直角柔性铰链单平行四杆机构输出位移分析

Output Displacement Analysis of Single Parallel Four-Bar Mechanism with Right Angle Flexure Hinge

为了分析直角柔性铰链单平行四杆机构在导向过程中的导向位移及耦合位移,根据其结构的对称性,在对支撑结构进行受力分析和变形分析的基础上建立了单个支撑的半段梁模型,采用椭圆积分法推导了导向梁在大载荷下导向位移及耦合位移计算公式,最后采用有限元方法和实验对理论模型进行验证,并分析了造成理论值、仿真值和实验值之间出现误差的原因.研究结果表明,在柔性梁的弹性范围内,力与导向位移近似成线性关系,与耦合位移成类指数关系,理论值和实验值之间的最大误差分别为5.1%和8.5%;理论、仿真和实验所得的导向位移-耦合位移曲线基本重合.

In order to analyze the guiding displacement and coupled displacement of the right angle parallel four-bar mechanism, a half beam model was established based on the force analysis and deformation analysis of the supporting arm according to the structural symmetry. Then the formulas of guiding displacement and coupled displacement were derived using elliptic integral and were verified by finite element method and experiments. The errors among theoretical values, finite element results and experimental results were analyzed. Results show that the guiding displacement is roughly linear with the force and the relationship between coupled displacement and force is likewise exponential within elastic range of compliant beam. The maximum errors between the theoretical and experimental values are 5.1% and 8.5% for guiding displacement and coupled displacement, respectively. The theoretical, finite element and experimental curves of guiding displacement and coupled displacement are in approximate coincidence.