Equilibrium Configurations of a Planar 3-DOF Parallel Robot with Flexible Joints

All previous research on design of parallel robots relates to analyzing and optimizing the kinematic geometry without regard to the equilibrium configurations of the parallel robot with flexural pivots once the external load is assigned. This article addresses the equilibrium configurations of a planar 3-dof parallel robot with flexural pivots. A system of four coupled transcendental equations with trigonometric functions in four unknowns is derived from the inverse static analysis. The initial configurations of the parallel robot are discussed firstly, then a numerical method is presented based on the Newton´s iterative method, which can find all the real roots of the system of transcendental equations with trigonometric functions without initial value selection in the specified intervals to detect the entire set of the initial configurations and the equilibrium configurations of the parallel robot with flexure hinges. Finally, a numerical example is provided