mechanical engineering crash course

Pre-Season Workshop – November 2010

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Mechanical Engineering Crash Course

Steve Evans

Team 1294


Acknowledgements

• Steve Evans - Team 1294• Brian Gattman - Team 2910• Andy Baker - Team 45

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Mechanical Engineering

• Very broad discipline– Design

• Modular Design, Mechanical Devices, Drive Base, Design Process– Drafting / CAD

• Inventor and ProE– Manufacturing methods– Thermodynamics / Heat Transfer– Fluid Mechanics

• Pneumatics– Control and Measurement

• LabView, Electrical Design– Dynamics and Vibrations– Organization

• Project Management, Team Dynamics, Sources of Parts

• We have only 2 hours…

MechE related workshops available today


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Agenda

• Example Problem Statement• FRC Knowledge Depth• Mechanical Engineering: FRC Introduction

– Forces & Moments– Free Body Diagrams– Stress & Strain– Mechanics of Materials– Work & Power– FRC Motors– Gear Ratios

• Problem Solution• Q&A (and throughout!)• Drivetrains• Arms & Lifts


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Quick Poll

• Who has taken or understands… (not a contest)

– Trigonometry

– Physics

– Calculus


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Example Problem Statement

• Lift a ball to the top of a goal– Start: ground

– End: 8 feet

– 5 lbs

– 3 ft diameter

• Use primitive design– Has many issues

– Not the point

Area of Interest


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FRC Knowledge Depth

• 6 weeks: impossibly short– Know enough to be dangerous

– Make informed decisions

• Following info is “truth”– Assumptions required

• 80/20 Principle– Good for FIRST

– Not so good for airplanes


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Non-Contact Forces

• Gravity– Holds you on Earth’s surface– Turns your “mass” into “weight”

– Holds planets in orbits, causes tides

• Magnetism– Cousin to electrical current– Motors, electromagnets, many more

– Why your microwave works

Tidal Force: Moon’s differential gravity field on earth’s surface


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Contact Forces

• High School Physics

– Good approximations

– Works for FRC

• Industry– Accuracy required

Bird Strike: Simulation on jet engine blades

Classic HS Physics Problem


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Moments (AKA Torque)

• Forces acting at a distance• M = r x F

– Moment = radius (distance) x Force (normal)

• Distance

• Force

• Sine of angle between

Bicep Curl: Looks a little like our robot problem…

Fr

M


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Fundamentals and Units

• F = m * a – Force = mass x acceleration

• T = I * α – Torque = Moment of Inertia x Angular Acceleration

English (abbr) SI (abbr)

Force Pound lb Newton N

Moment Inch Pound in-lb Newton Meter N-m


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Free Body Diagram

• BEST way to start a new problem

• Pictorial representation which isolates body from world• Shows all loads acting on a body• Problem can be better understood

We cut through the robot!Forces needed to represent.


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Free Body Diagram

• Why this state?• Draw all forces and moments• Solve for reactions

36in36in

Motor & Gearbox attached to robot and arm

Arm

Gripper

Ball


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Free Body Diagram

WBWA

36in36in

WG

TM

FRΣFY = m * aY = m * (ΔvY/Δt) = 0

+FR – WA – WG – WB = 0

X

Y

FR = WA + WG + WB

Forces Moments

FR = 10lb+4lb + 5lb = 19lb

ΣMO = I * α = m * (Δω/Δt) = 0

+TM–18in*WA–36in*WG– 54in*WB=0

? ?

Point O

+TM=180inlb+144inlb+270inlb = 594inlb

Z


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Question Break


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Tension & Compression

• Tension pullsσ > 0

• Compression squishes

σ < 0


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Bending

smile

frown

Which portions are in states of tension, compression, or zero stress?


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Cross Section Selection

• Intuitively, which cross section is preferred for the arm?

