Design and analytical model of a compact flexure mechanism for translational motion

This paper presents the design and analytical model of a compact flexure mechanism with a general beam shape, which can offer desirable single-axis translational motion capabilities. This design comprises two parallelogram flexure modules in a nested parallel arrangement and is termed the parallel double parallelogram flexure mechanism (or parallel-DPFM). Compared to the previously known parallel-DPFM, the proposed mechanism is more compact while offering several desirable performance characteristics including motion direction stiffness that is independent of bearing direction load, robustness against buckling, and suppression of error motion in the bearing direction. Closed-form planar force-displacement relations for the new design with a general beam shape have been derived to confirm these performance characteristics and provide design insights via parametric analysis. Nonlinear finite element analysis (FEA) and experimental testing are carried out to validate the analytically predicted performance characteristics for a specific beam shape that corresponds to the uniformly distributed-compliance case.