How to be sure your robot will turn

My Name: Chris Hibner

Mentor FRC 51 - Wings of Fire

chiefdelphi.com: “Chris Hibner”

Who has taken the following courses? Physics Algebra Trigonometry Calculus

F = *N

is the “coefficient of friction” and it depends on the materials in contact.

Mg

N

F

F (maximum friction force) = (coefficient of friction) * N (normal force)F = *N

On a level surface, N = weight

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

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

Nf NrL

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

W

Nf NrL

Lcom

F = T / rF (force at edge of wheel) = T (torque) / r

(radius of wheel)

F

T

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.

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.

These slide side-to-side. They “push-off” with normal force fore-aft.

Link:

http://www.real-world-physics-problems.com/physics-of-skiing.html

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.

Title: Drive Train Basics (How to be sure your robot will turn)

Link: http://www.chiefdelphi.com/media/papers/1443

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

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.

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.

Assumptions for the simple case:Same torque at all 4 wheelsCOM is left/right centeredSame wheels at all 4 corners, and friction is

same in all directions.

Lwb

Ltw

Lcom

General case:

(See appendix for derivation)

122

wb

twwb

comx

LL

L

WLF

Worst case – Lcom is Lwb/2:

2

14

wb

tw

whl

LL

WF

To be sure your robot will turn:1.Use the 2003 paper or the above friction

equation to determine the force at the wheel needed to make the robot turn.

2.Know the stall torque of your motor. Better yet, use the motor torque at peak power.

3.Twhl = Ffrict * Rwhl (Torque at the wheel = friction force * wheel radius)

4.GearRatio = Tmotor / TwhlDon’t forget to account for losses due to

gearing (10% per stage is a good rule), and add some safety margin.

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)

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

F

Spring torqueFrom Frame

Top view of frame:

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:1.6 wheel drive with dropped center wheel2.8 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.

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:1.Omni wheels2.Consider machining a radius or slope to the

side of hard wheels:

2Nf 2NrL

LcomW

(2) 02 0

(1) 022 0

comwbfr

frz

WLLNM

WNNF

Solve equation 2 for Nf:

Substitute into eq 1 and solve for Nr:

(3) 2 wb

comf L

LWN

(4) 12

22

2

wb

comr

wb

comr

fr

L

LWN

L

LWWN

NW

N

Lwb

Ltw

Lcom

Fy Fy

FyFy

Fx

Fx

Fx

Fx

(5)

:Ffor Solve

022

:0

y

0

wb

twxy

wbytwx

L

LFF

LFLF

M

(7)

:is magnitude whose,F and F of sum vector theis F

(6) 2

:above theinto (3) eq from N Substitute

:friction of force maximum theexceed

must wheel theof force the turn,start to To

22_

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_

f

_

xyfwhl

wb

comfwhl

ffwhl

FFF

L

LWF

NF

12

21

:Fxfor solve Now

2

:(8) into (5) eq Substitute

(8) 2

:(6) eq into (7) eq Substitute

2

2

2

2

2

22

wb

twwb

comx

wb

com

wb

twx

wb

comx

wb

twx

wb

comxy

LL

L

WLF

L

LW

L

LF

L

LWF

L

LF

L

LWFF

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