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

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Q4

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Dev

elop

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t Cos

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st-4

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keti

ng &

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port

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ucti

on C

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t Pro

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