developed, they were screened
and scored for selection. The Cycloid Race Exhibit was deemed the most likely to accomplish
the team’s project goal. In this demonstration, three tracks will be home to three separate
spherical masses, which will race to the finish line. Children will find it interesting that the mass
rolling down the inverted cycloid will win every time, and will be kept engaged through the
interactive nature of the exhibit. The exhibit will give users a visual lesson on gravity’s effect on
masses rolling down slopes.
Throughout the design process, the team will keep in mind some general tips for
designing exhibits for children. According to the Discovery Space Museum staff, the exhibit
must be intuitive, allowing children to approach the exhibit and begin interacting with it
immediately. The design should be interactive to help engage the user, while at the same time
maintaining a completely safe environment [4]. It should be easily disassembled for storage, as
the displays will be periodically rotated. And finally, the exhibit needs to be durable in order to
withstand the abuse that users will put it through.
1.3 Project Planning
A collaborative effort from all team members is expected to successfully achieve immediate
and final project goals. The team’s design process and schedule was formally documented in a
Gantt chart, presented in Appendix A. Major tasks included identifying customer needs, concept
development, and concept selection. Each team member was assigned tasks with appropriate
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time frames for completion. Project planning and continuous monitoring of the schedule are
essential if the team is to meet the final concept demonstration deadline on December 6, 2011.
2. Customer Needs and Specifications
2.1 Identification of Customer Needs
One of the first steps of the project was determining the customer needs. The goal of any
project is to satisfy and ultimately delight the customer, so accurately understanding what the
customer needs is crucial. Two members of the staff from the Discovery Space Museum,
Michele Crowl and Yanling Wang, presented the basic scope of what was expected from any
exhibit produced by the class. This presentation explicitly stated several customer needs, but it
was not a comprehensive list.
Because the museum caters to children of ages 2-12, one of the primary customer needs
explicitly expressed was safety. Crowl and Wang encouraged everyone to make at least one visit
to the museum to see first-hand the amount of space available and to observe how children of
different ages interact with exhibits. The team performed this task, as it was clearly a crucial step
in accurately determining the customer needs.
After all team members visited the museum, the consensus was that it was important to
have an exhibit of reasonable size that could easily be disassembled and arranged with other
exhibits. After observing children interact with exhibits, the team acknowledged that the final
product must be intuitive and easy to use. Long and complicated directions would not be
effective, as the attention span of young users is relatively short.
Now that the preliminary list of customer needs was complete, the team met with the
Discovery Space Museum staff to review the list and determine whether or not any crucial needs
were overlooked. The staff was satisfied with the team’s list of customer needs, and provided
two additional criteria: the exhibit must be able to accommodate a single user as well as small
groups, and it must be durable. The list of customer needs was now complete and consisted of:
interactive, safe, easy to use, reasonable size, professional appearance, easy to
disassemble/portable, educational, durable, and should facilitate use by a single user or a group
of users. The team prioritized these needs and developed subsequent design specifications.
2.2 Design Specifications
When developing design specifications, the team first had to create a Quality Function
Deployment (QFD) table (Appendix B), which related customer needs to product specifications
[5, Pg. 95-97]. The customer needs were put in terms of metrics and values so they could be
properly utilized by the team in the design process. Next, the team used an Analytical Hierarchy
Process (AHP) chart (Appendix C) to weight the needs relative to one another [6]. This allowed
the concepts to be easily ranked based on their ability to satisfy each area of the AHP chart. The
weights are listed below in Table 1.
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Table 1: Concept Selection Criteria and Weights
Need Weight
Interactive 15%
Safe 20%
Easy to use 12%
Reasonable size 6%
Professional appearance 6%
Easy to disassemble/portable 8%
Educational 15%
Usable by groups 12%
Durable 6%
3. Concept Development
3.1 External Search
In order to effectively brainstorm possible products capable of delighting customers, it is
essential that all team members be well educated on existing solutions. During the external
research process, it is inevitable that internal ideas arise. The team wanted to keep an open mind
with regard to potential concepts and not focus too much attention on any one idea at this time.
Any designs developed by the team during external research were written down but given no
more immediate thought. This allowed the team to fully research and take note of factors that
make an exhibit successful, as well as those that make it unsuccessful. These factors are all
included within the customer needs criteria. Many existing science museums such as the
Exploratorium [3], Franklin Institute [7], and Carnegie Science Center [8] have extensive
websites, which proved to be valuable resources. Some of these museums have existing exhibits
similar to the Cycloid Race, which helped us visualize a basic concept. The team also spent time
with family members in the specified age group, interviewed museum staff, and observed users
in the museum environment.
3.2 Concept Generation
The next step in the development process was concept generation. The team had several
in-class and out-of-class brainstorming sessions, and recorded all ideas that came to mind. Some
of the educational concepts used for inspiration included astronomy, magnetism, and properties
associated with gravity (acceleration, velocity, force components). With the completion of a
comprehensive and organized list of possible exhibits as seen in Appendix D, concept screening
was used to narrow the focus to the three most promising concepts. A majority vote was used to
determine the concepts to be further developed and presented in a concept proposal presentation.
