Architecture optimisation of three 3-P̲RS variants for parallel kinematic machining

The 3-P̲RS parallel manipulator has recently been prototyped as a machining centre. PRS denotes the prismatic–revolute–spherical architecture of each limb where only the prismatic joint is actuated and hence underlined. Three variations of this manipulator have been independently presented in the literature. The architectural parameters affecting the size of the dexterous workspace volume are identified for each of the three models. The influence of these parameters on each of the three models is studied. Next, the manipulators’ dexterity is defined as the architecture's ability to lend stiffness and accuracy to the machine tool.By studying the singular values and condition number of a newly developed square, dimensionally homogeneous Jacobian matrix, regions of the workspace corresponding to capabilities for high end effector (EE) velocities in each of the degrees of freedom (DOF) are identified. Optimisation of the architectural parameters is then completed to provide the largest possible size for this region.The dexterous workspace size, obtained using optimal architectural parameters unique to each variant, is then compared between each of the three variants of the 3-P̲RS manipulator.