Abstract
Complete kinematic is an essential and a challenging work for series–parallel manipulators (S–PMs). This paper studied the complete kinematic of a 2(3-SPS+UP) series–parallel manipulator. First, a S–PM formed by two well-known Tricept parallel manipulators (PMs) connected in serial is presented. Second, the forward and inverse displacements are studied using sylvester dialytic elimination method. Third, the forward and inverse Jacobian matrices are established based on integrating the constraint and coupling information of the single PMs into the S–PM. Fourth, simple and compact formulae for the forward and inverse acceleration are derived using vector approach. Finally, the workspace of this S–PM is constructed using CAD variation geometry approach. The results show that the 2(3-SPS+UP) S-PM has multiple forward and inverse position solutions. The existence and uniqueness of the forward, inverse Jacobian matrices and the acceleration formula are shown from their explicit form. The workspace analysis shows that this S–PM has large workspace. The research works provided a theoretical basis for the novel 2(3-SPS+UP) S–PM, as well as a feasible approach for establishing the complete kinematics for S–PMs.
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