An Approach for Stiffness Modelling of Lower Mobility Parallel Manipulators using the Generalized Jacobian

This paper presents an approach for stiffness modelling of the lower mobility parallel manipulators using the generalized Jacobian. The approach can be implemented by two steps:(1) The first order deflection analysis by decomposing twist space of the end-effector into a pair of complementary twist subspaces associated with the permitted and restricted instantaneous motions, (2) The kinestatic analysis by decomposing wrench space of the end-effector into a pair of complementary wrench subspaces associated with the actuations and constraints imposed by all the limbs, and (3) Formulation of the component stiffness matrices using the semi-analytical approach. The merits of this approach lies not only in its generality but also in its capability to explicitly decompose the stiffness matrix into two meaningful components associated with respect to respectively with actuations and constraints. A 3-PRS mechanism used as a spindle head is taken as an example to illustrate the detailed procedure to implement the stiffness analysis throughout the entire workspace.