Kinematics of rigid bodies — point about which combined translation and rotation occurs: The point about which the combined motion of rotation and translation of a rigid body is instantaneously equivalent to pure rotation is called what?

Introduction / Context:
Any general plane motion of a rigid body can be represented instantaneously as a pure rotation about a specific point in the plane. Identifying this point simplifies velocity and acceleration analysis in linkages, wheels, and mechanisms.

Given Data / Assumptions:

• Planar motion of a rigid body.
• Instantaneous kinematics (at a given instant).
• No special constraints beyond rigidity.

Concept / Approach:

The instantaneous centre (I-centre) of rotation is the point in or out of the body about which, at that instant, the motion is equivalent to pure rotation. All velocities are perpendicular to lines joining points to the I-centre. Although related, the “instantaneous axis” is a spatial 3D concept; “virtual centre” is not standard terminology here.

Step-by-Step Solution:

Verification / Alternative check:

Using relative velocity v_B = v_A + ω × r_BA, choosing I such that v_I = 0 recovers the same geometric construction.

Why Other Options Are Wrong:

(a) is not the accepted term; (c) refers to a line in space, not a point in plane motion; (d) is vague; (e) is unrelated here.

Common Pitfalls:

Confusing instantaneous centre (a point) with instantaneous axis (a line); assuming the I-centre is fixed in space—it generally moves.

Final Answer:

Instantaneous centre