The paper focuses on synthesizing optimal contact curves that can be used to ensure a rolling constraint between two bodies in relative motion. We show that geodesic based contact curves generated on both the contacting surfaces are sufficient conditions to ensure rolling. The differential geodesic equations, when modified, can ensure proper disturbance rejection in case the system of interacting bodies is perturbed from the desired curve. A corollary states that geodesic curves are generated on the surface if rolling constraints are satisfied. Simulations in the context of in-hand manipulations of the objects are used as examples.

翻译：本文侧重于综合最佳接触曲线,这些曲线可用于确保两个相对运动体之间的滚动限制。 我们显示,在接触的表面产生的基于大地测量的接触曲线足以确保滚动。 不同的大地测量等式在修改后,可以确保在互动体系统受到所期望的曲线的干扰时适当拒绝扰动。 必然结果显示,如果满足滚动限制,则在表面产生大地测量曲线。 以对物体进行手动操纵的模拟为例。