Structural Conditions of Two Types of 3-DOF Parallel Mechanisms with Zero-Torsion Characteristics

The tilt-and-torsion angles are used for representations of the orientation workspace of parallel mechanisms (PMs). For the zero-torsion PMs, it needs only two angles to represent the orientation workspace. However, there are few studies about the structural conditions of zero-torsion PMs. This paper deals with the derivation of structural conditions of two types of three-degree-of-freedom (3-DOF) parallel mechanisms with zero-torsion characteristics. The PMs include a class of 3-[PP]S PMs and the 3-RSR one, both of which have been widely used as the orientational stages. The structural conditions of these PMs that satisfies zero-torsion characteristics have been derived from a conventional kinematics-based approach. The results indicates that the zero-torsion 3-[PP]S PMs have at least the characteristic of z-axial symmetry, while the zero-torsion 3-RSR PM should be mirror-symmetrical in structure.