A study on design optimisation of a spatial, cable-actuated variable stiffness joint

• Multiple inverse kinematics solutions are obtained using homotopy continuation. • The wrench-feasible workspace and its boundaries are identified. • Effect of mechanism geometry on stiffness is investigated. • A force model computing joint reaction forces and moments is presented. • Expensive objective functions are maximised using surrogate optimisation. Robotic manipulators synthesised using lower-mobility cable-actuated joints are interesting candidates that bridge the stiffness gap between soft and rigid counterparts. Their inherently higher stiffness over soft robots facilitates higher payload manipulation capabilities. At the same time, their lower but variable-stiffness capabilities and higher payload-to-mass ratios when compared with rigid industrial manipulators encourage deploying such classes of mechanisms for cobotic applications. In this work, an optimal design of a 3-cable-actuated, 2-degree-of-freedom spatial variable-stiffness mechanism is investigated. For kinematic modelling, the loop-closure constraint equations are solved using polynomial homotopy continuation, which yields multiple inverse-kinematic solutions for a given pair of independent task-space inputs. In static modelling, the wrench-feasible workspace (WFW), stiffness characteristics, and the design of extension springs mounted in parallel with the cables for stabilising the mechanism are discussed. A screw-theory-based static force model is also presented to determine the reaction wrenches developed at each joint, and its predictions are validated using the ADAMS multibody dynamics package. Finally, a Gaussian-process-assisted multiobjective optimisation framework is employed for the simultaneous maximisation of the WFW and stiffness parameters.