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One good turn deserves another

One good turn deserves another. How to be sure your robot will turn. Welcome. My Name: Chris Hibner Mentor FRC 51 - Wings of Fire chiefdelphi.com: “Chris Hibner”. Background. Who has taken the following courses? Physics Algebra Trigonometry Calculus. Simple friction model. F =  *N

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One good turn deserves another

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  1. One good turn deserves another How to be sure your robot will turn

  2. Welcome My Name: Chris Hibner Mentor FRC 51 - Wings of Fire chiefdelphi.com: “Chris Hibner”

  3. Background Who has taken the following courses? • Physics • Algebra • Trigonometry • Calculus

  4. Simple friction model F = *N  is the “coefficient of friction” and it depends on the materials in contact. g M F N

  5. Simple friction • F (maximum friction force) =  (coefficient of friction) * N (normal force) • F = *N • On a level surface, N = weight

  6. Simple friction Example • Let’s say the mass weighs 150 lb and the coefficient of friction is 0.8. How much force is required to move the object? • F = *N • F = 0.8 * 150 lb • F = 120 lb

  7. Multiple Contact Points • The above example has one continuous contact area – what if there are multiple contact areas? Nf = W*(Lcom / L) Nr = W (1 – Lcom / L) W Lcom Nr Nf L

  8. Multiple Contact Points W Lcom Nf = W*(Lcom / L) Nr = W (1 – Lcom / L) If Lcom is L/2, then Nf = Nr = W/2 If Lcom is L/3, then Nf = W/3 and Nr = 2W/3 Nr Nf L

  9. Force from Motors F = T / r F (force at edge of wheel) = T (torque) / r (radius of wheel) T F

  10. What happens when F > N? • Simple answer: wheel “breaks free” and starts to slip. • The force from the wheel to the ground: which direction does it point? • Answer: in the direction of the force applied by the torque.

  11. When the standard friction model doesn’t apply • If there is significant deflection of the surface and/or interlock between mating surfaces, the simple friction model breaks down. • Especially if interlock only occurs in one direction. • In this case, the friction model does not work in the direction with interlock. The force in this direction is more of a normal force, and not a friction force. • In the direction without interlock, the simple friction model still works well.

  12. Simple friction model doesn’t Work Well: examples These slide side-to-side. They “push-off” with normal force fore-aft.

  13. A Better Model for the above wheels and treads – Ski Physics

  14. A Better Interlock Model – Ski Physics Link: http://www.real-world-physics-problems.com/physics-of-skiing.html

  15. ski physics (don’t bother) • The physics of skiing is not worth learning for FIRST robots. A model can be created from the simple friction model that is “close enough”. • Just use different “friction coefficients” in the different directions • Dynamically changing friction coefficients is a common way to model complex surface interaction. • The ski physics was brought up to show a point: when interlock occurs, slipping can occur in one direction without affecting the friction in the transverse direction.

  16. The 2003 Paper • Title: Drive Train Basics (How to be sure your robot will turn) • Link: http://www.chiefdelphi.com/media/papers/1443

  17. The 2003 Paper - History • Prior to 2003, there were no rules on materials that interact with the carpet. • Metal to carpet contact was common, and cleated wheels and treads were also common. • Omni-wheels were very common

  18. The 2003 Paper – strengths and limitations • Cleated wheels and treads follow skiing physics very closely. This is due to “trenching” of the cleat in between the carpet fibers. • The radius in the transverse direction moves the fibers out of the way in that direction (see picture on previous slide). • Starting in 2003, FIRST outlawed cleated wheels. Wheels with symmetric friction are now the norm.

  19. The 2003 Paper - Limitations • The 2003 paper is entirely accurate for symmetric wheels. • If you design your drive train using the 2003 paper – it will still turn. The 2003 paper is overly conservative for symmetric wheels. • If you want to design at the limit of turning, you can be more accurate. However, I wouldn’t recommend designing at the turning limit.

  20. calculations for wheels with symmetric friction • Assumptions for the simple case: • Same torque at all 4 wheels • COM is left/right centered • Same wheels at all 4 corners, and friction is same in all directions. Lwb Lcom Ltw

  21. calculations for wheels with symmetric friction General case: (See appendix for derivation)

  22. calculations for wheels with symmetric friction Worst case – Lcom is Lwb/2:

  23. Gear Calculations To be sure your robot will turn: • Use the 2003 paper or the above friction equation to determine the force at the wheel needed to make the robot turn. • Know the stall torque of your motor. Better yet, use the motor torque at peak power. • Twhl = Ffrict * Rwhl (Torque at the wheel = friction force * wheel radius) • GearRatio = Tmotor / Twhl Don’t forget to account for losses due to gearing (10% per stage is a good rule), and add some safety margin.

  24. How to stop the hippity hop • Introduce the students to Led Zeppelin. • Just kidding. • What causes it? • Ever see a stop sign flutter in the wind? Wind force Spring torque (from sign post)

  25. How to stop the hippity hop • How road sign flutter relates to a robot. • How to stop it: increase torsional stiffness of the frame. • Gussets • closed box sections (not open channel sections) • Truss shapes F Top view of frame: Spring torque From Frame F

  26. Rules of thumb • There is no substitute for doing a gear calculation. • Wider is better – the higher the Ltw/Lwb ratio is, the easy is will be for your robot to turn. • But be careful – you don’t want your robot to flip over during acceleration. • Ways to compromise: • 6 wheel drive with dropped center wheel • 8 wheel drive with dropped center 4 • COM at the center of the robot is worst for turning. Moving the COM forward or rearward helps the robot turn.

  27. Rules of thumb, continued • If all else fails: • Consider using high friction wheels on one end of the robot, and low friction wheels on the other end. • Consider wheels with asymmetric friction: • Omni wheels • Consider machining a radius or slope to the side of hard wheels:

  28. Derivation of symmetric wheel friction calculation W Lcom 2Nr 2Nf L

  29. Solve equation 2 for Nf: Substitute into eq 1 and solve for Nr:

  30. Fx Fy Fy Fx Fx Lwb Lcom Fy Fy Ltw Fx

  31. Great resources • JVN mechanical design calculator: http://www.chiefdelphi.com/media/papers/2755 • apalrd Battery Voltage in Robot Drivetrain Simulation and Modeling: http://www.chiefdelphi.com/media/papers/2750

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