Dynamics of a 3-DOF spatial parallel manipulator with flexible links

In this paper, the dynamics of a three-degree-of-freedom (3-dof) spatial parallel manipulator with flexible links is studied. Finite elements are used for discretization of the flexible links, while the Euler-Lagrange formulation is used to derive the equations of motion of the uncoupled links. The equations of motion of all the links are then assembled to obtain the governing equations of the manipulator. The method of the natural orthogonal complement is used to eliminate the constraint forces and to derive the minimum number of equations of motion. To highlight the link flexibility effect, the governing equations of motion are used in a simulation of the manipulator at hand for both rigid and flexible-link models.