Stiffness modeling of n(3RRlS) reconfigurable series-parallel manipulators by combining virtual joint method and matrix structural analysis

Stiffness is one of the critical performance indexes for robotic manipulators. In this study, a method for establishing the stiffness models of n(3RRlS) reconfigurable series-parallel manipulators (RSPMs) is proposed by combining the virtual joint method and matrix structural analysis. First, the constraint wrench system of the 3RRlS reconfigurable parallel manipulator (RPM) is obtained based on the reciprocal screw theory. Second, the stiffness matrices of the limbs along the axes of the constraint wrenches are analyzed using matrix structural analysis, and the overall stiffness matrix of the limbs is then assembled. Third, the stiffness matrices of the 3RRlS RPM and the n(3RRlS) RSPM are successively derived using the principle of virtual work. Finally, the theoretical and the finite-element-analysis deformations of the 3RRlS RPM and 3(3RRlS) RSPM are solved, and their average relative error is within 3.78%. It can be concluded that increasing actuation constraints can effectively improve the stiffness of manipulators in the directions of six degrees of freedom (DOFs) while increasing structural constraints can effectively improve the stiffness of manipulators in the directions of constrained DOFs.