Static and stiffness analyses of a class of over-constrained parallel manipulators with legs of type US and UPS

This paper deals with a class of over-constrained parallel manipulators that can be obtained from architecturally singular parallel mechanisms with legs of type US (U and S stand for universal and spherical joints respectively) by the addition of legs of type U (P) under barS ((P) under bar stands for actuated prismatic pair). These manipulators can be internally preloaded in order to tune the system stiffness, to diminish system backlash and to control the state of tension of their structural elements. The paper, in particular, addresses the static and stiffness analyses of this class of manipulators. A symmetric stiffness matrix defined as the Hessian of the elastic potential energy of the system is used, as an alternative to the Cartesian stiffness matrix used in this field, to describe the stiffness characteristic of these manipulators. An over-constrained 2-dof parallel spherical wrist is analyzed as a case study.