Optimum design of spherical metamorphic mechanism used for bionic joint based on prescribed workspace

A novel bionic joint spherical metamorphic mechanism was analyzed. It consisted of a base platform, moving platform, three circle legs and one middle metamorphic leg had two configurations named configuration 1 (normal configuration) and configuration 2 (metamorphic configuration). The metamorphic mechanism can transform normal configuration to metamorphic configuration with the change of middle leg. Firstly, kinematic equation was established, and the solutions to inverse kinematic and velocity Jacobian matrix were given. Then the relationship between workspace and links length was discussed based on inverse kinematic solutions. According to regular pattern, the workspace of the mechanism was optimized and the default workspace was determined. Finally, the optimization of links length was given based on the evaluation of payload capacity index and stiffness index for a prescribed workspace. The size ranges of links were respectively obtained when each performance index at a better level. The best design size of the mechanism was obtained based on the comprehensive two indexes.