# Instantaneous Center of Zero and Known Velocities - Example Problem 4.4-8

Shown below, the autonomous ground robot is geometrically symmetric about the y-axis. The two large wheels of the robot are driven by their own electric motors that cause the wheels to turn, propelling the vehicle forward. The vehicle is able to turn by commanding each of the two wheels to rotate at different speeds. If the left wheel is commanded to rotate at 4 rad/sec and the right wheel is commanded to rotate at 6 rad/sec, determine for the instant shown

1. the translational velocity of the center of the left wheel (point A) and the translational velocity of the center of the right wheel (point B),
2. the translational velocity of the vehicle's mass center G, and
3. the vehicle's overall angular velocity ω.

Assume that each of the two wheels roll without slip.

Given:

• ωA = 4 rad/s
• ωB = 6 rad/s
• r = 12.5 cm
• No slip

Find:

• ω
• vA, vB and vG

Since the wheels are rolling without slip, we can use the rolling equations to determine the velocity of the wheel centers.

vA = m/s

vB = m/s