Control of Contact Coordinates of a Sphere Rolling on a Plane with Constraint on Range of Rolling Motion

Abstract

In this paper, we discuss control of contact coordinates for a contact point between a sphere and a plane with pure rolling contact by using iterative closed paths on the sphere with contstraint on range of rolling motion. First, we analyze the boundary of the reachable area by the closed path with constraint on range of rolling motion. Utilizing the result, we propose a method which brings all the contact coordinates to a target point by the iteration of a finite number of the closed paths. A numerical example where the rolling motion is restricted to the area on the semisphere shows the effectiveness of the proposed method.