The Conveyor Belt

Materials Polystyrene ABS Extrusion Grade Nylon (extruded)

Modulus of Elasticity 3-3.5 * 109 n/m2 1.4-3.1 * 109 n/m2 2-4 * 109 n/m2

Coefficient of Friction (between

identical materials) 0.5 0.08-0.46 0.15-0.25

Density 1.05 g/cm^3 1.052 g/cm^3 1.135 g/cm^3

Properties

High impact strength, low cost,

easily extruded, injection mold-

ed, or compression molded.

Rigid low cost thermoplastic easily

machined and thermo-formed

Thermoplastic, impact re-

sistant, ideal for bearings and

gears, sometimes self lubricat-

ing

* the gears and belt shown in this image

are not the same as the components being

used.

COMPONENT 1: THE STAND

This component is used to hold the other components in place for the function of

the rube Goldberg device. They are multiuse and provide varied heights to be

used based on the users desires. Another feature on the device is that there are

holes on the top and bottom of the component so that it can be attached to a

base part for more stability. Due to the thickness of the part, the stand will be able

to stand on its own, however a base part will keep it from toppling over as the de-

vice is running. The stand will be made with ABS plastic.

ABS Plastic

ABS plastic is used in children’s toys with examples including Legos. This plastic

was chosen for the stand so that the shape would not deform easily and the holes

will be sturdy enough to act against the pulling forces in the conveyor belt system.

ABS plastic is also highly available, has low material cost, and can be easily pro-

cessed. Because ABS plastic is already used in children’s toys, it is clear that it will

be safe for use in schools as a kit for children. An added benefit of using this mate-

rial for children is that it is lightweight and due to a low melting temperature it can

be quickly manufactured with 3D printing or injection molding. The quick manu-

facturing time means that if the students do need replacement parts, or would like

to expand their kits, they can be made and sent within a short period of time.

FR DP A R R C

Stand

Must stand against

pulling forces from

motor

Tension and force

equations Resource 3

It could snap if

there is not enough

elasticity in the part.

Allow a moderately high

elasticity component.

Attach to base

Must have support to

keep it from falling

over

Slip fit parts Legos

Brackets

The pin could not

be long enough to

prevent tilting

Create additional support

systems that will act as

anchors going from the

stand to the base.

Multiuse Must be adaptable

for different designs

Legos

Chaos Tower

Tinker Toys

The adjoining parts

could not fit due to

tolerances

The kit will have spare

parts so that the odds are

one of them will fit

Withstand

Deformity

Must be structurally

sturdy

Tension equations

Modulus of Elasticity

Resources 1, 2, and 6

(Found on last page)

Impurities in the

material can cause

deformity to occur

even under the lim-

iting strength

Periodic testing of the

material being used and

ensuring it comes from a

reputable source will

lower this chance.

FRDPARRC

COMPONENT 2: THE GEAR

The gears are multifunctioning pieces. The red gear shown will be a

sliding fit part on to the pins. To hold the part in place, small rubber

bands will be provided that will create friction between the two parts.

This will allow the gear to rotate around the pins without sliding hori-

zontally. The gear teeth will be used in different configurations. One

configuration is to move the linkages in the conveyor belt system. An-

other is to move the linkages in the pulley module shown in previous

assignments. The gear shown in the top image will attach to the mo-

tor. The hub will attach the gear to the motor and the gear teeth will

use the motion provided by the motor to move the linkages. The

bottom gear will be used at the top of the conveyor belt system and

will be where the linkages turn around to go back towards the motor.

Both gears have a pitch diameter of 2 inches and will be made of Ny-

lon. These gears were pulled from resource 7.

Nylon

Nylon is typically used in gears. This plastic was chosen for the gears

so that the shape of the teeth would not deform easily. The features

will be sturdy enough to act against the pulling forces in system. Ny-

lon is highly available, is affordable, and can be easily processed. Ny-

lon is nontoxic and is durable to last through classroom use. An added

benefit of using this material for children is that it is lightweight and

due to a low melting temperature it can be quickly manufactured with

3D printing or injection molding.

