Structural Condition for [PP]S Parallel Mechanism without Parasitic Motion

The family of [PP]S parallel mechanism consists of 3-PRS, 3-RPS, 3-RRS and 3-PPS parallel mechanisms, which can undergo one translational degree of freedom (DOF) and two rotational DOFs, and thus, has great potential in practical application. Parasitic motion is the motion occurring in the non-independent DOFs of a [PP]S parallel mechanism, which is a key issue affecting its application. The kinematic model of the parasitic motion of the general 3-PRS parallel mechanism is established, revealing the inherent link between the geometrical structural parameters and the parasitic motion. The sufficient and necessary structural condition for a 3-PRS parallel mechanism without parasitic motion is proved. Based on the structural condition, the 3-PRS parallel mechanism without parasitic motion can be constructed. Local mobility in the 3-PRS parallel mechanism without parasitic motion is identified. Actuation selection considering the local mobility is presented. Mobility analysis of the 3-PRS parallel mechanism without parasitic motion is performed and the two finite rotational axes of the moving platform are identified. The sufficient and necessary structural condition is applicable to all [PP]S parallel mechanisms.