Synthesis of multiple degrees-of-freedom spatial-motion compliant parallel mechanisms with desired stiffness and dynamics characteristics

•A novel structural optimization approach for synthesizing spatial-motion compliant parallel mechanisms (CPMs).•Multiple DOF CPMs with optimized stiffness and dynamic characteristics.•Well-defined fitness (objective) function derived from a new analytical approach.•Develop a novel 3-DOF (θx − θy − Z) CPM with large workspace, high stiffness ratios and desired dynamic behavior.

This paper presents a new design method to synthesize multiple degrees-of-freedom (DOF) spatial-motion compliant parallel mechanisms (CPMs). Termed as the beam-based structural optimization approach, a novel curved-and-twisted (C-T) beam configuration is used as the basic design module to optimize the design parameters of the CPMs so as to achieve the targeted stiffness and dynamic characteristics. To derive well-defined fitness (objective) functions for the optimization algorithm, a new analytical approach is introduced to normalize the differences in the units, e.g., N/m or N m/rad, etc., for every component within the stiffness matrix. To evaluate the effectiveness of this design method, it was used to synthesize a 3-DOF spatial-motion (θx − θy − Z) CPM that delivers an optimized stiffness characteristics with a desired natural frequency of 100 Hz. A working prototype was developed and the experimental investigations show that the synthesized 3-DOF CPM can achieved a large workspace of 8°×8°×5.5 mm, high stiffness ratios, i.e., >200 for non-actuating over actuating stiffness, and a measured natural frequency of 84.4 Hz.