FR DP A R R C

Withstand

linkage forc-

es

Must not deform

while linkages pull

on cylinder

Nylon elasticity Resource 2 and 3 The linkages dent

the cylinder

It is plastic, you can

remove the dent sim-

ilar to how you re-

move a dent from a

ping pong ball.

Act as gear

teeth

Gear teeth can not

deform with use Gear ratio equations Resource 4 The gears slip

Tighten the toleranc-

es between the gear

teeth and links

Be safe

enough for

use in a

child's toy

Shatter proof, easy

assembly, not hard

enough to cause

damage

Elasticity and density cal-

culations Resource 1 and 2

The teeth could

cause harm if too

sharp

Add rounds to the

edges of teeth to pre-

vent sharp edged

from causing dam-

age

FRDPARRC

COMPONENT 3: THE PIN

FR DP A R R C

Withstand

forces

Slip fit into the

stand parts while

being sturdy yet

easily removable

when finished

Fits and fasteners equa-

tons

The pins slip out

from the holes in

the stand

The holes need to be

lengthed so that

there is more surface

area between the

stand and the pin

Be safe

enough for

use in a

child's toy

Shatter proof, easy

assembly, not hard

enough to cause

damage

Elasticity and density cal-

culations Resource 1 and 2

The parts dent up-

on impact

Dents in ABS plastic

can sometimes be

removed, however

since this is easily

manufactured parts,

they can order re-

placement pieces.

The pin is used to hold components between or off of the stand

pieces. They will be sliding fit parts that can be easily placed and

removed by students but still have a sturdy enough connection

to stay in place while the machine is running.

ABS Plastic

This part will be made with ABS plastic. Because it is one solid

piece it can be extruded and cut into shape. The benefit with us-

ing ABS plastic is that it is rigid and is easily machined.

FRDPARRC

COMPONENT 4: THE MOTOR

I chose the Arduino motor. This motor is easily accessible for students, teachers, and companies. It will make the kit easy to

assemble and disassemble by users and does not require any outside tools to assemble into the Rube Goldberg device. De-

tails on this motor are listed below. To attach this motor to the system, a case will be made to go around the motor. The small

gear coming from the Arduino motor will be attached to the first gear shown on page 3 through a hole in the motor case. The

gear will already be attached to the motor so that the user will not need outside tools to put the system together. There will

be an additional pin coming from the motor case so that it can be attached to one of the stand components for support. This

will keep the torque of the system from twisting the motor rather than the gears and help ensure that the device does not

topple over. The motor box will be made of Polystyrene. This will keep the Arduino motor safe and ensure that the box does

not break around the motor.

Rated voltage - 6V DC

No load speed - 12000 ±15% rpm

No load current - ≤ 280 mA

Operating voltage - 1.5-6.5 V DC

Starting torque - ≥ 250 g.cm (according to self developed blade

Starting current - ≤ 5 A

Insulation resistance - above 10 Ω between the case and the terminal DV 100 V

Rotation direction - CW based on the direction of the output shaft

Shaft gap - 0.05-0.35 mm

This information is found using resource 5.

FR DP A R R C

Turn conveyor

belt

Must have enough

torque to activate

conveyor belt and

move linkages

T=(F1+F2)/2

F1=F2e^(mue*theta)

F1=P/(Ve^(mue*theta))

Motor and torque notes The motor pulls

the system over

Create an anchor

system

Turn conveyor

belt

Must be a pre-

made motor that

can be brought in

from another com-

pany

Resource 5

The outside man-

ufacturer does not

deliver parts on

time for shipment

Always have spare

motors in stock after

initial purchase

Turn conveyor

belt

Must attach to

stand pieces Sliding fit parts

May rotate motor

instead of gears

Tighten the space

between the motor

box pins and the

stand or lower the

gear teeth tolerances

FRDPARRC

COMPONENT 5: THE LINK

FR DP A R R C

Hold marble

Must hold marble as

the linkages move up

to the top gear

KE=1/2*M*V2

General forces equa-

tions

Sling shot The marbles fall

off

Raise the height so the

rubber band is held

higher up on the mar-

ble.

