Kinematic modeling and design optimization of flexure-jointed planar mechanisms using polynomial bases for flexure curvature

Abstract

Kinematic design optimization of compliant mechanisms requires accurate yet efficient mathematical models of elastic behavior. A method to predict large-deflection behavior of flexure joint elements using polynomial curvature functions is described in this paper. The method is generalized and extended for kinematic prediction and design optimization of planar multi-flexure mechanisms. It is shown that the kinostatic configuration problem may be solved efficiently and accurately via an energy-based constrained relaxation approach. A class of design optimization problems is further considered where prescribed link positions must be achieved within an overall motion path. Case studies are introduced and theoretical solutions presented. The first of these involves a double Hoeken’s linkage, designed to achieve rectilinear translation of an end link. The second involves an X-Y motion stage mechanism, designed to achieve translational motion of a platform over a targeted workspace while minimizing its rotation. Experimental results involving a realization of the optimized X-Y motion stage design are reported and compared with numerical predictions. To complete the paper, a sensitivity analysis for assembly errors is undertaken via a Monte Carlo simulation. This gives further insight on expected mechanism performance and confirms the efficiency and practical utility of the proposed methods.