Improving static stiffness of the 6-R̲US parallel manipulator using inverse singularities

The accuracy of parallel manipulators is linked to their stiffness and this has been shown to be configuration dependent. Indeed, certain types of singular configurations are usually avoided because of the associated loss of stiffness. These undesirable singularities are direct singularities, in which actuators cannot balance external loads. By contrast, inverse singularities do not cause this loss of stiffness. With appropriate design, the 6-R̲US manipulator can be operated in a workspace with no direct singularities but which does contain some inverse ones. In this paper, a methodology for calculating the stiffness matrix of parallel manipulators is presented. Applied to the 6-R̲US manipulator, it is demonstrated that inverse singularities are much stiffer than non-singular configurations. In addition, an approach to motion planning is devised which makes use of inverse singularities to obtain stiffer trajectories. Results show a significant improvement in the stiffness along the trajectory.

► We present a stiffness matrix calculation methodology for parallel manipulators.
► Stiffness matrix of 6-R̲US manipulator is calculated.
► The methodology detects the robot component with the worst stiffness performance.
► Inverse singularities (IS) are configurations with the best stiffness performance.
► IS are exploited to improve the stiffness of the 6-R̲US along certain paths.