When two links are connected by a pin joint, their instantaneous center lies

Solution (By Examveda Team)

Option A: On their point of contact
While two links connected by a pin joint are in contact, the instantaneous center is not necessarily at the contact point.
The contact point could be any part of the surface where the links meet, but the instantaneous center lies specifically at the pin joint, where relative motion occurs.

Option B: At the center of curvature
The center of curvature refers to a point associated with the curvature of a specific path or trajectory, not the location of the instantaneous center for two links connected by a pin joint.
This option does not apply to pin-jointed links.

Option C: At the center of circle
The center of a circle might be the instantaneous center in circular motion, but in the case of two links joined by a pin, the instantaneous center lies at the actual pin joint rather than any arbitrary center of a circle.

Option D: At the pin joint
When two links are connected by a pin joint, the instantaneous center of rotation for the motion between them lies precisely at the pin joint.
This is because the pin joint is the exact point where the two links rotate relative to each other.

Conclusion:
The correct answer is Option D: At the pin joint.
In pin-jointed links, the instantaneous center of rotation is located at the pin joint itself, where the relative rotation occurs.