Mechanisms & Manipulators
FRC Conference 4/21/05
By Raul Olivera
Some Basic Physics
• Forces, Angles & Torque
• Power
Forces, Angles & Torque
• Example #1 - Lifting
10 lbs
– Same force, different angle,
less torque
10 lbs
D
<D
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 / Time
OR
• Power = Torque x Rotational Velocity
Power is all about how fast you can move
something
Power
• Example - Lifting
– Same torque, different speed
10 lbs
0.1 HP, 100 RPM
Motor w/ 1” sprocket
10 lbs
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
–
–
–
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High strength
Many types (alloys) available
Heavy, rusts,
Harder to processes with hand tools
• Aluminum
–
–
–
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Easy to work with for hand fabrication processes
Light weight; many shapes available
Essentially does not rust
Lower strength
Materials
• Lexan
–
–
–
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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”
0.8”
1.0”
Hollow w/ 0.1” walls
0.8”
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:
Bending
  Mc
I
Where:
 = Bending Stress
M = Moment (bending force)
I = Moment of Inertia of Section
c = distance from Central Axis
Tensile
 tens 
Ftens
A
Where:
 = Tensile Stress
Ftens = Tensile Force
A = Area of Section
Shear
 
Fshear
A
Where:
 = Shear Stress
Fshear = Shear Force
A = Area of Section
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:
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–
–
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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 Advice
Feedback 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
•
Slider
(Stage3)
Stage2
Stage1
I do not prefer this one!
Base
Arms vs. Extension Lifts
•
•
•
•
•
•
•
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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?
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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:
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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
Conveyors
Why 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 nonmoving 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
Dowel Pins
1/4-20 Screw
(grind flats)
1/4-20 Nut
1/2 Alum Sq Bar
3/8 Dia. Rod
Pneumatics vs. Motors
Some, 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
2.5
Time (Sec)
2
1.5
1
0.5
0
0
10
20
30
40
50
Weight (Kg)
Power Vs Weight (Push)
Power (Watt)
• Warning: rated load is
only for holding
• Actual power curve is
much lower
Time Vs Weight (Push)
90
80
70
60
50
40
30
20
10
0
0
10
20
30
Weight (Kg)
40
50