Structural synthesis of a class of kinematically redundant parallel manipulators based on modified G-K criterion and RDOF criterion

Based on the modified Grübler-Kutzbach (G-K) criterion and relative degrees of freedom (RDOF) criterion, a novel method is proposed for structural synthesis of a class of kinematically redundant parallel manipulators (KR-PMs) with spherical joints attached to a moving platform. First, a formula that can be used to calculate the number of kinematic joints not limited to basic joints is proposed, which is affected by the number of links including fixed base, links with multi-node, compound hinges, and the INTERNAL independent loops in parallel manipulators. Furthermore, the sum degrees of all the kinematic joints possesses a direct relationship with the number of kinematic joints, the number of spherical joints, and the type combination of spherical joints attached to the moving platform. Then, the relationship between the mobility M and the RDOF with intermediate variables is derived based on modified G-K criterion and RDOF criterion, which is the base of the proposed synthesis procedure. Next, the proposed synthesis procedure is performed with the synthesis conditions RDOF = 3 or 4, and some typical KR-PMs are obtained. Finally, the condition for proper selection of actuators for KR-PM is revealed. And the reasons for large configuration randomness of the synthesized KR-PMs are discussed.