A B C D

Section Cut Here

Neutral axis

E F G


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Stress and Strain

• A BRIEF overview• For any individual element

– Stress is the average amount of force per unit area

σNormal = F / A

σBending = M * c / I

(Bending Stress = Moment x centroid / Area Moment of Inertia)

-centroid is the distance from neutral axis to extreme fiber

– Strain is the percent elongation

ε = ΔL / L

Thanks, Wikipedia!


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Stress and Strain

• Young’s Modulus (E) relates them

σ = E * ε (like spring theory F = k * x)• Everything is a spring, nothing is truly rigid• Higher modulus denotes a stiffer material (spring)

E

Elastic Deformationσ = E * ε

σ


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Material Failure

Tensile Test SpecimenAtomic bonds and dislocations


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Material and Gauge Selection

• Determine needed size of elements based on criteria– Displacement– Stress– Strain– Buckling, Crack Propagation, Resonance, etc

• Can predict failure of elements– Way beyond the scope of this workshop


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Material Properties

Plastic Wood Aluminum Titanium Steel

E (106psi)

.35 1.9 10 15 29

Density (lb/in3)

.043 .017 .098 .161 .284

Yield (103psi)

9 35 120 50

Ultimate (103psi)

9.5 15 38 130 65

Ult / ρ 220 880 390 810 230

Values are for:Tension conditionPolycarbonate, Air Dried Douglas Fir, 6061-T6 Aluminum, 6-4 Titanium, ASTM-A992 Gr 50 Steel


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Question Break


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Work

• Work is a measure of energy added to a systemW = F · d

W = T * Θ

– For the Ball, only gravitational energy is added

W = m*g*h

W = 5lb*8 feet = 40 ft-lb = 52 Joules

Is there other work done?


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Power

• Power is how fast the work is doneP = dW / dt– Lets say we wanted to raise the ball in 2 seconds

P = 52J / 2s = 26W– This is the average power delivered, for pure height gain– Arm must trace arc, power required isn’t constant for

constant speed– Peak power required is much higher


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Motors!


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DC Permanent Magnet Motor

T


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Motor Properties

• Important Characteristics– ω (speed, in RPM or rot/s)

– T (torque, in N-m)

– P (power, in W)• P = T * ω


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Motor Properties

ω0

T

Tstall

ωfree

P

Ppeak

ωfree/2


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2009 FRC Motors

QTY Supplier

Reference Voltage on data sheet Gear ratio

Stall torque (Nm)

Stall current (A)

Free speed (rpm)

Free speed (rad/s)

Free current (A)

Peak power, 10.5 V supply (W)

1Nippon-Denso 12 10.6 18.6 84 8.8 1.8 22.0

1 Keyang 12 11.8 19 65 7 0.75 20.1

1Fisher-Price 12 0.5 70 15600 1634 1.25 183.8

2 Globe 10 117:1 17.0 21.58 81 8.5 0.82 55.04 CIM 12 2.4 133 5310 556.1 2.7 337.02 Mabuchi 20 0.1 6.2 16400 1717 0.18 28.2

2Banebots - Mabuchi 12 0.2 37 17500 1833 0.95 108.0

Lets pick one

From our FBD and AnalysisT = 594 inlbs = 67.1 NmPmin = 26 W


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Globe Motor Properties

ω0

T

17 Nm

81 rot/s

P

55 W

40.5 – 48.6rot/s

8.5Nm

6.8Nm


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Question Break


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Gear Types

Spur

Worm Rack and PinionPlanetary

BevelCrossed Helical


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Gear Torque and Speed

Ratio = Ndriven = 30 = 0.5 (:1) Ndriver 60

Tdriven = R*Tdriver = 0.5 Tdriver

ωdriven = ωdriver/R = 2 ωdriver


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Gear Selection

• 6.8 Nm is available from motor at 60% free speed• 67.1 Nm is needed to raise the arm

