Maximal Operational Workspace of Parallel Manipulators

Parallel manipulators are an interesting alternative to serial robots given the important mechanical and kinematic advantages offered. Nevertheless, they often present more complex and smaller workspaces with internal singularities (Altuzarra et al., 2004; Gosselin & Angeles, 1990). Thus, the workspace size, shape and quality are considered some of the main design criteria of these robots (Merlet et al., 1998). These robots often present multiple solutions for both the DKP and the IKP. The workspace singularity-free region where the manipulator is initially configured, i.e., the set of postures that a manipulator can reach in the same direct and inverse configuration, has been traditionally considered its operational workspace. This is due to the fact that it is widely extended the idea that to perform a transition between different kinematic solutions, the robot must cross a singular position where the control is lost, and that must be avoided (Hunt & Primrose, 1993). This idea leads to very limited operational workspaces. In this chapter, a general methodology for obtaining the maximal operational workspace where a parallel manipulator can move in a controllable way will be presented. The basis for enlarging the operational workspace consists in superimposing all the singularity-free regions of the workspace associated with the same assembly mode for all different robot work3