Multiple uses Must be able to have

varied lengths

Resources 1, 2, 3, 6, and

9

Links unsnap

apart easily

Change tolerance be-

tween the red pin and

the hooks

Stay locked

together Be a press fit part Press fit calculations Resource 3

The hooks do not

clip over the pin

Alter how the two sur-

faces interact

FRDPARRC

The two pieces at the top of the part are to keep the marbles from fall-

ing off the linkages as they carry them up the conveyor belt system. The

small pieces each have extra material protruding on the top to the

sides. This is so a rubber band can be wrapped around them and help

onto the parts to hold the marble. The red pin in the image will be press

fit into the two hook shaped parts. This will allow the link components

to stay together even though it will not be one solid piece of material.

Nylon

This component will be made with nylon. This was chosen so that there

was good elasticity in the material so that the hook end could be slight-

ly bent to fit width wise onto the bar end.

COMPONENT 6: THE BASE

This component will be used to secure the other components in the system.

The grey pins shown on the top of the part will slide into the holes on the

stand components. So the students can set up multiple configurations, the

pins have been placed so that the stands can either be standing straight up or

lay horizontally across the base. To lower the weight of the base, it has been

shelled out. To add more stability that was lost in shelling out the part, ribs

have been placed on the bottom of the feature. This will further prevent

breakage and deforming of the base as the device is used. The base will be

the maximum part size at 10inches x 4inches x 1 inch. Clipable features have

been added to the sides so that users can combine base pieces to extend the

stability and size of their machine.

Polystyrene

This component will be made with polystyrene. The purpose of using polysty-

rene is so that the base is less flexible than other features and will not de-

form as easily. Polystyrene is a strong, lightweight plastic and can be easily

injection molded.

FR DP A R R C

Provide sup-

port for an-

chors

Strong enough to

add counter torque

against motor

torque

Resources 1, 2, and 6 The material is too

brittle and snaps

Change the material

to ABS plastic or Ny-

lon

Does not de-

form

Will not deform or

stay bent from a

small amount of

pressure

Stress strain curve Resource 6

Solids notes

FRDPARRC

COMPONENT 7: THE MARBLE

The marbles being used in the conveyor belt system will be steel marbles

bought from an outside manufacturer. They will weigh 0.04 kg which is a

standard steel marble weight. Steel was chosen because this type of marble is

easily accessible, it is a safe material, and the marbles will be unlikely to break

when dropped from the conveyor belt if they miss their target.

FR DP A R R C

Do not break

Marble must be able

to withstand con-

sistent falls from var-

ied heights

Stress Strain curves Childhood experiences

Resources 1, 2, and 9

The marbles are

too small and are

easily lost

Choose a marble

that anyone can buy

from any standard

store.

Does not de-

form

Will not deform or stay

bent from a small

amount of pressure

Stress strain curve Solids notes

The marbles are

too hard and dent

the component they

fall onto

Make that compo-

nent out of a harder

material.

PROJECT REQUIREMENTS Press fit part

The bars of the links will be press fit into the links to hold them together as one solid piece.

Sliding fit

The pins will be sliding fit with the holes on the stand.

The pins on the base will be sliding fit with the holes on the stand.

The gears will be sliding fit with the pins.

The base will be sliding fit with other base pieces if the user decides to clip them together.

Motor

An Arduino motor is being incorporated into the module to act as a power source. It will be safely encased and rotate the

first gear in the system.

