# Wheel Turning's Math

1. Mar 30, 2005

### PrudensOptimus

Hello,

Due to my meager mechanical physics knowledge and my meager math talent, I am stuck on this matter: How are the angle of a vehicle turning related to its wheel's displacement. Let me elaborate:

I have a 3 wheel vehicle. It relies on the 2 motors in the back to motivate it. Each of those turning in opposite direction produce a turning effect. However, is there a possible way to find the displacement of the back 2 wheels when given the angle? Say I want to turn the vehicle 20 degrees NE from the spot, how "far" should I set the motors to go?

Any advice would be greatly appreciated. Of course your time is the greatest contribution.

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2. Mar 31, 2005

### FredGarvin

In a perfect world and in a nutshell:

$$s = r \Theta$$
where:
$$s = arc \ length$$
$$r = radius$$
$$\Theta = angle\ in\ radians$$

You should first estimate where your pivot point would be during a turn and then the radius would be from that point to either of the back wheels. If you want to go 20° then there is your angle (don't forget to convert it to radians). That will tell you how long of an arc the back wheel must travel to turn 20°. That is making the assumption that both motors are turning you exactly about a single pivot point and that point is stationary. If the point is moving, that will complicate the situation. I'd say start with the easy stuff first.

Last edited: Mar 31, 2005
3. Apr 15, 2005

### aminakoyum

if there is two motors it is a differrential mechanism. and w=w1*wm1+w2*wm2
w=wheels velocity of angel
w1=velocity when the other motor stops
w2=velocity when the other motor stops
wm1=1st motor's velocity
wm2=2nd motor's velocity
s=w*l*t
Q=S/r