1. Mechanisms & Manipulators FRC Conference 4/15/04 By Joe Johnson and Raul Olivera

2. Some Basic Physics Forces, Angles & Torque Power

3. Forces, Angles & Torque Example #1 - Lifting –Same force, different angle, less torque 10 lbs < D D

4. Forces, Angles & Torque Example #2 - Pulling on object –One angle helps secure object –The other does not

5. 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

6. Power Power = Force x Distance / Time OR Power = Torque x Rotational Velocity Power is all about how fast you can move something

7. Power Example - Lifting –Same torque, different speed 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

8. 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

9. Structural Integrity Materials Shapes / Weights Fabrication processes Environment

10. 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

11. 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” Hollow w/ 0.1” wallsSolid bar

12. 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

13. Stress Calculations It all boils down to 3 equations: Where:  = Bending Stress M = Moment (calculated earlier) I = Moment of Inertia of Section c = distance from Central Axis Where:  = Tensile Stress F tens = Tensile Force A = Area of Section Where: = Shear Stress F shear = Shear Force A = Area of Section BendingTensileShear

14. 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

15. 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)

16. 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

17. 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

18. Going Up Arms Vertical Lifts Arms vs. Lifts Passive Assistance

19. What is an “Arm”? An “Arm” is a device for grabbing and moving objects using members that rotate about their ends

20. 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

21. 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

22. 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)

23. 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

24. 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”

25. Four Bar

26. Four Bar - Design Considerations Pin Loadings can be very high Watch for buckling in lower member Counterbalance if you can Keep CG aft

27. Vertical Lifts Extension Scissors

28. Extension

29. Scissors

30. 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!

31. 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

32. Extension - Rigging Continuous Cascade

33. 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

34. Extension - Rigging - Continuous - All Internal cabling Even More complex cable routing Cleaner and protected cables Slider (Stage3) Stage2 Stage1 Base

35. 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

36. 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

37. Passive Assistance

38. 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

39. Handling Objects Accumulators Conveyors Grippers Latches & Grabbers

40. 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

41. 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

42. 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 non- moving surface (Teflon sheet works great)

43. Grippers

44. 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

45. Latches / Grabbers

46. Other Clever Mechanisms Wonderful Uses for Spectra cable Chain turnbuckle x

47. 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

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

49. 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 Nut1/2 Alum Sq Bar 3/8 Dia. Rod Dowel Pins

50. 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

51. Choosing the Right Motor

52. BACKUP SLIDES (from ChrisH’s presentation)

53. 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

54. 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

55. 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

56. Four Bar - Calculations L link M base F object F gripper1 F gripper2 M gripper D object D gripper F hit H gripper F link2 D link F link1 D lower /2 M link Under Construction Check Back Later

57. Stress Calculations (cont.) A, c and I for Rectangular and Circular Sections bobo c hoho bibi hihi dodo didi

58. Stress Calculations (cont.) A, c and I for T-Sections X Y b1b1 h2h2 b2b2 cycy h1h1 c x1 c x2

59. Stress Calculations (cont.) A, c and I for C-Sections (Assumes Equal Legs) X Y b1b1 h2h2 b2b2 cycy h1h1 c x1 c x2

60. Stress Calculations (cont.) A, c and I for L-Angles X Y b1b1 h2h2 b2b2 c y1 h1h1 c x1 c x2 c y2

61. 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!

62. Allowable Stresses Here are some properties for typical robot materials MaterialDesigTemperYieldTensileShearModulus (ksi)(ksi)(ksi)(msi) Alum6061O8181210 Alum6061T640453010 BrassC3600018-4549-6830-3814 CopperC17000135-165?165-200?19 Mild Steel1015-22HR486530 PVCRigid6-80.3-1