Calculate angular velocity of each wheel: differential drive kinematics?

Question

Hey, so I've got a problem for my robotics homework that I need help on. There's a wheeled, differential drive robot traveling 2 meters/second and turning left with a radius of curvature = 30 meters. There's .5 meters between the wheels, and the the robot is .2 m long (with the wheels in the center, .1m in front and .1m behind the wheel axle). The wheels all have a radius of .1 meters. What are the angular velocities of the left and the right wheel? If you can't solve it, what extra information is needed?

My confusion here is that looking through all of the formulas our professor taught us, I can only find ones that solve for the robots angular velocity as a whole. How do I solve for the angular velocity of the individual wheels? I'm using the formula omega = Velocity of right wheel - velocity of the left wheel / length between the wheels, but that's as far as I can get. If you do answer please include how you got the answer, thanks!

Answer 1

I'd suggest U might want to concentrate on the simple relationship between angular (rotating) velocity and linear velocity of wheels.

That formula being: V = wR {where "w" = sml case omega}

If each of the two wheels move forward at 2 m/s = V then:

the inner wheel (to the turn) must rotate at w = V/R1 = 2/R1

the outer wheel (to the turn) must rotate at w = V/R2 = 2/R2



U understand that the turning radius is slightly different for ea wheel.

If the turning radius for the CENTER of ROBOT = 30 m then for each wheel it is:

29.75 m for inner wheel = R1 & 30.25 m for outer wheel = R2

inner (left) wheel rolls at w1 = 2/(29.75) = 0.0672 rad/s

outer (outer) wheel rolls at w2 = 2/(30.25) = 0.0661 rad/s

Answer 2

Differential Drive Kinematics

Answer 3

once you have rolling with slipping, the values of translational velocity and angular velocity are no longer promptly linked. on your occasion, you are able to calculate the angular velocity of the wheel when you consider which you comprehend the engine velocity, and that's theory which you comprehend the gearing ratio between the engine and the wheel. (extra desirable assumption: your transmission is direct-coupled, i.e. no viscous torque converter). because of the fact the wheels are slipping, you haven't any longer any way of understanding without direct length what the translational velocity is. in case you comprehend the coefficient of friction between the wheels and dirt, and you comprehend preliminary velocity, mass, and time of acceleration, you are able to calculate translational velocity from here: F = (coefficient of kinetic friction) * (universal stress between sliding gadgets) A = F/M V = V0 + AT word that those equations do no longer point out the angular velocity of the wheel, as sliding friction does not (in maximum cases) matter on the relative velocity of the sliding surfaces. So: because of the fact the wheels are slipping, there is not any direct relationship between angular velocity of the wheel and translational velocity of the motor vehicle.

Answer 4

sophisticated thing. query in google. that could help!