Parametric Dynamic Modeling of Cable-Driven Parallel Manipulators

A two-dimensional parametric model for the study of the nonlinear dynamic response of cable-driven parallel manipulators is presented in this work. The model considers the distributed dynamical properties a generic number n of cables undergoing time-varying length. The cable equations of motion are obtained via a lagrangian formulation and the equations providing the connectivity between the end-effector and the cables are derived analytically; finally, the balance of the linear and angular momentum of the end-effector is enforced. The partial differential equations of motion of the system are reduced to a set of ordinary differential equations through a discretization procedure based on admissible trial functions, so as to couple the latter equations with the equations of motion of the end-effector. Finally. the direct dynamic problem is formulated and solved numerically for a selected case-study manipulator.