Mechanisms & Manipulators FRC Conference 4/21/05

By Raul Olivera

Some Basic Physics

• Forces, Angles & Torque

• Power

Forces, Angles & Torque

• Example #1 - Lifting– Same force, different angle,

less torque

10 lbs

10 lbs

< DD

Forces, Angles & Torque

• Example #2 - Pulling on object– One angle helps secure object – The other does not

Forces, Angles & Torque

• Example #2 - Pulling on object (cont’d)

This one want to rotate clockwise and let go

This one want to rotate counter- clockwise and grab even harder

Power

• Power = Force x Distance / TimeOR

• Power = Torque x Rotational Velocity

Power is all about how fast you can move something

Power

• Example - Lifting– Same torque, different speed

10 lbs 10 lbs

0.1 HP, 100 RPM Motor w/ 1” sprocket

0.2 HP, 200 RPM Motor w/ 1” sprocket OR 100 RPM w/ 2” sprocket

Power

• In Summary:– All motors can lift the same amount (assuming

100% power transfer efficiencies) - they just do it at different rates

• BUT, no power transfer mechanisms are 100% efficient – If you do not account for these inefficiencies,

your performance will not be what you expected

Structural Integrity

• Materials

• Shapes / Weights

• Fabrication processes

• Environment

Materials• Steel

– High strength

– Many types (alloys) available

– Heavy, rusts,

– Harder to processes with hand tools

• Aluminum – Easy to work with for hand fabrication processes

– Light weight; many shapes available

– Essentially does not rust

– Lower strength

Materials• Lexan

– Very tough impact strength

– But, lower tensile strength than aluminum

– Best material to use when you need transparency

– Comes in very limited forms/shapes

• PVC– Very easy to work with and assemble prefab shapes

– Never rusts, very flexible, bounces back (when new)

– Strength is relatively low

My Favorite Materials• Spectra Cable

– Stronger than steel for the same diameter– Very slippery

• Easy to route• Needs special knots to tie

– Can only get it from Small Parts and select other suppliers

• Pop Rivets – Lighter than screws but slightly weaker - just use more– Steel and Aluminum available– Great for blind assemblies and quick repairs

Structural Shapes• Take a look at these two extrusions - both made from same

Aluminum alloy:– Which one is stronger?– Which one weighs more?

1.0”

1.0” 0.8”

0.8”

Hollow w/ 0.1” walls Solid bar

Structural Shapes

• The solid bar is 78% stronger in tension

• The solid bar weighs 78% more

• But, the hollow bar is 44% stronger in bending– And is similarly stronger in torsion

Stress Calculations

• It all boils down to 3 equations:

IMc

A

Ftens

tens

A

Fshear

Where: = Bending StressM = Moment (bending force)I = Moment of Inertia of Sectionc = distance from Central Axis

Where: = Tensile StressFtens = Tensile ForceA = Area of Section

Where: = Shear StressFshear = Shear ForceA = Area of Section

Bending Tensile Shear

Structural Shapes

• I am willing to bet that none of our robots are optimized with respect to strength to weight ratios– We all have more material than we need in some areas

and less than we need in others.

– It would take a thorough finite element analysis of our entire robot with all possible loading to figure it all out

– We only get 6 weeks!!

• But, this does not mean we cannot improve

Structural Shapes• Things to avoid or carefully design:

– Sharp inside cuts - leave a radius / fillet– Fastener holes that are too close to an edge– Welding corners without adding a gusset– Brittle materials - bending is easy to repair - cracks are not

• Things that might help:– Add thin tension members to stabilize structures

• i.e. guy wires, strips of sheetmetal

– Use multiple smaller fasteners rather than one big one (did I say I like pop rivets?)

– Design in mechanical fuses - a desired place for failure during excessive and unusual forces to avoid catastrophic failure

• Crumple zones• Break-away parts - using weaker fasteners that can break (i.e.

aluminum pop rivets)

Fabrication Processes• Laser cutting causes localized hardening of some

metals– Use this to your benefit when laser cutting steel

sprockets

• Cold forming causes some changes in strength properties– Some materials get significantly weaker– Be aware of Aluminum grades and hardness's

• Welding - should not be a problem if an experienced welder does it

Environmental Effects

• UV exposure - causes some plastics to change their structure and become brittle– ie. Lexan, PVC

• Cold temperatures - cause some materials, especially plastics to become brittle– Can cause damage when shipping from cold

climates

Going Up

• Arms

• Vertical Lifts

• Arms vs. Lifts

• Passive Assistance

What is an “Arm”?

• An “Arm” is a device for grabbing and moving objects using members that rotate about their ends

General Arm Advice

• Thin Walled Tubing is your friend– 1/16 wall is a good compromise

• Known good sources– Mcmaster.com

– Onlinemetals.com

– Airpartsinc.com

General Arm Advice• Every Pivot has to be engineered

– reduce, reuse, recycle ;-)

• “Virtual 4 bars”– Drive motors low with chain acting as “4 bar”– Advantage over real 4-bar:

• low motor• range of motion

• Think about operator interface – very important

General Arm AdviceFeedback Control is HUGE

– Measure Current Position

– Compare to Desired Position• Calculate Error

– Take Action Based on Error (Search Internet for PID control)

– SW/Feedback cannot fix all control problems effectively

Four Bar

Four Bar - Design Considerations

• Pin Loadings can be very high

• Watch for buckling in lower member

• Counterbalance if you can

• Keep CG aft

Vertical Lifts

• Extension

• Scissors

Extension

Scissors

Scissors vs. Extension

• Advantages

– Minimum retracted height - can go under field barriers

• Disadvantages

– Needs to be heavy to be stable enough

– Doesn’t deal well with side loads

– Must be built very precisely

– Stability decreases as height increases

– Loads very high to raise at beginning of travel

• I recommend you stay away from this!

