Question

Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground. 

Select the correct statement about instantaneous centers in the mechanism. 
 

• A. Only points P, Q, and S are instantaneous centers of mechanism
• B. Only points P, Q, S and T are instantaneous centers of mechanism
• C. Only points P, Q, R, S, and U are instantaneous centers of mechanism
• D. All points P, Q, R, S, T and U are instantaneous centers of mechanism

Hint:

In rolling contact without slip, the instantaneous centers of rotation are determined by the geometry and velocity relationships between the components of the mechanism.

Answer 1

The Correct Option is D

In a rolling contact mechanism without slip between the disc and the ground, the instantaneous centers of rotation (ICR) are points where the velocity is zero at any given instant. These points are crucial in the analysis of mechanisms and help us understand the relative motion between the components.

For the given mechanism, the instantaneous centers are as follows:
1. Point P: This is a point on the disc, and it is an instantaneous center of rotation for the disc relative to the ground.
2. Point Q: This is another point on the disc, and it also serves as an instantaneous center for the motion of the disc.
3. Point R: This is another point that could act as an instantaneous center.
4. Point S: This point is on the contact surface between the disc and the ground, and it is an instantaneous center due to the rolling motion.
5. Point T: This point is on the ground and acts as an instantaneous center due to the rolling without slip.
6. Point U: This is an additional instantaneous center that comes from the configuration of the rolling motion.

Thus, all points P, Q, R, S, T, and U act as instantaneous centers in the mechanism.
Final Answer: (D)