What is the term for a curve formed by the path of a point on a straight line as it rolls along a convex base?

The correct term for a curve formed by the path of a point on a straight line as it rolls along a convex base is known as an involute. An involute is generated when a point on a taut string is unwound from a fixed circle or curve, and it traces a path as the string is extended. This concept is widely used in mechanical design, especially in gear design, where the involute profile is critical for ensuring proper engagement and smooth operation between gears.

In the context of machine design, the involute shape allows for constant angular velocity when gears mesh, which is essential for efficient power transmission. The properties of the involute curve help minimize the effects of misalignment and variability in center distances between gears, making it a fundamental aspect of gear design.

The other choices do not fit the definition of the curve described. The axial plane refers to the plane that divides an object into sections or halves along its axis, while the arcs of recess and action refer to specific components or features in design but do not describe the same type of curve as the involute.