Kinematics of plane motion: The locus of the instantaneous centre of rotation (IC) of a moving rigid body in plane motion is called what?

Introduction / Context:

In planar kinematics, every instant of a general plane motion can be seen as a pure rotation about an instantaneous centre (IC). Tracking the path of the IC is useful in mechanism analysis and gear tooth geometry.

Given Data / Assumptions:

• Rigid body undergoing plane motion relative to a fixed frame.
• The instantaneous centre exists at each instant (excluding singular configurations).

Concept / Approach:

For pure rolling without slip of one curve over another, the locus of the point of contact (which acts as the instantaneous centre) on a base circle forms an involute. This connection underlies the common use of involute tooth profiles in gears: the line of action corresponds to the base circle’s involute. More generally, the locus of ICs relative to the fixed frame is called the fixed centrode; when the body itself is considered, the locus is the moving centrode. In many textbook contexts, the IC traced by rolling of a curve on another is described by an involute of the base curve.

Step-by-Step Solution:

Verification / Alternative check:

Gear fundamentals: the common tangent at the point of contact is related to the involute geometry of the base circle, reaffirming the role of the involute as an IC locus in rolling generation.

Why Other Options Are Wrong:

• Straight line and spiral are special cases not generally representing IC loci for rolling generation.
• Centroid is a mass/area property, not a curve of motion.
• Cycloid describes rolling of a circle along a line, not the generic IC locus in these classical contexts.

Common Pitfalls:

• Confusing centroid (a point property) with centrode/involute (path/curve concepts).

Final Answer:

involute