| This dissertation presents a novel methodology for detecting collisions of cylindrically shaped rigid bodies moving in three dimensions. The algorithm created uses line geometry and dual number algebra to exploit the geometry of right circular cylindrical objects to facilitate the detection of collisions. First, the rigid bodies are modelled with infinite length cylinders and a necessary condition for collision is evaluated. If the necessary condition is not satisfied then the two bodies are not capable of collision. If the necessary condition is satisfied then a collision between the bodies may occur and we proceed to the next stage of the algorithm. In the second stage, the bodies are modelled with finite length cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is a straight-forward and efficient approach of detecting collisions of cylindrically shaped bodies moving in three dimensions. This methodology has applications in spatial mechanism design, robot motion planning, workspace analysis of parallel kinematic machines such as Stewart Gough platforms, nuclear physics, medical research, computer graphics, protein and polymer packing, carbon nanotubes and well drilling. Case studies examining a real-time two cylinder model, a spatial 4C robotic mechanism for self collisions and an industrial robotic work-cell application are included. |