The chosen concepts were the cycloid race, the mechanical sundial, and the levitating magnets.
Each of these concepts satisfied the customer needs in a unique way, and the goal from that point
forward was to determine which had the greatest potential to leave the customer truly delighted.
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3.3 Design Concepts
3.3.1 Magnet/Levitation Concept
One of the team’s concepts displayed the invisible forces experienced between magnets.
This concept demonstrated the repulsion between like poles and attraction between unlike poles
by placing ring magnets onto vertical dowels.
Magnetic poles can be placed north (N) to south (S) to demonstrate the attraction between
the unlike poles, or S to S and N to N to demonstrate
the repulsion between like poles. The dowel is
necessary in order to restrict opposing magnets from
flipping over.
This interactive concept provides a way to
feel and visualize the forces between magnetic poles
in various configurations. Figure 2 displays the
repulsive and attractive forces between magnets. Figure 1: Magnetic rings on a vertical dowel
3.3.2 Mechanical Sundial System Design Concept
The mechanical sundial was formulated around educational concepts involving a
calibrated sundial and a movable light source. External research revealed a variety of sundial
models and configurations, which were narrowed based on their feasibility of production [9].
Team 1D’s concept design was intended to model the actual system, in which sunlight is
used to cast a shadow on the face of a sundial, accurately displaying the time of day. Through
fabrication of a mechanical system housing a horizontal sundial face and a properly oriented
style, users are able to vary the displayed time based on the position of the light source. Figures 2
and 3 display the general design concept for a mechanical sundial system.
Figure 2: View one of mechanical sundial concept. Figure 3: Side view of sundial
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3.3.3 Cycloid Race Concept
The objective of the cycloid race is to visually demonstrate that an inverted cycloid is the
curve of fastest descent. To get a clear image of this curve, first imagine a cycloid traced onto a
piece of paper. This is done by attaching a pencil to the outermost edge of a circular disk, and
rolling the disk along a straight line, allowing the pencil to make the trace. Now the cycloid can
be flipped to create an inverted cycloid, the curve in question. This inverted cycloid traces the
fastest path for an object to travel between two specified points. This is the case under the
influence of gravity, as long as the starting point is above the terminal point. For simplicity’s
sake, the terms cycloid and inverted cycloid are used interchangeably throughout this proposal. It
should also be noted that this inverted trace has two other names, the tautochrone and the
brachistochrone [10].
The team’s basic design will consist of three curves: a cycloid curve, a linear curve, and
an intermediate concave curve. Each track will be mounted side-by-side, and the entire assembly
will be free standing. The linear and concave curves will be adjustable in order to change the end
point of the race. They will be held in place at the various locations by dowels. The design will
use a mechanical starting gate to ensure that all spheres start simultaneously. A mechanical or
electrical gate at the finish line will help the user clearly identify which mass won the race.
Figure 4: Pictured here are the cycloid track, straight line track, gate system, and legs.
Similar products have been used for educational purposes, reinforcing the same concepts
[11]. The team has yet to see any exhibits with more than two tracks, or starting and finishing
gates. The proposed exhibit will be more interactive than these designs, helping engage the user.
An image of a common exhibit model can be seen below in Figure 5 [12].
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Figure 5: Pictured is a snapshot from a similarly modeled cycloid race. Note that the ball rolling on
the cycloidal path reaches the terminal point as the ball on the straight path just passes the half-
way mark. Notice that in this case, the curved track is only a half-cycloid.
3.4 Concept Selection
Having completed the concept generation phase, the team was tasked with selecting the
single most promising concept. A combination of a Selection Matrix and feedback from the
Discovery Space Museum panel was used to select a final concept [5, Pg. 154]. The Discovery
Space Museum staff agreed that the cycloid race exhibit was the most promising. The weighted
scores for all three concepts can be seen in the full selection matrix in Appendix E. The relative
rankings of the three concepts are as follows: 1- Cycloid Race. 2- Levitating Magnets. 3-
Mechanical Sundial.
4. System Level Design
4.1 Overall description
The cycloid race exhibit will give the user a more intuitive understanding of the effects
that gravity has on solid objects. A trough in the shape of a full inverted cycloid will stand freely
on the floor, approximately 6 feet long and 3 feet high. Two other tracks with adjustable slopes
will rest on either side of the cycloid track, as seen in Figures 4 and 5. This exhibit displays the
relationships between velocity, acceleration, distance, and gravity in an interactive manner. The
user will be intrigued by the fact that the ball rolling on the cycloid will always reach the finish
line first. This is counterintuitive to many users, for it is a common misconception that a straight
line, being the shortest distance between two points, is also the fastest path to follow. In order to
gain a better understanding of the concept, a poster will present pertinent figures and
descriptions. Safety, our number one priority, is easily ensured with this design. To eliminate the
potential choking hazards, spheres with a sufficiently large diameter will be used, as discussed
later in section 5.8. No dangerous moving parts will compose the exhibit and the weight of the
display will not be significant enough to pose a threat (<25 lbs.). As soon as a user sees this
product, it will be instantly clear what the general procedure for use is. The user will be given
Terminal Point
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three spheres, each corresponding to a respective track. The balls are to be placed in a starting
gate, which is triggered by the user to open, ensuring a synchronous start to the race. Due to the
nature of the full cycloid, the user will enjoy watching the ball roll back and forth, gaining
experience with the concepts of damped harmonic motion and frequency/period of oscillation.
