Screw theory tools for the synthesis of the geometry of a parallel robot for a given instantaneous task

This investigation deals with the optimization of the kinematic parameters of a parallel robot structure, with respect to a given instantaneous twist deformation (ITD) of the moving platform. Drawing principally upon tools from screw theory, a parametric objective function is derived which quantifies the robots’ performance with respect to the given ITD. Physically, the objective function quantifies the instantaneous work generated by the robotic structure via its platform, while the latter undergoes an instantaneous motion in the twist direction. The parameters which are optimized represent the pose of the robots platform and the geometry of the robot. This method can be used as one of other criterions in the design stage of a task-oriented new robot, while performing ITD using a fixed geometry robot or when using a reconfigurable robotic structure capable of changing its geometry to perform an ITD. The proposed algorithm is demonstrated on the Stewart platform and the 3-UPU parallel robot as examples.