Cartesian Parallel Manipulators With Pseudoplanar Limbs

Based on the Lie-group-algebraic properties of the displacement set, the three-degree-of-freedom (3DOF) pseudoplanar motion often termed $Y$ motion for brevity is first introduced. Then, all possible general architectures of the mechanical generators of a given $Y$ subgroup are obtained by implementing serial arrays of 1DOF Reuleaux pairs or hinged parallelograms. In total, five distinct mechanical generators of $Y$ motion are revealed and seven ones having at least one parallelogram are also derived from them. In order to avoid the singularity that may occur in the limbs, all singular postures of $Y$-motion generators are also located by detecting the possible linear dependency of the joint twists and the group dependency of displacement sets. The parallel layout of three 4DOF limbs including $Y$-motion generators with orthogonal planes make up a Cartesian translational parallel manipulator, which produces a motion set of spatial translations. The 3DOF translation of the moving platform is directly controlled by the three 1DOF translations in three orthogonal prismatic fixed joints.