The accompanying poster will not use technical language of this sort, but will be easily read and
understood by children above the age of five. Supplemental information and instructions for use
will be provided in order to explain proper use and why the cycloid path wins. A small display
will describe the method of creating a cycloid, as well as providing suggestions for use.
Although the sphere must travel a greater distance on the cycloid track than on the straight track,
the initial acceleration is far greater. This imparts a greater velocity to the sphere rolling on the
cycloid, causing it to cross the finish line first.
5. Detailed Design
Figure 6: The cycloid race exhibit will display principles relating gravity, acceleration, velocity, and
time. The user will roll two spheres down two separate tracks as seen in the above figure, noting the
order in which they cross the finish line.
5.1 Modifications to Proposal Sections
A fully adjustable track was incorporated into the alpha prototype of the exhibit. The
team planned to also include an adjustable track in the beta prototype. However after extensive
trial and error, it was determined that the adjustable track was not feasible with the budget and
resources available. The team attempted using flexible hose supported by a rigid wire to make
the adjustable track, but the right combination of rigidity and flexibility could not be found. The
team has made only minor adjustments to its schedule and the remainder of the design has
remained the same.
Linear Path
Cycloid Frame Support
Gate System
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5.2 Theoretical Analysis
A cycloid is the path that a point on the circumference of a circle traces while rolling on a
flat surface. In order to generate a cycloid, the team will use a circle of chosen radius with a
marker attached to the perimeter of the circle. The circle will be rolled on the floor while being
pressed against a wall in order to trace the cycloid’s shape. The team will use this paper trace to
transfer the cycloid onto the chosen building material.
Figure 7: Image displaying the method used to create a cycloid. Where the radial line intersects the
circumference of the circle is where a marker would be mounted to create a cycloid.
The following parametric equations describe the position of the point along the cycloid path, as
seen in Figure 6.
x = r ( Ѳ - sinѲ ) r = radius of circle
y = r ( 1 - cosѲ ) Ѳ = angle (in radians)
The team will use these equations to verify the accuracy of the trace produced by the
method described above. Various angles will be used to compute the x and y locations of specific
points. The team will check these locations on the paper trace to ensure the trace is a true
cycloid. For a more rigorous proof of the cycloids properties, refer to Appendix F.
5.3 Component and Material Selection Process
All components and materials for the exhibit were chosen with safety in mind. Aesthetics
and professional appearance also weighed heavily on what components and materials were
chosen. The main structure was made from 3/4” furniture grade plywood, giving a professional
appearance to the exhibit. The spherical masses are 7/8” in diameter and made of stainless steel.
They had to have sufficient weight in order to overcome the effects of friction, and be large
enough to eliminate any choking hazard. The dowels used to hold tracks in place were made out
of ¾” diameter wood. The starting gate was made using 3/8” aluminum stock metal and ¾”
wood dowels.
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5.4 Fabrication Process
Each component of the cycloid race exhibit was fabricated out of the specified materials
using the required tools. The shapes of the linear path, cycloid frame, and support blocks were
cut out using a jigsaw to obtain their respective geometries. The straight line track was mounted
to the cycloid frame using a wooden dowel pin of specified diameter. This dowel acts as the
pivot point for the straight line track. Six thru holes were drilled in the cycloid frame, allowing
the insertion of dowels. These dowels act as resting points for the straight track in its various
orientations.
5.5 Industrial Design
Because the exhibit is aimed at an audience of ages 9-12, one of the team’s primary tasks
was making it safe and intuitive. Safety was the primary concern and all design decisions were
aimed at minimizing risks. One obvious area that posed a problem was the size of the spherical
masses that would be rolling down the tracks. The balls had to be large enough not to be a
choking hazard. When meeting with the Discovery Space Museum staff, the team was made
aware that a ball of roughly one inch diameter would be acceptable for the exhibit. The wood
used in the display will be sanded and finished in order to prevent any splinters.
Although the exhibit was designed to be intuitive, there will be accompanying
instructions and an explanation of why the mass rolling on the cycloid wins. Figure 7 will be
included in the display to visually show how a cycloid is made. The instructions that will be used
can be seen below. The display will also include a picture showing how to operate the gate,
arrows pointing to the different ending locations of the straight track, and guidance questions.
Instructions:
Here you have a cycloid track and a straight line track. These instructions serve as
a guide to using the exhibit.
