A method for solving all joint reactions of 3R2T parallel mechanisms with complicated structures and multiple redundant constraints

Abstract Joint reaction solution of a mechanism is an important basis of its strength check, fatigue analysis and friction analysis. This paper presents a general method for solving all joint reactions of three-rotation and two-translation (3R2T) parallel mechanisms with complicated structures and multiple redundant constraints. First, joint reaction expressions with unknown intensities of limb wrenches are derived based on screw theory. Then, the statically indeterminate problem of the class of mechanisms is presented through solving the static equilibrium equation of the moving platform. Third, the statically indeterminate problem of 3R2T parallel mechanisms is dealt with by establishing the deformation compatibility equation and stiffness models of limbs along constraint wrenches. Finally, all joint reactions are determined by substituting the solved wrench intensities into their expressions. Comparisons show the computational results obtained from the proposed method can match well with those obtained from finite element analysis (FEA) models. The proposed method can reveal clearly internal statics relations of a 3R2T mechanism with redundant constraints.