Efficient formulation approach for the forward kinematics of 3-6 parallel mechanisms

This paper presents a new formulation approach to obtain a simplified form of the forward kinematic solution that can reduce the computational burden involved in determining the solution of the forward kinematics of the 3-6 parallel mechanism with three connecting joints on the moving platform. The conventional forward kinematics of haptic devices with serial-parallel mechanisms is formulated through employing the Denavit-Hartenberg notation, and results in complicated formulation procedures and computational burden. In order to reduce these problems, this paper transforms the haptic devices into an equivalent kinematic model of the 3-6 Stewart-Gough platform. The conventional forward kinematics of the 3-6 platform is formulated. with trigonometric functions through complicated steps and results in the computational burden. Thus we introduce the new formulation approach, based on tetrahedron geometry, in order to simplify the formulation of the forward kinematics and to reduce the computational burden. The proposed formulation approach can allow intuitive derivation and considerable abbreviation of the number of calculations involved in the forward kinematic solution. The feasibility and convergence of the formulation approach is verified through a series of simulations and experiments.