1. Choose an end point for the straight line track by placing the rod into one of the holes
on the cycloid frame.
2. Load the balls into the gate at the starting point of each track.
3. Push the gate up and watch to see which ball reaches the end point first.
One of the biggest problems the team anticipated with the “race” aspect of the exhibit
was children arguing about which mass won. After developing and testing the alpha prototype,
the team was reassured that it will be visually obvious which mass wins, however the team
needed to have a way to ensure a synchronous start to the race. A gate system was used in which
the user will load the balls into the starting gate and then push up on the gate to release the balls
and have a simultaneous start to the race.
One of the customer needs was having an exhibit with a professional appearance, so the
materials chosen to construct the exhibit were aimed at making it as aesthetically pleasing as
possible. The exhibit was made primarily of wood, so the team decided staining it would give it a
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quality appearance. The poster including instructions and explanations was also made with
professional quality.
5.6 Detail Design Drawings
Detailed design drawings in Appendix G provide dimensional and geometric
specifications for all the components of the cycloid race exhibit. The assembly model and
isometric drawing shown below serve as accurate illustrations of the exhibit’s configuration and
primary components.
Figure 8: An assembly drawing of the cycloid race exhibit.
5.7 Economic Analysis
5.7.1 Unit Production Cost
It will cost approximately $108 to produce one cycloid race exhibit. Labor and tooling
are not included in the bill of materials because the team members will provide labor, and the
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Learning Factory will provide tools. A detailed description of the bill of materials can be seen in
Appendix H.
5.7.2 Business Case Justification
In order to decide whether to produce the cycloid race exhibit in quantity, a base-case
financial model is needed. The model requires estimating the timing and magnitude of future
cash flows and then calculating the Net Present Value (NPV) for the cash flows assuming the
team sells five units per quarter, or twenty units in a year. This financial model would help the
team decide whether or not to produce the exhibit for additional customers. The team’s NPV
chart can be seen in Appendix H. According to the NPV chart, it is a good investment.
According to the team’s financial model, it is possible to create a business out of
producing the cycloid race exhibit for additional customers. At first the team would be losing
money due to overhead costs such as: development costs, ramp-up costs, marketing and support
costs. The exhibit would be sold for approximately $200, or twice the production cost. Six
months after start-up the team would begin making a profit. Using the financial model for
support the team can confirm the decision to start producing the cycloid race exhibit in quantity.
5.8 Safety
The primary safety concern with the cycloid race exhibit is the potential choking hazard.
Although choking standards state that a sphere should be no smaller 1.75” in diameter for
children under the age of three, it was concluded that a sphere with a diameter of 7/8” will meet
the safety requirements [13]. This decision was made based on feedback from the Discovery
Space Museum staff after reviewing the alpha prototype. The justification is that our exhibit is
aimed at users five years and up, who are far less likely to place objects in their mouths. There
are very few areas where children could pinch their fingers and with a small amount of adult
supervision, the exhibit is highly unlikely to be tipped over or tripped over.
6. Construction Instructions
The following instructions give detailed steps of how to construct the Cycloid Race
Exhibit, as produced by Team 1D. The process will be decomposed into three sections: 1)
Purchasing of materials, 2) Preparation of materials, and 3) Assembly of the exhibit. This
instruction set assumes the builder has access to common hand and power tools.
Step 1
The builder must purchase the following.
a. One 4' x 8' x ¾” furniture grade plywood.
b. One 1/2” inner diameter, 8' electrical conduit.
c. One box (>30) 1 1/4” wood screws.
d. One 3/4” wooden dowel, >2'.
e. 2' of 3/8” aluminum dowel.
f. One 8” x 3/4” outer diameter steel pipe, inner diameter not critical.
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g. Two 7/8” steel spheres.
h. One 68” x 1/2” x 1.5” piece of wood.
Step 2
Now that all materials have been gathered, preparation for assembly may begin. The first
step is to cut 19” off of the length of the plywood, making it 48” x 69”. This scrap will used later.
The second step is to cut the plywood in half lengthwise. To do this, place the wood onto a flat
table. Using a measuring tape and a chalk-line, mark a line from center to center. Using a circular
saw, cut the plywood in half along the line. Set one of these identical pieces of wood aside; it
will be used momentarily. The second step is to trace out the cycloid shape. To do this, one must
locate a circular object with a diameter of 22”. Many trashcans have this diameter, however if
nothing is immediately available, a circle can be easily traced and cut out of scrap wood or
cardboard. Attach a pencil to the edge of the circle using tape. Have a helper hold one of the
pieces of plywood against a wall, with the 8’x3/4” side resting on the floor and the unfinished
side against the wall. Take the circular object with the attached pencil, and place it against the
wood with the pencil touching the lower edge, 4 inches from the bottom left corner. Keeping the
pencil in contact with the plywood, roll the circular object along the floor, ensuring that it does
not slip. Take your time; you may need to try several times to get a smooth trace. Once the
circular object has done one complete revolution, the cycloid trace is complete. Now take the
two pieces of plywood and lay them flat on a table with the unfinished sides touching each other.
