An efficient explicit dynamic formulation of a Stewart platform parallel robot via new formalism

In this paper, an explicit dynamic model for the 6-DOF Stewart platform parallel manipulator is established using a new formulation. The main principle of this formulation is to provide the final form of dynamic models based on a direct and systematic procedure; in more detail, the analytical expression of each term due to the dynamic effects, that is, the system inertia tensor, centrifugal/Coriolis tensor and the environment forces are developed according to only the physical parameters of the system (i.e., mass, inertia tensor, position of the center of mass and geometrical parameters) and generalized coordinates without the need for any complicated intermediate calculations such as the potential, kinetic and acceleration energy development. In this approach, the parallel manipulator is first opened into six serial legs and a free platform. Next, the dynamic models of each sub-structure can be easily obtained based on the new formulation in their own local space. The Jacobian and Hessian matrices of the constraint equations, resulting from the closed-loop chains, are then used to combine the substructure dynamics. Finally, a detailed dynamics model of the entire robot with respect to the workspace or the actuation space is developed. After that, a simulation of the suggested methodology is investigated and analyzed in comparison to the more established dynamic modeling techniques provided in the literature; the efficiency and correctness of our approach are then verified. It is shown that our method requires a lower computational cost and even competes with the implicit form of dynamic models. Finally, a trajectory-tracking problem using model-based control is presented. It is shown that our approach can be totally and efficiently computed online without the need for symbolic form of equations of motion, which is highly challenging for parallel manipulators.