Type Synthesis of Fully-Decoupled Three-Rotational and One-Translational Parallel Mechanisms

Abstract

Based on screw theory and the principle of one- leg driving by an independent motor, a methodology for the structural synthesis of fully-decoupled three-rotational and one-translational (3R1T) parallel mechanisms is proposed by analysing the characteristics of the input-output relationships for fully-decoupled parallel mechanisms. Firstly, the desired forms for both the direct and the inverse Jacobian matrices of fully-decoupled parallel mechanisms are constructed by virtue of screw theory; this is in order to satisfy the demand that these two Jacobian matrices should be non-zero diagonal matrices. Secondly, the effective screw, the actuated screw and the mobile un-actuated screws of each limb are established via reciprocal screw theory, while all the possible topology structures fulfilling the requirements are obtained, based on different connectivities for each limb. Finally, the desired fully-decoupled parallel mechanisms can be synthesized using the structural synthesis rule, while the structural synthesis of fully-decoupled 3R1T parallel mechanisms can be obtained by exploiting the above-mentioned methodology. Moreover, the Jacobian matrix of a synthesized 3R1T parallel mechanism is deduced to demonstrate the decoupling feature of the parallel mechanism, which also validates the correctness of the methodology for the type synthesis of fully-decoupled 3R1T parallel mechanisms. The contents of this paper provide a reference and possess significant theoretical meanings for the synthesis and development of the 3R1T fully-decoupled parallel mechanisms. Motors are mounted one per leg, with each one of them actuating a one Degree-of-freedom (DoF) of the fully-decoupled parallel mechanism through a one-to-one velocity relationship.