• Ratio = Tdriven = 67.1 Nm = 9.9:1 = 10:1

Tdriver 6.8 Nm

~

10:1 may need a very large gearfor a single stage…


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Gear Trains

Ratios multiply across gear trains


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Solution

Globe Motor selected for worst case10:1 ratio gear trainRaise ball in ~2s


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Questions


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Extra Statics Problem

d=20mm

50mm

30kN

800mm

A

C

B

600mm

AB 30x50 rectangularBC 20mm rodPinned JointsFind the stress in AB and BC


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Free Body Diagram

30kN

0.8m

Cy

B

0.6m

Cx

Ay

Ax

ΣMC = 0 = AX(0.6m) – 30kN(0.8m) AX = +40kN

ΣFX = 0 = AX + CX

CX = -AX CX = -40kN

+

+

ΣFY = 0 = AY + CY – 30kNAY + CY = 30kN

+


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Breakout FBD

30kN

Ay

Ax

ΣMB = 0 = -AY(0.8m) = 0 AY = 0

CY = 30kN

+

B

0.8m


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2 Force Members

30kN

0.8m

Cy

B

0.6m

Cx

Ay

Ax

CX = -40kNCY = 30kN


FIRST Robotics Drive Systems

• Importance• Basics• Drive Types• Resources• Traction• Mobility• Speed• Timing• Importance

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Importance

The best drive train… is more important than anything else on the

robot meets your strategy goals can be built with your resources rarely needs maintenance can be fixed within 4 minutes is more important than anything else on the

robot45


Basics

Know your resources Decide after kickoff:

› Speed, power, shifting, mobility Use most powerful motors on drivetrain Don’t drive ½ of your robot… WEIGH IT

DOWN! Break it early Give software team TIME to work Give drivers TIME to drive

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Drive Types: 2 wheel drive

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Caster

DrivenWheel

+ Easy to design+ Easy to build+ Light weight+ Inexpensive+ Agile

- Not much power- Will not do well on ramps- Less able to hold position

Motor(s)Motor(s)


Drive Types: 4 wheel drive, 2 gearboxes

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Chain or belt

DrivenWheels

+ Easy to design+ Easy to build+ Inexpensive+ Powerful+ Sturdy and stable

- Not agile-Turning is difficult-Adjustments needed

Motor(s)Motor(s)

DrivenWheels

Resource:Chris Hibner white paper on ChiefDelphi.comProves that a wide 4wd drive base can turn easily



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DrivenWheels

+ Easy to design+ Easy to build+ Powerful+ Sturdy and stable+ Many options Mecanum, traction

- Heavy- Costly

Motor(s)Motor(s)

DrivenWheels

Motor(s) Motor(s)



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Gearbox Gearbox

+ Easy to design+ Easy to build+ Powerful+ Stable+ Agile*

- Heavy **- Expensive **

** - depending on wheel type

*2 ways to be agile

A)Lower contact point on center wheelB)Omni wheels on front or back or both

This is the GOLD STANDARD in FRC

+ simple+ easy+ fast and powerful+ agile


Drive Types: N wheel drive, 2 gearboxes

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Gearbox Gearbox

+ Powerful+ Stable+ Agile*

- HEAVY- EXPENSIVE

*2 ways to be agile

A)Lower contact point on center wheelB)Omni wheels on front or back or both

Sole benefit: Ability to go over things


Drive Types: Tank tread drive, 2 gearboxes

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Gearbox Gearbox

+ Powerful+ VERY Stable

- NOT AGILE- HEAVY- Inefficient- EXPENSIVE- Hard to maintain For turning, lower the contact

point on center of track wheel

Sole benefit: Ability to go over things

Will NOT push more than a well-controlled 6wd


Drive Types: 3 wheel

Various types Lightweight Fast Non-standard

› (design intensive)

Examples:› 16 in 2008› 67 in 2005

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Gearbox Gearbox


Drive Types:Holonomic - Killough

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4 wheel drive or 3 wheel drive Stephen Killough, 1994

+ Simple Mechanics

+ Immediate Turning

+ Simple Control – 4 wheel independent- No brake- Minimal pushing power- Jittery ride, unless w/ dualies- Incline difficulty


