mechanisms & manipulators frc conference 4/15/04 by joe johnson and raul olivera
TRANSCRIPT
Mechanisms & Manipulators FRC Conference 4/15/04
By Joe Johnson and 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
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 (calculated earlier)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 ;-)
• Pivots on Pivots are confusing to drivers– Follow my own advice?– NO… …1996, 1997, 1999, 2000, 2001, 2003 (2/3rds)
• “Virtual 4 bars” help, but are still confusing – 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 Advice
Feedback Control is HUGE– Measure Current Position
– Set Desired Position
– Calculate Error
– Take Action Based on Error (Search Internet for PID control)
General Arm Advice
• Software can only fix so much– Typical: Design for Stall Torque, live with free
speed (try to limit in software – extremely hard)
– Better: Design for Free Speed, verify that you have “enough” torque (try to limit torque in software – merely difficult)
– Best: Do “Better”, but have a mechanical limit to stall torque – friction drive or slip clutch for example
General Arm Advice
• You can calculate stress!– Pure Compression/Tension: F/A– Beam: Mc/I– Twisting: ??– Buckling: ??– Buy Beer & Johnston – Mechanics Text
• 6 Degrees of Freedom – Consider them all
• Design in “Fuseable Link”
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
– Tends 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
Braking - to Prevent Back-driving
• 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 directions– Disc brakes - like those on your car
– Gear brakes - applied to lowest torque gear in gearbox
• Note : any gearbox that cannot be back-driven is probably very inefficient
Handling Objects
• Accumulators
• Conveyors
• Grippers
• Latches & Grabbers
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
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
• 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
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)
Grippers
General Arm Advice
• 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
Latches / Grabbers
Other Clever Mechanisms
• Wonderful Uses for Spectra cable
• Chain turnbuckle
• x
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
Choosing the Right Motor
BACKUP SLIDES(from ChrisH’s presentation)
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
Four Bar - Advantages & Disadvantages
• Advantages
– Great For Fixed Heights
– On/Off Control
– Lift Can Be Counter-Balanced or Spring Loaded to Reduce the Load on Actuator
– Good candidate for Pnuematic or Screw actuation
• Disadvantages
– Need Clearance in Front During Lift
– Can’t Go Under Obstacles Lower Than Retracted Lift
– Got to Watch CG
– If Pneumatic, only two positions, Up and Down
Four Bar - Calculations
Llink
Mbase
Fobject
Fgripper1
Fgripper2
Mgripper
Dobject DgripperFhit
Hgripper
Flink2DlinkFlink1
Dlower/2
Mlink
• Under Construction Check Back Later
Stress Calculations (cont.)
• A, c and I for Rectangular and Circular Sections
1212
3ii
3oo
hbhbI
bo
c
2
hc
iioohbhbA
ho
bi
hi
2
i
2
odd
4A
do
di
2o
dc
4
i
4
odd
64I
Stress Calculations (cont.)
• A, c and I for T-Sections
X 2
2
x222
322
2
1
x111
311
x 2
hchb
hb
2
hchb
hbI
1212
A2
hhhb
2
hhb
c
2
1221
11
x1
2211hbhbA Y
b1
h2
b2
cy
h1 cx1
cx2
x121x2chhc
2
bc 1
y
1212
322
311
y
bhbhI
Stress Calculations (cont.)
• A, c and I for C-Sections (Assumes Equal Legs)
X 2
2
x222
322
2
1
x111
311
x 2
hchb2
hb2
2
hchb
hbI
1212
A2
hhhb2
2
hhb
c
2
1221
11
x1
2211hb2hbA Y
b1
h2
b2
cy
h1 cx1
cx2
x121x2chhc
2
bc 1
y
1212
322
311
y
bh2
bhI
Stress Calculations (cont.)
• A, c and I for L-Angles
X 2
2
x222
322
2
1
x111
311
x 2
hchb
hb
2
hchb
hbI
1212
A2
hhhb
2
hhb
c
2
1221
11
x1
2211hbhbA Y
b1
h2
b2
cy1
h1 cx1
cx2
x121x2chhc
cy2
A2bbh
2
bbh
c2
221
11
y1
y11y2
cbc
2
2
y122
322
2
y1
111
311
y 2
bcbh
bhc
2
bbh
bhI
1212
Allowable Stresses
allowable = yeild / Safety Factor
• For the FIRST competition I use a Static Safety Factor of 4.
• While on the high side it allows for unknowns and dynamic loads
• Haven’t had anything break yet!
Allowable Stresses
• Here are some properties for typical robot materials
Material Desig Temper Yield Tensile Shear Modulus(ksi) (ksi) (ksi) (msi)
Alum 6061 O 8 18 12 10Alum 6061 T6 40 45 30 10Brass C36000 18-45 49-68 30-38 14Copper C17000 135-165? 165-200? 19Mild Steel 1015-22 HR 48 65 30PVC Rigid 6-8 0.3-1