Mechanical Linkage

The link components

Both gear components

MATHEMATICS In homework 4, the basic mathematics behind each module was shown. Because I chose module one, I will continue with those formulas to show

why I made the material selections I did. I placed each equation into an excel spreadsheet and changed the variables until I found a design and ma-

terial that worked for the factor of safety I wanted to have.

The first equation used was to find the deflection in each bar on the links as they go around the conveyor belt.

Deflection = (W*L3)/(192*E*I)

The second equation used was to find the tension in each bar based off of the deflection.

Tension= (Deflection*A)/(F.S.)

The next three equations were used to find F1, F2, and torque of the system given that I knew the power and velocity of the system.

P=(F1-F2)V

F1+F2=2T

F1=F2eμθ

These of course where T=Torque, V=Velocity, P=Power, L=Length, W=Weight, E=Elasticity, I=Moment of Inertia, A=Area, F.S.=Factor of

Safety, μ=Coefficient of Friction, and θ=Angle

Because I chose the Arduino motor first, I knew my minimum torque was 250 g.cm. I chose a power of 2Kw, an angular ve-

locity (ω) of 12 rad/sec and a radius of 2inches. From this information I can find F1, F2, and Tension of the system.

V=ω*R=12*2=24

P=(F1+F2)*V

P/V=F1+F2

F1=F2eμθ

(P/V)=F2(eμθ+1)

F2=(P/V)/(eμθ

+1)

T=(F1+F2)/2

From the bold equations I can plug in various coefficients of friction to determine the tension in my system. This will help me choose my material

for the link and gear components. If we use the highest coefficient of friction for each material we get the following numbers.

Nylon T= 0.04166

Polystyrene T=0.0833

ABS Plastic T=0.1663

To allow the lowest amount of tension on each link, Nylon has been chosen as the material to be used for both the links and the gear pieces. To

make sure this amount of tension will not break using Nylon, the deflection will be calculated and then compared to the ultimate tensile strength of

nylon if it were to be in the pin shape designed.

For a clamped ended beam (or pin) the deflection equation is

(W*L3)/(192*E*I)

The calculated deflection of this part is 0.00982 cm

A factor of safety of 3 will be used for this part.

The ultimate tensile stress for Nylon, in this shape,

based on the stress strain curve to the left, is found

by the equation

UTS=Maximum load/Area of cross section

This gives us 1107 lb-ft

Because the tension in the system is much lower

than this, nylon will be fine to use as a material for

the links and the gears.

This diagram came from resource 8.

Resources

1. "Coefficient Of Friction Equation And Table Chart - Engineers Edge". Engineersedge.com. N.p., 2017. Web.

11 Apr. 2017.

2. "Modulus Of Elasticity Or Young's Modulus - And Tensile Modulus For Common Materi-

als". Engineeringtoolbox.com. N.p., 2017. Web. 12 Apr. 2017.

3. Oberg, Erik. Machinery's Handbook. 1st ed. New York: Industrial Press, 2000. Print.

4. "Plastic Gears - Custom Made Gears Or Order From Stock". Sdp-si.com. N.p., 2017. Web. 18 Apr. 2017.

5. "Purchase Small DC Motor". Studica.com. N.p., 2017. Web. 18 Apr. 2017.

6. Scott, Chris. "Polystyrene Information And Properties". Polymerprocessing.com. N.p., 2017. Web. 14 Apr.

2017.

7. "Small Mechanical Components: Precision Gears, Gear Assemblies, Timing Belts, Timing Belt Pulleys

And Couplings - SDP/SI". Sdp-si.com. N.p., 2017. Web. 18 Apr. 2017.

8. Stress Strain. Available at: https://www.saylor.org/site/wp-content/uploads/2012/09/ME1022.2.4.pdf. Ac-

cessed April 18, 2017.

9. Tower, The. "The Chaos Tower - Scientificsonline.Com". Scientificsonline.com. N.p., 2017. Web. 18 Apr.

2017.