Analysis and design of spatial compliant mechanisms using a 3-D dynamic stiffness model

There have been a number of studies on the analysis and design of planar compliant mechanisms. However, it is more difficult to obtain an exact and concise description of the kinetostatics and dynamics for spatial compliant mechanisms. A general approach is herein presented for analyzing and designing spatial compliant mechanisms by combining a three-dimensional (3-D) dynamic stiffness model with the Pareto multi-objective optimization strategy. The investigation is devoted to small deformation providing a programmable solution for serial-parallel configurations with out-of-plane degrees of freedom (DOFs). Particularly, the 3-D dynamic stiffness model is well applicable to describe the kinetostatic and dynamic behaviors of spatial compliant mechanisms with both distributed and lumped compliance involving irregular-shaped rigid bodies. The Pareto optimal solution set in terms of concerned performances is provided and the optimum structural parameters can be straightforwardly determined. With the presented method, a new piezoelectric Z-θx-θy precision tilting manipulator is optimally designed. Experimental results show the strokes of 0.27 mm, 4.3 mrad, 4.3 mrad and the fundamental resonance frequencies of 470 Hz, 520 Hz and 520 Hz in the three motion DOFs.