Wheel Turning's Math: Angle & Displacement

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In summary, the conversation discusses the relationship between the angle of a vehicle turning and its wheel's displacement. The person is seeking advice on how to determine the displacement of the back two wheels when given an angle, such as wanting to turn the vehicle 20 degrees. The proposed solution involves estimating a pivot point during the turn and calculating the radius from that point to the back wheels. It is assumed that both motors are turning about a single stationary pivot point. However, if the pivot point is moving, the situation becomes more complicated. The conversation also mentions a differential mechanism and provides equations for calculating the wheels velocity and angle.
  • #1
PrudensOptimus
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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
In a perfect world and in a nutshell:

[tex]s = r \Theta[/tex]
where:
[tex]s = arc \ length[/tex]
[tex]r = radius[/tex]
[tex]\Theta = angle\ in\ radians[/tex]

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.
 
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  • #3
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
Q=angle (rad)
l=length
 

1. What is the difference between angle and displacement?

Angle refers to the amount of rotation around a specific point, while displacement refers to the change in position of an object from its starting point to its ending point.

2. How are angles and displacement calculated?

Angles are typically measured in degrees or radians, and can be calculated using various geometric formulas. Displacement is calculated by subtracting the initial position from the final position of an object.

3. How does wheel turning relate to angles and displacement?

Wheel turning involves the rotation of a circular object, such as a wheel. This rotation can be measured in terms of angle and displacement, as the wheel moves a certain distance and rotates a certain amount.

4. What is the importance of understanding angles and displacement in wheel turning?

Understanding angles and displacement in wheel turning is crucial for various applications, such as designing machinery and vehicles that rely on rotating parts. It also helps in accurately measuring and predicting the movement of these objects.

5. Can angles and displacement be negative?

Yes, angles and displacement can be negative. Negative angles indicate rotation in the clockwise direction, while positive angles indicate rotation in the counterclockwise direction. Negative displacement indicates movement in the opposite direction of the positive direction.

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