Drive Types: Mecanum

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+ Simple mechanisms

+ Immediate turn

+ Simple control – 4 wheel independent- Minimal brake- OK pushing power- Needs a suspension- Difficulty on inclines


Drive Type:Swerve or crab steering

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High-traction wheels Each wheel rotates to steer+ No friction losses in wheel-floor interface+ Ability to push or hold position+ Simple wheels- Complex system to control and program- Mechanical and control issues- Difficult to drive- Wheel turning delay- Omnidirectional drive systems

presentation:- http://first.wpi.edu/Workshops

2008CON.html/


Mobility

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• Move +/- 1 foot in any direction in under 1 second

• Generally speaking, the more mobile your robot is, the less it can resist a push

More mobile less mobile

Kill

ough

Mec

anum

Swer

ve

6+ w

heel

4wd

long

Tank

Tr

eads

4wd

wid

e


Traction

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Static vs Dynamic (10% lower)› Once you slip, you will get pushed› Design encoders into your system› Dynamic breaking & traction control

Pushing force = Weight * › = friction coefficient

Normal Force

(weight)Static friction coefficients = 0.1 = caster (free spinning) = 0.3 = hard plastic = 0.8 = smooth rubber, 80A durometer = 1.0 = sticky rubber, 70A durometer = 1.1 = conveyor treads

Pushing Force


More on Traction

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• You can determine

mass Fpull

Fweight

Material w/

Fpull / Fweight


Center of gravity (Cg)

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Robot mass is represented at one point Mobility increases when Cg is low and centered High parts = light weight Low parts = heavy (within reason)

Battery motors pump,

etc.

Battery motors pump, etc.

Ms Mobile

Mr Tippy


Speed

• Game dependent, however… this increases every year

• 2008 max: 20 ft/sec

• Controllable top speed: 15 ft/sec

• Average 1-speed rate: 9 ft/sec

• Good pushing speed: 5 ft/sec

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Timing

• Get something driving early– End of week 2– Practice for operators– Lessons learned for electrical– Strategy lessons

• Continuously improve– Good enough is not good enough

• Finish final drivetrain by week 4

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Importance

Boat anchor = any heavy mass that does not move

A non-reliable or non-repairable drive base will turn your robot into a boat anchor

Good drive bases win consistently Reliable drive bases win awards Well-controlled, robust drive bases win

Championships

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Articulating ArmsArticulating Arms

• Shoulder• Elbow• Wrist

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Arm: Forces, Angles & TorqueArm: Forces, Angles & Torque

Example: Lifting at different anglesTorque = Force x DistanceSame force, different angle, less torque

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10 lbs

< D

10 lbs

D


Arm: Design TipsArm: Design Tips

Lightweight Materials: tubes, thin wall sheetDesign-in sensors for feedback & control

limit switches and potentiometers

Linkages help control long armsKISS

Less parts… to build or breakEasier to operateMore robust

Use off-the-shelf itemsCounterbalance

Spring, weight, pneumatic, etc.66


Four Bar LinkageFour Bar Linkage

• Pin loadings can be very high• Watch for buckling in lower member• Counterbalance if you can• Keep CG aft• Limited rotation• Keeps gripper in known location

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4 bar linkage example: 340 & 4 bar linkage example: 340 & 217 in 2007217 in 2007

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Arm Example: 1114 in 2004Arm Example: 1114 in 2004

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Telescoping LiftsTelescoping Lifts

Extension LiftMotion achieved by stacked members sliding on each other

Scissor LiftMotion achieved by “unfolding” crossed members

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Extension Lift ConsiderationsExtension Lift Considerations

Drive cables up AND down, or add a cable recoil device

Segments must move freelyCable lengths must be adjustableMinimize slop and free-playMaximize segment overlap

20% minimummore for bottom, less for top

Stiffness and strength are neededHeavy system, overlapping partsMinimize weight,

especially at the top

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Pink Team 233 - 2008Pink Team 233 - 2008

