Mobility analysis of the 3-UPU parallel mechanism assembled for a pure translational motion

The occurrence of singular configurations in parallel mechanisms must be avoided during motion since the actuators cannot control motion even in the neighbourhood of these configurations. As a consequence, the knowledge of the singular configurations of the mechanism is important for control purposes, for singularity-tree path planning and also represents basic information for the synthesis of a desired mechanism workspace free front singularities. In this paper the mobility analysis of the 3-UPU parallel mechanism assembled for obtaining a pure translation motion of the output platform is performed and both translation and rotation singularity loci are presented in an analytic form and their geometric interpretation is given