基于2R伪刚体模型的柔顺机构动力学建模及特性分析

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As a new kind of mechanisms, the compliant mechanism accomplishes the transmission or transformation of motion, force and energy by the elastic deformation of component itself. It is an advanced aspect in the study of the mechanisms. A new dynamic model of compliant links with different loads （end moment or vertical force） is proposed based on 2R pseudo-rigid-body model （PRBM）. The kinetic energy and deformation energy are obtained based on the new dynamic model. The dynamic equations of compliant links are derived via Lagrange equation. Compared with the 1R pseudo-rigid-body dynamic model （PRBDM）, the equation property and dynamic response of each pseudo-rigid-body dynamic model are analyzed. The superiority of the 2R pseudo-rigid-body dynamic model is presented. The validity of the new model is verified in the example of a planar compliant parallel-guiding mechanism. The numerical results indicate that not only the motion trend but also the internal local deformation of compliant links are described in the 2R pseudo-rigid-body dynamic model. The 2R pseudo-rigid-body dynamic model can be used to show the dynamic behavior of compliant mechanisms and is suitable for the dynamics analysis and design of compliant mechanisms.柔顺机构是利用机构中柔性构件的自身变形来实现运动、力和能量的传递和转换的一种新型机构,是机构学研究领域的前沿课题之一。以柔顺机构中的柔顺杆为研究对象,基于2R伪刚体模型（Pseudo-rigid-bodymodel,PRBM）提出末端受不同载荷形式（力矩或垂直力）作用下的动力学新模型,分析其动能和变形能,应用拉格朗日方程推导其动力学方程。通过与1R伪刚体动力学模型（Pseudo-rigid-bodydynamicmodel,PRBDM）对比,从方程特征、响应曲线等方面分析各动力学模型的特点,从而展示基于2R伪刚体模型的动力学模型优越性,并以平行导向柔顺机构为例验证了模型的有效性。分析结果表明,基于2R伪刚体模型的动力学模型不仅可以反映柔顺杆整体大范围变形状况,而且描述出杆件内部局部变形状况,可以更真实地体现柔顺机构的动力学特性,更加适合于柔顺机构的动力学分析与设计。＊