双曲余弦曲线轮廓柔性关节的设计与分析

基于弹性力学中的应变能理论和卡式第二位移最小定理,推导出了利用双曲余弦曲线轮廓设计的单轴平面微动关节在平面内3个自由度微运动中的柔度解析表达式.在此基础上将各方向柔度变化规律与目前广泛应用于柔性机构设计中的半圆弧曲线平面微动关节的对应规律进行比较,揭示了这种类型微动关节在柔性机构设计中一些有用性能,如不存在变形耦合,且柔度随关节尺寸变化较为稳定.

Design and Analysis of Compliant Joints with Hyperbolic Cosine Profiles

The paper formulates an analytical method for displacement and compliance calculations of planar compliant joints in three degree-of-freedom's micromotions(x and y directional translations and rotation about z axis) with single-axis symmetrical hyperbolic cosine profiles.The procedure is based on the strain energy and Castigliano's displacement theorem and develops closed-form equations that incorporate the geometrical dimensions and material properties of the joints.The analytical results have been compared with those of micro-motion and single-axis flexure hinges with semicircle profiles,which have been widely used since micro-motion manipulators occurred.As a result,some useful characteristics have been obtained in application of flexure hinges with hyperbolic cosine profiles for compliant mechanism's design,therefore,no deformation coupling exists and more stability presents in the relationship of compliance coefficient to the joint dimensions.