Self-Collision Detection in Spatial Closed Chains

Abstract

A novel methodology for detecting self-collisions in spatial closed kinematic chains is presented. In general these chains generate complex three dimensional motions in which their own links will collide with each other (i.e., a self-collision) without effective motion planning. The self-collision detection is accomplished via a novel algorithm for definitively detecting collisions of right circular, cylindrically shaped, rigid bodies moving in three dimensions. The algorithm uses line geometry and dual number algebra to exploit the geometry of right circular cylindrical objects to facilitate the detection of collisions. In the first stage of the algorithm, cylindrically shaped rigid bodies are modeled by infinite length right circular cylinders. Sufficient and necessary conditions are then used to determine if a pair of infinite length cylinders collide. If the actual finite length rigid bodies collide, then it is necessary that their associate infinite length cylinder models collide, and we proceed to the next stage of the algorithm where the bodies are modeled with finite length cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is an efficient approach of detecting collisions of cylindrically shaped bodies moving in three dimensions that has applications in spatial mechanism design and motion planning. A case study examining a spatial 4C mechanism for self-collisions is included.