Consider the two-steerable-wheeled bicycle sketched in figure 2.1. This is a bicycle in which the front wheel is powered, whereas the rear wheel just rolls on the ground. The front wheel makes an...

Consider the two-steerable-wheeled bicycle sketched in figure 2.1. This is a

bicycle in which the front wheel is powered, whereas the rear wheel just rolls on

the ground. The front wheel makes an angle af with respect to the bike frame, and

the rear wheel makes an angle ar. The front wheel is powered with ground contact

speed vf, and the rear wheel rolls on the ground with ground contact vr.

a. If the steering axle of the bike’s rear wheel is located at (x, y) and bike’s

frame points in direction theta as shown in the figure, identify the location

of the instantaneous center of the curvature (ICC) for this vehicle.

b. Under what condition does the ICC exist?

c. At what speed does the rear wheel need to revolve in order for all of the

wheels to roll smoothly on the ground surface?