A general approach on collision-free workspace determination via triangle-to-triangle intersection test

This paper introduces a new general systematic approach using the so-called triangle-to-triangle intersection test in order to obtain the collision-free workspace of robotic mechanical systems. In this geometric constructive approach, a collision test will be performed, based on the STL file, for all possible configurations of the robot which leads to obtain the collision-free workspace. By introducing a bounding sphere, the obtained results from the proposed algorithm reveal that the computational time on average is 0.0490μs per test which is reduced by 23% comparing to one of the recent algorithm proposed in the literature. Furthermore, the collision-free workspace determination approach provides a statistical data about the percentage of collision for each constituting part of the mechanism. By resorting to the latter statistical data, an index for collision-free workspace is introduced which provides some insights into designing a well-conditioned workspace in terms of mechanical interference. The approach is implemented on two cases studies, namely 3-RRR and the so-called Tripteron parallel mechanisms.