Join the two pieces together using approximately twelve wood screws. Place one screw in each
corner and 8 screws 1.5 inches away from the trace you just made. There should be four screws
evenly spaced on either side of the cycloid trace. Now that these two pieces are attached to each
other, you are ready to cut along the traced path with a jigsaw. The piece that looks semi-circular
is scrap, but don't get rid of it because it will be used later. Sand any imperfections in the cut.
What you have just created is the main body of the exhibit. Orient the body such that the curve is
concave, with the flat side of the body facing downward. It is now time to drill several holes in
the body for mounting purposes. These will all be done with a 3/4” drill bit. The first hole should
be drilled 2” from the left edge, and 1” from the top. This is where the straight track will pivot.
The second hole should be drilled 1.5” below the first. The starting gate will be mounted here.
Drill six holes in the frame, 2 inches below the track, spaced 12 inches apart. A dowel rod will be
placed into these, allowing the user to adjust the terminal point of the race.
The next step is making the track on which the ball will roll. Take the 1/2” conduit, and
cut it in half lengthwise using a band saw and a guide. De-bur the edges of the cut using a razor
blade. Pre-drill clearance holes for wood screws every 8 inches along the centerline of the
conduit. Start 2 inches from both ends and work your way toward the center. If the distance
between holes needs to be modified near the center, that is fine.
Now you can prepare your materials for the starting gate. Cut your 2' section of
aluminum rod in half, creating two 1' sections. Drill clearance holes for a wood screw 3/8” from
both ends of both rods, for a total of 4 holes. Make sure that the holes through each rod are
parallel to one another. Next, cut two 6” sections off of the 3/4” wooden dowel. Pre-drill holes
for the wood screws in both ends of the two dowels. They should be drilled along the centerline
of the dowel, and no less than 1” deep. Now take the 8 inch section of 3/4” steel pipe, and drill
two 1/2” holes through the pipe, one inch from either side. Ensure these two holes are parallel.
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Cut two additional 4” sections off of the dowel. These will be used in assembly.
Now take the scrap plywood, and trace out two triangles, 18” along the base, and 20”
high. Cut these out using a jigsaw. Now create a flat top to the triangle, making a cut parallel to
the base, 2” from the top. Cut a notch in the top of each of these, 2” deep and 1.5” wide. Cut
corresponding notches in the cycloid body, 3” from either side of the base. This will allow these
triangular legs to slide nicely into the body, creating a stable and easy to disassemble structure.
Step 3
You are now ready to assemble the exhibit. Slide the legs into the corresponding notches
in the body. Attach one of the pieces of conduit to the 68” x 1/2” x 1.5” piece of wood using
wood screws every 8”. Do the same with the other piece of conduit, attaching it to the curved
cycloid track with wood screws in the pre-drilled holes. To mount the straight track to the body,
take one of the previously cut 4” sections of wooden dowel rod and attach it to the underside of
the straight line track using wood screws. The dowel should be perpendicular to the track and
flush on one end. Place the other end of the dowel through the first hole that was drilled in the
frame. To allow the dowel to rotate, but not slide out of the hole, place a wood screw about ¾”
from the edge of the dowel to act as a stopper. To support the terminal end of the straight track,
place the other 4” section of dowel into any one of the six holes drilled below the cycloid track.
To mount the starting gate, insert the ¾” steel pipe through the hole directly below the pivot for
the straight track. Now take the two 1’ sections of aluminum rod and one 6” section of wooden
dowel and attach the 2 aluminum rods into both ends of the wooden dowel using wood screws,
creating 3 sides of a rectangle. Insert the two free ends of the aluminum dowels through the two
holes in the steel pipe, and attach the last 6” section of wooden dowel in the same manner. You
should now have a rectangular assembly that is capable of both pivoting, and sliding through the
steel pipe. The last step in assembly is to create a stopper for the straight line track by mounting a
perpendicular piece of wood with a magnet attached to it at the end of the track. Leftover wood
can be used to create this stopper.
7. Test Results and Discussion of Results
The basic test procedure used to ensure proper function was a series of races of the steel
balls down each track. This tested all the mechanisms of the exhibit including the performance of
the gate, the ability of the stopper at the end of the straight track, and whether or not the ball on
the cycloid track will win the race every time regardless of the chosen ending point. The first
step is to choose an end point of the race by placing the dowel in the desired hole in the cycloid
frame and resting the straight track on top of the dowel. Next, the balls must be loaded onto the
gate, making sure that the starting height of the balls is the same on each track. Then the gate had
to be pushed up to release the balls and start the race. Finally, the race had to be observed to see
which ball won and to make sure the stopping mechanism at the end of the straight track was
effective. This procedure should be repeated for each ending point of the race to make sure the
ball on the cycloid track wins every time. How smoothly the ball rolls down each of the tracks
must also be taken into consideration during testing. Additional runs on each track should be
performed to observe how well the ball rolls and to make sure the ball does not fall off of either
track. The tracks should be sanded accordingly until the ball consistently rolls smoothly down
both of the tracks. The team’s test results showed clear visual evidence that the ball on the
14
cycloid track will win every time regardless of the ending point chosen. Both tracks required
sanding to ensure that the balls rolled smoothly and did not fall off of either track, but the
finished product performed as expected.
