Improved general solution for the dynamic modeling of Gough–Stewart platform based on principle of virtual work

Abstract

This paper presents an improved general dynamic formulation, inverse and direct dynamics, of 6-UPS Gough–Stewart parallel robot based on the virtual work method. The new formulation offers a reduction in the computational time and improves accuracy of the dynamics equations. This method allows elimination of constraint forces/moments at the passive joints from equations of motion. Since, the dynamic formulations are derived in joint space, the concept of direct link Jacobian matrices are employed to obtain all rigid bodies’ twists. The direct link Jacobian matrices convert the twist of the rigid bodies to actuated joints velocities. Moreover, more accurate formulation is obtained by considering the angular velocity and acceleration vectors of the robot’s legs. In the process of solving the direct dynamics problem, a modified hybrid strategy is employed to obtain the near-exact solution for the direct kinematics problem (DKP). The modified hybrid strategy combines the artificial neural network and the third-order Newton–Raphson method. This strategy satisfies both goals to find the nearest exact solution and reduces execution time for the DKP. Next, two numerical examples are presented and the results are verified using a commercial dynamics modeling software. Finally, for comparison, Euler–Lagrange formulation is also obtained. Results indicates that the proposed dynamics formulation offers a significant improvement in both accuracy and execution time.