Development of structural schemes of parallel structure manipulators using screw calculus

Abstract

The paper considers the approach to the structural analysis and synthesis of parallel structure robots based on the mathematical apparatus of groups of screws and on a concept of reciprocity of screws. The results are depicted of synthesis of parallel structure robots with different numbers of degrees of freedom, corresponding to the different groups of screws. Power screws are applied with this aim, based on the principle of static-kinematic analogy; the power screws are similar to the orts of axes of not driven kinematic pairs of a corresponding connecting chain. Accordingly, kinematic screws of the outlet chain of a robot are simultaneously determined which are reciprocal to power screws of kinematic sub-chains. Solution of certain synthesis problems is illustrated with practical applications. Closed groups of screws can have eight types. The three-membered groups of screws are of greatest significance, as well as four-membered screw groups [1] and six-membered screw groups. Three-membered screw groups correspond to progressively guiding mechanisms, to spherical mechanisms, and to planar mechanisms. The four-membered group corresponds to the motion of the SCARA robot. The six-membered group includes all possible motions. From the works of A.P. Kotelnikov, F.M. Dimentberg, it is known that closed fifth-order screw groups do not exist. The article presents examples of the mechanisms corresponding to the given groups.