Kinematics of the $$\text {S}_\text {n}$$-2U PS Spherical Robot

In this chapter, we analize the kinetostatics of a non-holonomic parallel spherical robot which can maneuver to reach any orientation for its moving platform. We show how by properly locating the actuators, and by representing the platform orientation using Euler parameters, the analysis admits a simple bilinear formulation after introducing a local feedback transformation. Interestingly enough, the singularities introduced by this transformation coincide with the singularities of the robot Jacobian. Thus, from the practical point of view, no extra singularities are added. A complete description of the robot’s workspace, which also takes into account the limits of all joints, is presented. Part of this work has previously been published in [4].