A finite screw approach to type synthesis of three-DOF translational parallel mechanisms

This paper for the first time presents a finite screw approach to type synthesis of three-degree-of-freedom (DOF) translational parallel mechanisms (TPMs). Firstly, the finite motions of a rigid body, a TPM and its limbs are described by finite screws. Secondly, given the standard form of a limb with the specified DOF, the analytical expressions of the finite screw attributed to the limb are derived using the properties of screw triangle product, resulting in a full set of the 3-, 4- and 5-DOF limbs that can readily be used for determining all the potential topological structures of TPMs. Finally, the assembly conditions for type synthesis of TPMs are proposed by taking into account the inclusive relationship between the finite motions of a TPM and those of its limbs. The merit of this approach lies in that the limb structures can be formulated in a justifiable manner that naturally ensures the full cycle finite motion pattern specified to the moving platform.