Extension - Design Considerations

• Should be powered down as well as up– If not, make sure to add a device

to take up the slack if it jams• Segments need to move freely• Need to be able to adjust cable

length(s).• Minimize slop / freeplay• Maximize segment overlap

– 20% minimum– more for bottom, less for top

• Stiffness is as important as strength

• Minimize weight, especially at the top

Extension - Rigging

Continuous Cascade

Extension - Rigging - Continuous

• Cable Goes Same Speed for Up and Down

• Intermediate Sections sometimes Jam

• Low Cable Tension

• More complex cable routing

• The final stage moves up first and down last

Slider(Stage3)

Stage2

Stage1

Base

Extension - Rigging - Continuous- All Internal cabling

• Even More complex cable routing

• Cleaner and protected cables Slider(Stage3)

Stage2

Stage1

Base

Extension - Rigging - Cascade

• Up-going and Down-going Cables Have Different Speeds

• Different Cable Speeds Can be Handled with Different Drum Diameters or Multiple Pulleys

• Intermediate Sections Don’t Jam

• Much More Tension on the lower stage cables

– Needs lower gearing to deal with higher forces

• I do not prefer this one!

Slider(Stage3)

Stage2

Stage1

Base

Arms vs. Extension Lifts• Arms can reach over objects; lifts have limited reach

• Arms can right a flipped Robot; lifts probably not

• Arms can fold down to “limbo” under barriers; lift stay tall

• Arms require complex controls and counter-balances; lifts use simple controls

• Lifts maintain a better center of gravity over the base; arms do not - can cause tipping

• Lifts can operate in confined spaces; arms need space to swing up

• Lifts can reach to any height with minimal added complexity; arms need extra articulated joints to reach higher

• Combo may be best in some cases

Passive Assistance

• What is passive assistance?– SPRINGS or BRAKES!

– Use Elastic Energy to your advantage.

– Surgical Tubing

– Constant Force Springs

– Gas Springs

– Torsion Springs

– Follow FIRST Regulations!

Braking - to Prevent Back-driving

• Ratchet Device - completely lock in one direction in discrete increments – ie. 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 directions– Disc brakes - like those on your car

– Gear brakes - applied to lowest torque gear in gearbox

• High ratio worm gear (window, van-door motors)– Note : any gearbox that cannot be back-driven is probably very

inefficient

Handling Objects (Balls)

• Accumulators

• Conveyors

Accumulators

• Accumulator = rotational device that pulls objects in

• Types:– Horizontal tubes - best for gathering balls from floor or platforms

– Vertical tubes - best for sucking or pushing balls between vertical goal pipes

– Wheels - best for big objects where alignment is pre-determined

• When it comes to gathering balls, there is nothing more efficient– If set up in the proper orientation, will not knock the ball away, just

suck it in

Accumulator as Gripper

• Rolling balls into and out of gripper can be VERY Effective

• Examples Off the top of my head:– Team 222 in 1996– Team 177 in 1998– Team 95 in 1998– Team 45 in 2004– Team 111 in 2004

Conveyors• Conveyor - device for moving multiple objects, typically

within your robot

• Types:– Continuous Belts

• Best to use 2 running at same speed to avoid jamming

– Individual Rollers • best for sticky balls that will usually jam on belts and each other

ConveyorsWhy do balls jam on belts?- Sticky and rub against each other as they try to rotate along the conveyor

Solution #1- Use individual rollers- Adds weight and complexity

Solution #2- Use pairs of belts- Increases size and complexity

Solution #3- Use a slippery material for the non-moving surface (Teflon sheet works great)

Other Clever Mechanisms

• Wonderful Uses for Spectra cable

• Chain turnbuckle

Wonderful Uses for Spectra Cable• First you must learn to tie a proper knot in this stuff

– I use a “triple pretzel knot” (I doubt you will find this name in any scouting

book - I made it up) :

• Simple lift cables - pretty obvious use, but how do you adjust the slack (steel cables use turnbuckles)?– Use a tourniquet like device - use a dowel pin to twist the cable on

the outside of the spool or actuated device, and tie-wrap in place

– This works great for adjusting the location of travel also

• If slack can occur, add a latex slack tensioner

• Remote actuations - this cable is so easy to route within your robot frame efficiently– Linear motions (come see team 111 bumper actuation)

– Rotary motions

Spectra Cable (cont’d)Remote Rotary Actuations - instead of chain

Chain Turnbuckle

Parts Needed:- 1/2” Sq Aluminum bar- 1/4-20 Nut- 1/4-20 Screw- 3/8” dia. CRS rod- 1/16” dia. Steel Dowel pins

1/4-20 Screw(grind flats)

1/4-20 Nut 1/2 Alum Sq Bar3/8 Dia. Rod

Dowel Pins

Pneumatics vs. MotorsSome, but not all important differences

• Cylinders use up their power source rather quickly • the 2 air tanks we are allowed do not hold much• Motors use up very little of the total capacity of the battery

• Cylinders are great for quick actuations that transition to large forces• Motors have to be geared for the largest forces

• Our ability to control the position of mechanisms actuated by cylinders is very limited• We are not given dynamic airflow or pressure controls• We are given much more versatile electronic controls for motors

• Since air is compressible, cylinders have built-in shock absorption

• Cylinders used with 1-way valves are great for Armageddon devices - stuff happens when power is shut off• This could be good or bad - use wisely

Force Values

Pneumatics

• Warning: rated load is only for holding

• Actual power curve is much lower

Time Vs Weight (Push)

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50

Weight (Kg)

Tim

e (S

ec)

Power Vs Weight (Push)

0102030405060708090

0 10 20 30 40 50

Weight (Kg)

Po

wer

(W

att)