Question

Say you have a differential drive robot that has an axle length of 30cm and wheel diameter of 10cm. Find the angular velocity for the left and right wheel if the robot is going to a. Spin in place at a rate of 6 rpm (revolutions per min), b. Drive a circle of radius 1 meter (measured center of circle to middle of axle) at 3 rpm, c. Drive a straight line at 1 meter/min.

Answer 1

Answer:

a) ω1 = 18rpm    ω2 = -18rpm

b) ω1 = 102rpm     ω2 = 138rpm

c) ω1 = ω2 = 3.18rpm

Explanation:

For the first case, we know that each wheel will spin in a different direction but with the same magnitude, so:

ωr = 6rpm   This is the angular velocity of the robot

$\omega = \frac{\omega r * D/2}{r_{wheel}}$  where D is 30cm and rwheel is 5cm

$\omega = \frac{6 * 30/2}{5}=18rpm$  One velocity will be positive and the other will be negative:

ω1 = 18rpm    ω2 = -18rpm

For part b, the formula is the same but distances change. Rcircle=100cm:

$\omega 1 = \frac{\omega r * (R_{circle} - D/2)}{r_{wheel}}$

$\omega 2 = \frac{\omega r * (R_{circle} + D/2)}{r_{wheel}}$

Replacing values, we get:

$\omega 1 = \frac{6 * (100 - 30/2)}{5}=102rpm$

$\omega 2 = \frac{\omega r * (100 + 30/2)}{5}=138rpm$

For part c, both wheels must have the same velocity:

$\omega = \frac{V_{robot}}{r_{wheel}}=20rad/min$

$\omega = 20rad/min * \frac{1rev}{2*\pi rad}=3.18rpm$