柔顺机构动力学建模新方法

由于柔性杆大变形所引起的几何非线性因素的影响，柔顺机构动力学模型的建立变得更加复杂、困难。基于此，在充分考虑柔性杆大变形特性的基础上，基于简化思想，提出一种柔顺机构动力学建模的新方法。该方法主要以末端受纯弯矩、垂直力以及固定—导向等3种模式下的柔性杆为研究对象，根据欧拉—伯努利方程，并结合伪刚体模型所得边界条件，利用最小二乘原理，拟合柔性杆的变形曲线方程；通过求解变形曲线对时间的导数，得到其上任意点的速度，进而推出柔性杆的动能表达。基于伪刚体模型，根据功能转换关系，推导出柔性杆的变形势能。在此基础上，建立平行导向柔顺机构的动力学模型。最后，结合具体算例，通过对几种不同模型所得系统频率比较分析，验证了该方法的有效性。

New Method for the Dynamic Modeling of Compliant Mechanism

The dynamic modeling of compliant mechanism becomes more difficult and complex because of the geometric nonlinear factor resulted by the large deformation of flexible beam. In order to solve this problem, based on the simplification principle, a new method for its dynamic modeling is studied with the consideration of large deformation character of flexible beam. Three kinds of flexible beams, i.e. end-moment, end-vertical force and parallel-guided mode are considered as research objects. With the consideration of large deformation characteristic and in the combination of boundary condition obtained from the pseudo rigid-body model, deformation curve of flexible beam under large deformation is obtained on the basis of the least square principle. And the kinetic energy of flexible beam is deduced. Based on the principle of energy conservation, the potential energy of flexible beam is easily calculated in the pseudo rigid body model. Then the dynamic model of parallel guided compliant mechanism is developed. Finally, the numerical analysis verifies the validity of the dynamic model by comparing with other methods.