This paper presents a novel methodology for detecting collisions of cylindrically shaped rigid bodies moving in three dimensions. This algorithm 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 cylinders and an efficient necessary condition for collision is evaluated. If the necessary condition is not satisfied then the two bodies do not collide. 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 cylinders and a definitive necessary and sufficient collision detection algorithm is employed. The result is a straight-forward and efficient means of detecting collisions of cylindrically shaped bodies moving in three dimensions. This methodology has applications in robot motion planning, spatial mechanism design, and workspace analysis of parallel kinematic machines such as Stewart-Gough platforms. A case study of motion planning for an industrial robot is included

This paper uses the kinematic mapping into the image space of spherical displacements to design a cooperating spherical robot system for workpiece orientating. The kinematic chain formed by the cooperating robots grasping the workpiece forms a multi degree of freedom closed chain which is also known as a robotic mechanism. The spherical robots considered are spherical RPR open chains and they rigidly grasp the workpiece to form a 9 degree of freedom closed chain. The design problem considered is to determine the base locations and grasp points that enable the cooperating robots to guide a workpiece, through an arbitrary number of desired orientations. An example of the design of a cooperating spherical RPR robot system for six (6) desired orientations is presented.

An evaluation is made of the performance of a cooperating robot system using movements planned for minimum time. Minimum-time movements characteristically require that a set of motors in the robot be driven at the maximum torque through the motion. Thus, these movements are limited by the combination of motor performance, mechanical advantage of the kinematic chain, and the location of the start and goal positions. Increasing the payload until a minimum-time solution is no longer feasible makes it possible to obtain the performance limit of the system for the associated path. The cases of two robots working individually and together are examined in order to find the performance enhancement obtained by having two robots cooperate.>