Direct and Explicit Formulation for Dynamic Modeling of Nonredundant Parallel Robots Based on a New Formulation and Jacobian/Hessian Matrices

This paper describes the derivation of an explicit and general dynamics model for nonredundant parallel manipulators according to a novel formalism and Jacobian/Hessian matrices of the constraint equations. This dynamic model is based solely on tensor theory and can be used for both inverse and direct dynamics. In the present model, all dynamic effects are directly derived from the system's structural parameters and generalized variables, without any intermediate complex computations such as velocity and acceleration-based energy, differentiation, or acceleration calculations, and without the need for symbolic expressions; consequently, they can be computed completely online. Next, an example of parallel manipulator is used in this study to verify the proposed general formulation in terms of simplicity, correctness, and efficiency. The model is more efficient in providing explicit equations of motion and can even compete with implicit formulations for a specific manipulator structure. In addition, it can be further optimized to perform real-time control. Finally, to address uncertainties in the system, robust model-based control is implemented based on the proposed model. Hence, this paper provides a theoretical basis for control strategies and structural parameter optimization.