A redundantly actuated 2-DOF 3RRR PKM with flexure joints: less is more

The development of a planar manipulator with flexure joints and redundant actuation has been considered before, showing that the redundancy can be exploited to increase the support stiffness and to reduce static actuator loads. In this previous design the manipulator’s workspace has been defined to encompass all kinematically accessible end effector positions. In the current paper we reconsider the design philosophy. It will be shown that limiting the workspace ("less") ultimately results in a better performance in a larger area ("more").

The dynamic performance of the manipulator is evaluated with a flexible multibody model. The links can safely be considered as rigid parts, but the model has to account for the nonlinear stiffness behaviour of the flexure joints undergoing relatively large deflections. The nonlinear spatial flexible beam elements implemented in the spacar software result in numerically efficient models that have proven to be well-suited for design optimisation. With such a flexible multibody model, the geometry of the manipulator is optimised to maximise the workspace area while assuring a minimal parasitic natural frequency and limiting the local stresses throughout the full workspace. Furthermore, the simulations show that preloading of the flexure joints results in reduced actuator torques that are needed to counteract the finite joint compliance for stationary positioning anywhere except for the equilibrium position of the end effector.

The optimised design has been build and validated experimentally. A control system that handles the actuator redundancy by minimising the 2-norm of the driving torques has been synthesised. It is demonstrated that the setup’s behaviour is similar to the model and that in particular the preloading significantly lowers the required actuator torques.