The next aspect of testing was observing how children interact with the exhibit to see if
any changes in directions, display, or any other part of the product were necessary to improve on
the final design. After observing children using the exhibit, it became clear that the age of
children who enjoyed using the exhibit and learned from it was slightly higher than what was
originally expected. Children nine years and older seemed to get the most benefit from the
cycloid race because they had a better understanding of the principles displayed by the exhibit.
The Discovery Space Museum staff recommended additional signage including guidance
questions to challenge the user and raise curiosity. Besides these minor improvements, the
museum staff was pleased with how children interacted with the exhibit.
8. Conclusion and Recommendations
The cycloid race exhibit demonstrates fundamental principles of distance, velocity,
acceleration, and time pertaining to solid objects under the influence of gravity. It shows how the
cycloid path is the fastest path between two points. The exhibit was successfully constructed and
met primary customer needs: demonstrating educational concepts and being safe and engaging
for children ages 9-12 years old. Major components of the exhibit include the cycloid and
straight-line tracks. These parts enable participants to send spherical masses racing down both
paths and witness the differences in speeds and travel times. Additional features include a
starting gate, support stands, a dowel rod for track adjustment options, and a stopper for the
straight track. The starting gate is used to ensure that balls on both tracks start at the same time
and height. Instructions are included with the exhibit for additional description and guidance.
Based on the economic analysis, it would cost about $108 to make the exhibit. If the
product could be sold for at least $200 a unit, some money could be made. Taking into account
labor time and limited demand, it would be difficult for this product to be economically viable.
Possible improvements for the design include implementation of an adjustable track and a
terminal gate. Although the team extensively explored integration of both options, time and
budget constraints limited feasibility. Another improvement would be to develop a more user
friendly and intuitive starting gate. The current starting gate required two degrees of freedom
because as you change the terminal point of the straight track, the starting height also changes.
To prevent this, the pivot point of the straight track should be on the surface of the cycloid. The
additional signage mentioned previously will also be implemented into the exhibit shortly.
This project helped the team in developing many important skills. Primarily, it was a
continuous exercise in teamwork. Leadership, delegation, and cooperation were practiced by all
team members. Working with a real customer was an extremely valuable learning experience,
which was something that set this project apart from many others of this sort. Most importantly
the team learned that the primary goal is to delight the customer. To improve the project
experience, the team suggests starting prototyping earlier to accommodate for the inevitable
problems that will arise with the design.
15
9. References
1. Weaver, Gabriela C., and Kamyar Haghighi. Attracting Students to STEM Caereers. Rep.
Purdue University, 2007. Print.
2. Virtual Counseling Center. Amanda Hardy and John J. Horan, 2008. Web. 04 Oct. 2011.
<http://vcc.asu.edu/stem.shtml>.
3. “Exhibit Services – Exhibit Catalog – Exploratorium.” Web. 13 Sept. 2011.
<http://exs.exploratorium.edu/exhibits/>.
4. Bell, Philip, and Bruce Lewenstein. "Learning Science in Informal Environments:
People, Place, and Pursuit." Scribd. The National Academies Press. Web.
15 Oct. 2011. <http://www.scribd.com/doc/26973411/Learning-Science-in-
Informal- Environments- People-Place-and-Pursuit>.
5. Ulrich, Karl, and Steven Eppinger. Product Design And Development. 5th
. McGraw -
Hill/Irwin, Print.
6. “Hyman, Barry I. "Chapter 9 Section 3." Fundamentals of Engineering Design. 2nd ed.
Upper Saddle River, NJ: Prentice Hall/Pearson Education, 2003. Print.
7. The Franklin Institute – Home – 215.448.1200. Web. 14 Sept. 2011.
<http://www2.fi.edu/>.
8. “Exhibits – Exhibits.” Carnegie Science Center. Web. 13 Sept. 2011.
<http://ww.carnegiesciencecenter.org/exhibits/>.
9 . "Types of Sundials." NASS. 25 Oct. 2011. Web. 25 Oct. 2011.
<http://sundials.org/index.php/art-of- dialing/types-of-sundials>.
10 . Lawlor, Gary. "A New Minimization Proof for the Brachistochrone." American
Mathematical Monthly 103.3 (1996): 242-49. Web. 4 Oct. 2011.
<http://www.maa.org/pubs/Calc_articles/ma060.pdf>.
11 . "Ball Race - Brachistochrone." Educators Outlet. Web. 20 Oct. 2011.
<http://www.educatorsoutlet.com/index.php?main_page=product_
info&cPath=129&products_id=3853>.
