基于刚度误差的直角柔性铰链设计可行域分析

Analysis of Feasible Design Region for Right-Angle Flexure-Hinge Based on Stiffness Error

应用伪刚体方法设计直角柔性铰链双柔性平行四杆结构时,为满足臂杆为刚性杆的假设,要求臂杆厚度远远大于柔性铰链厚度.设计常根据经验,缺乏相关的理论依据.本文通过对直角柔性铰链平行四杆结构进行刚度误差分析,得到臂杆等效为刚性杆的设计可行域.首先利用积分法求得考虑臂杆变形的精确刚度;然后利用有限元分析方法验证此刚度为精确理论计算刚度;最后,分析虚功原理法求得的理想刚度和积分法精确刚度之间的相对误差,研究其随结构参数的变化规律,并得到臂杆等效为刚性杆的值域,即应用伪刚体模型设计直角柔性铰链双柔性平行四杆的设计可行域.

When pseudo rigid body （PRB） method is employed in the design of rightangle flexure hinged double parallel fourbar mechanism, the thickness of support arm bar should be much larger than that of flexurehinge in order to meet the assumption that the support arm bar is a rigid rod. The design is usually based on the experience and there is no authentic theoretical principle for the design of this mech anism. In this paper, through the stiffness error analysis of rightangle flexurehinged double parallel fourbar mechanism, the feasible design region where the support arm bar can be equivalent to rigid rod is derived. First, the precise stiffness of the mechanism is derived by the integral method. Then, taking the deformation of support arm bar into account, the stiffness is validated as the precise theoretical stiffness by finite element analysis （FEA） method. Finally, the relative error between the stiffness derived by vir tual work principle and that by integral method is analyzed and its change laws with structural parameters are investigated, and the feasible design region where the support arm bar can be equivalent to a rigid rodis derived.