Analytical forward kinematics algorithm and static stiffness model for a novel invertible Stewart-type parallel mechanism

Abstract In this paper, an invertible ‘5-4’ Stewart-type parallel mechanism (STPM) with analytical forward kinematics (FK) solutions is designed, and the relationship between FK and static stiffness is revealed. First, in order to reduce the structural coupling of STPMs, novel triple and double overlapping Hooke joints are developed. Then, a tetrahedron-based kinematic algorithm is proposed to solve the analytical FK by introducing one virtual limb for the ‘5-4’ STPM and two virtual limbs for the inverted ‘5-4’ STPM. Numerical experiments verify the accuracy of the algorithm. Subsequently, velocity Jacobian matrices and static stiffness models are established for the analysis of these two mechanisms. The finite element simulation results demonstrate the effectiveness of the static model, and the maximum relative error is less than 24.84%. Finally, the kinematic repeated roots and stiffness degradation of two STPMs are analyzed respectively, and the results show that the repeated-root FK leads to directional stiffness loss. These achievements provide theoretical foundations for the practical applications of reconfigurable STPMs.