A closed-form nonlinear model for spatial Timoshenko beam flexure hinge with circular cross-section  

作　　者：Dan WANG Jie ZHANG Jiangzhen GUO Rui FAN 

机构地区：[1]School of Mechanical Engineering and Automation, Beihang University

出　　处：《Chinese Journal of Aeronautics》2019年第11期2526-2537,共12页中国航空学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 51305013)

摘　　要：Beam flexure hinges can achieve accurate motion and force control through the elastic deformation. This paper presents a nonlinear model for uniform and circular cross-section spatial beam flexure hinges which are commonly employed in compliant parallel mechanisms. The proposed beam model takes shear deformations into consideration and hence is applicable to both slender and thick beam flexure hinges. Starting from the first principles, the nonlinear strain measure is derived using beam kinematics and expressed in terms of translational displacements and rotational angles. Second-order approximation is employed in order to make the nonlinear strain within acceptable accuracy. The natural boundary conditions and nonlinear governing equations are derived in terms of rotational Euler angles and subsequently solved for combined end loads. The resulting end load-displacement model, which is compact and closed-form, is proved to be accurate for both slender and thick beam flexure using nonlinear finite element analysis. This beam model can provide designers with more design insight of the spatial beam flexure and thus will benefit the structural design and optimization of compliant manipulators.Beam flexure hinges can achieve accurate motion and force control through the elastic deformation. This paper presents a nonlinear model for uniform and circular cross-section spatial beam flexure hinges which are commonly employed in compliant parallel mechanisms. The proposed beam model takes shear deformations into consideration and hence is applicable to both slender and thick beam flexure hinges. Starting from the first principles, the nonlinear strain measure is derived using beam kinematics and expressed in terms of translational displacements and rotational angles. Second-order approximation is employed in order to make the nonlinear strain within acceptable accuracy. The natural boundary conditions and nonlinear governing equations are derived in terms of rotational Euler angles and subsequently solved for combined end loads. The resulting end load-displacement model, which is compact and closed-form, is proved to be accurate for both slender and thick beam flexure using nonlinear finite element analysis. This beam model can provide designers with more design insight of the spatial beam flexure and thus will benefit the structural design and optimization of compliant manipulators.

关 键 词：Compliant mechanism Load-displacement model Nonlinear analysis Spatial beam flexure hinge(SBFH) Timoshenko beam 

分 类 号：O17[理学—数学]