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Extension - RiggingExtension - Rigging

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Continuous Cascade


Extension: Continuous RiggingExtension: Continuous Rigging

Cable Goes Same Speed for Up and Down

Intermediate Sections sometimes Jam

Low Cable TensionMore complex cable

routingThe final stage moves up

first and down last

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Slider(Stage3)

Stage2

Stage1

Base


Extension: Continuous Extension: Continuous Internal RiggingInternal Rigging

Even More complex cable routing

Cleaner and protected cables

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Slider(Stage3)

Stage2

Stage1

Base


Extension: Cascade RiggingExtension: Cascade Rigging

Up-going and Down-going Cables Have Different Speeds

Different Cable SpeedsCan be Handled withDifferent Drum Diameters or Multiple Pulleys

Intermediate SectionsDon’t Jam

Much More Tension on the lower stage cablesNeeds lower gearing to deal

with higher forces

76

Slider(Stage3)

Stage2

Stage1

Base


Scissor LiftsScissor Lifts

AdvantagesMinimum retracted height –

can go under field barriersDisadvantages

Tends to be heavy to be stable enough

Doesn’t deal well with sideloads

Must be built very preciselyStability decreases as height

increasesLoads very high to raise at

beginning of travelI recommend you stay away

from this!77


Arm vs. LiftArm vs. Lift

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FeatureFeature ArmArm LiftLift Reach over objectReach over object YesYes NoNo

Fall over, get upFall over, get up Yes, if strong enoughYes, if strong enough NoNo

Go under barriersGo under barriers Yes, fold downYes, fold down Maybe, limits lift heightMaybe, limits lift height

Center of gravity (Cg)Center of gravity (Cg) Not centralizedNot centralized Centralized massCentralized mass

Small space operationSmall space operation No, needs swing roomNo, needs swing room YesYes

How high?How high? More articulations, more More articulations, more height (difficult)height (difficult)

More lift sections, more More lift sections, more height (easier)height (easier)

ComplexityComplexity ModerateModerate HighHigh

Powerful liftPowerful lift ModerateModerate HighHigh

CombinationCombination Insert 1-stage lift atInsert 1-stage lift at bottom of armbottom of arm


Braking: Prevent Back-drivingBraking: Prevent Back-driving

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Ratchet Device - completely lock in one direction in discrete increments - such as used in many winches

Clutch Bearing - completely lock in one direction Brake pads - simple device that squeezes on a

rotating device to stop motion - can lock in both directionsDisc brakes - like those on your carGear brakes - applied to lowest torque gear in gearbox

Dynamic Breaking in electrical components let go when power is lost

Any gearbox that cannot be back-driven alone is probably very inefficient


Power

SummaryAll motors can lift the same amount (assuming 100% power

transfer efficiencies) - they just do it at different ratesNo power transfer mechanisms are 100% efficient

Inefficiencies (friction losses, binding, etc.)Design in a Safety Factor (2x, 4x)

80


Design is an Iterative ProcessDesign is an Iterative Process

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Final Design


Best Practices 1/2

• Use Gracious Professionalism• KISS – Simplicity wins • Use ALL resources on main concept• Don’t give up on good designs• Look at the game differently• Plan for automode – is it worth it?• Be very good at 1 thing, at least• Drive by end of week 2, but weigh it down!• Make good prototypes

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Best Practices 2/2

• Support shafts in two places. No more, no less• Avoid long cantilevered loads• Avoid press fits and friction belting• Alignment, alignment, alignment!• Break it early• Finish early: debug start in week 4• “Good enough” is only OK• Practice, practice, practice• Checklists, checklists, checklists

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Final Questions?


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Thanks

• … Engineering?

– “Scientists investigate that which already is; Engineers create that which has never been.”

Dr. Albert Einstein

– “To the optimist, the glass is half full. To the pessimist, the glass is half empty. To the engineer, the glass is twice as big as it needs to be.”

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mechanical engineering crash course

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