12 . "Brachistochrone - Slow Motion." YouTube. 24 June 2007. Web. 20 Oct. 2011.
<http://www.youtube.com/watch?v=Y05nIAGiIqw>.
16
13. "Avoiding Choking Hazards in Children's Toys." Child Safety Central | Child Safety
News and Information. Web. 13 Nov. 2011.
<http://childsafetycentral.com/toy-choking- hazards.html>.
17
Appendix A – Gantt Chart
18
Appendix B – QFD Chart
Met
rics
Fit
s in
muse
um
wel
l
Sci
ence
and t
echnolo
gy r
elat
ed
Qual
ity m
ater
ials
Subje
ctiv
e te
st (
wat
ch p
arti
cipan
ts)
No s
har
p c
orn
ers/
movin
g p
arts
/sta
ble
Needs
Interactive x x
Educational x x
Easy to use x x
Easy to disassemble x x
Reasonable size x
Safe x x
Professional appearance x x
Durable x
19
Appendix C – AHP Chart
Inte
ract
ive
Safe
Easy
to u
seR
easo
nable
siz
eP
rofe
ssio
nal appeara
nce
Easy
to d
isass
em
ble
Educa
tional
Usa
ble
by g
roups
Dura
ble
Tota
lW
eig
ht
Inte
ract
ive
(1/3
)3
77
51
15
29.3
30.1
8
Safe
37
77
51
35
38
0.2
3
Easy
to u
se(1
/3)
(1/7
)3
55
(1/3
)1
519.8
0.1
2
Reaso
nable
siz
e(1
/7)
(1/7
)(1
/3)
1(1
/3)
(1/7
)(1
/5)
(1/3
)2.6
30.0
2
Pro
fess
ional appeara
nce
(1/7
)(1
/7)
(1/5
)1
(1/3
)(1
/7)
(1/5
)1
3.1
60.0
2
Easy
to d
isass
em
ble
(1/5
)(1
/5)
(1/5
)3
3(1
/7)
(1/5
)3
7.1
40.0
4
Educa
tional
11
37
77
17
34
0.2
1
Usa
ble
by g
roups
1(1
/3)
15
55
15
23.3
0.1
4
Dura
ble
(1/5
)(1
/5)
(1/5
)3
1(1
/3)
(1/7
)(1
/5)
5.2
70.0
3
Tota
l16
2.67
20
Appendix D - List of Concepts
Natural
Mechanical sundial – Create a sundial with a moving light source that could still be used
to display time.
Rotating planets – Develop a mechanical planetary model that would show how planets
rotate.
Structural Material
Build a bridge – Have children build a bridge and then test it by walking over it.
Beam Bridge – Build a bridge with a beam placed on its edge and on its side. Show that
the beam placed on its edge has twice as many fibers resisting the forces that make it sag.
Electricity/Motors/Lights
Levitation with magnets – Use the repulsive force created by two like magnet poles to
levitate objects.
Robotics – Have children use a robot to perform different tasks by using different
programs downloaded onto the microcontroller.
Projecting shapes with lasers – Use lasers and adjustable mirrors to reflect different
patterns onto a panel.
Hands-on dynamic education
Rotating chair with bicycle wheel – Use the angular momentum of the bicycle wheel to
rotate a chair.
Downhill race - Show that angular acceleration depends on how the mass is distributed.
Bicycle cycloid - Bicycle uses square wheels on a cycloidal track.
Catapult - Build a catapult with an adjustable lever for position and length.
Fluids
Buoyancy experiments – Show that objects have different buoyancy in fluids with
different densities.
Floating ball – Use a fan to create a high velocity airstream that will suspend a ball in
mid-air.
Tornado bottle – Rotate liquids inside of a bottle to create a vortex that looks like a
tornado.
Corn starch and water – Demonstrate how corn starch and water behaves like a Non-
Newtonian fluid.
Smoke launcher – Make a mini smoke ring launcher using dry ice and water.
21
Appendix E - Concept Selection Matrix
Concepts
Cycloid Race Mechanical Sundial Levitating Magnets
Selection Criteria Weight (%) Rating Weighted
Score Rating
Weighted Score Rating
Weighted Score
Safety 25 5 1.25 5 1.25 4 1
Engaging 25 4 1 3 0.75 4 1
Educational Value 20 4 0.8 3 0.6 4 0.8
Usable by Groups 15 3 0.45 2 0.3 2 0.3
Portable 10 3 0.3 5 0.5 5 0.5
Professional appearance
5 Subj. Subj. Subj.
Total Score (Sum of weighted scores) 3.8 3.4 3.6
Rank
1 3 2
22
Appendix F - Theoretical Analysis
The brachistichrone problem consists of determining the path that minimizes the time
required for a bead to travel between two prescribed points in the vertical plane. The elevation of
A is greater than that of B, and the bead begins at rest at point A sliding without friction under
the influence of gravity. The problem was posed by Bernoulli, who also solved it. He discovered
that the brachistichrone curve is a part of an inverted cycloid with a cusp at A and passing
through B.
