THE SINGULARITIES AND DYNAMICS OF A STEWART PLATFORM MANIPULATOR

The Stewart platform manipulator is a fully parallel kinematic linkage system that has major mechanical differences over typical serial link robots. Its closed kinematic chain and parallel linkage structure give it great rigidity and a high force-to-weight ratio. In this paper, based on the forward and inverse kinematic analysis, the Jacobian matrix and the dynamic equations of the six-degree-of-freedom Stewart platform are derived. The singularities of the Stewart platform are also studied. Four singular positions are proved and some other conditions under which the possible singular positions may occur are given. These results provide us with the necessary information to avoid passing through singular points. The dynamic equations in Cartesian space appear in a very simple form. Especially in some applications if there is no rotation about the fixed X-axis, then the 'inertia matrix' reduces to a constant, diagonal matrix and the 'Coriolis and centrifugal matrix' goes to zero, which makes the Stewart platform become a decoupled, linear system in Cartesian space.