Bernoulli’s solution was based on Fermat’s principle of light minimizing time when
traveling between two points. A more general solution was discovered by Euler and Lagrange.
Here, yet another solution is presented, this one based on mechanics rather than optics.
To begin, we write the time required for a mass to move from point A to B as
where v is the speed determined from conservation of energy as follows. The potential energy of
the particle is given by -mgy, where y is the vertical coordinate of the particle. Since the particle
is at rest at A, both the kinetic and potential energies are zero. By conservation of energy, the
total energy of the particle must be zero at all times:
Solving for v, we obtain:
x
y
23
Substituting this v into the time integral, we obtain:
The question reduces to minimizing integrals of the form:
We approximate this integral with a sum by replacing F with its piecewise constant function as
follows: Choose where b is the y coordinate of B, and Fk=F(yk).
Then
where sk is the length of the kth
segment, as seen in the following figure.
The problem reduces to minimizing this sum. The sum can be interpreted as the potential
energy of the mechanical system in the above figure. This system consists of a series of rings
connected by constant tension springs, with each ring free to slide without friction along its
respective rod. The tension of the kth
spring is chosen to be Fk and the length of the spring is sk.
The potential energy of a spring is then Fksk. Therefore, the potential energy of the total system is
24
the above sum. The sum is minimal when the potential energy is minimal, i.e. when the system is
in equilibrium, i.e. when the forces on each ring in the x direction are equal:
For the entire system to be in equilibrium, this must hold true for all discrete segments.
Consequently,
In our case, with in the limit of infinitely many segments, we get:
Now let us show that this equation describes a cycloid.
Combining these two equations, we obtain an expression for D as a function of y and θ.
25
Because θ and θ’ are complimentary angles, our expression for D reduces to
Taking the square root and inverting both sides, we are left with
which coincides with the equation we obtained for the brachistichrone. To summarize, because
the cycloid represents the shape of minimal potential energy, it also represents the shape of the
least time.
Note: Information in Appendix F gathered through an interview with Penn State University
Professor of Mathematics, Mark Levi. Images provided by Eric Levi in collaboration with Mark
Levi.
Levi, Mark. Personal Interview. 12 November 2011.
26
Appendix G - Detail Design Drawings
27
28
29
30
31
Appendix H – Bill of Materials
Item # Description Quantity Price per
unit
Cost
1 Plywood (0.75”x4’x8’) 1 $ 37.02 $ 37.02
2 Wood Board (0.5”x1.5”x8’) 1 $ 4.42 $ 4.42
3 Conduit (0.5”x10’) 2 $ 1.21 $ 2.42
4 Utility Plywood (0.25”x4’x8’) 1 $ 10.25 $ 10.25
5 Wood Dowel (0.75”x36”) 1 $ 3.56 $ 3.56
6 Wood Dowel Pins (0.25”x1.25”) 1 (pack of 20) $ 1.98 $ 1.98
7 Aluminum Rod (3/8”x24”) 1 $ 1.10 $ 1.10
8 Steel balls (7/8”) 1 (pack of 10) $ 34.90 $ 34.90
9 Velcro (2”x8” strip) 1 $ 2.97 $ 2.97
10 Steel Pipe (0.75”ODx8”) 1 $ 2.31 $ 2.31
11 Wood Screws (1.25”) 1 (1lb. pack) $ 6.93 $ 6.93
Total cost
per unit
$107.86
32
Appendix I – NPV Chart
Year
1Ye
ar 2
Year
3Ye
ar 4
($ V
alue
in T
ENS)
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Q1
Q2
Q3
Q4
Dev
elop
men
t Cos
t-1
08
Ram
p-U
p Co
st-4
32-4
32
Mar
keti
ng &
Sup
port
Cos
t-5
0-5
0-5
0-5
0-5
0-5
0-5
0-5
0-5
0-5
0-5
0-5
0-5
0-5
0
Prod
ucti
on C
ost
-540
-540
-540
-540
-540
-540
-540
-540
-540
-540
-540
-540
-540
-540
Pro
duct
ion
Vol
ume
55
55
55
55
55
55
55
Uni
t Pro
duct
ion
Cost
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
Sale
s Re
venu
e10
0010
0010
0010
0010
0010
0010
0010
0010
0010
0010
0010
0010
0010
00
Sal
es V
olum
e5
55
55
55
55
55
55
5
Uni
t Pri
ce0.
20.
20.
20.
20.
20.
20.
20.
20.
20.
20.
20.
20.
20.
2
Peri
od C
ash
Flow
-108
-432
-22
410
410
410
410
410
410
410
410
410
410
410
410
410
PV Y
ear 1
, r =
5%
-108
-426
.667
-21.
4601
395.
0015
390.
125
385.
3086
380.
5517
375.
8535
371.
2134
366.
6305
362.
1042
357.
6338
353.
2185
348.
8578
344.
5509
340.
2972
Proj
ect N
PV42
15.2
2
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