A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms
A Polynomial Homotopy Formulation of the Inverse Static Analysis of Planar Compliant Mechanisms
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DOI：
10.1115/1.2202137
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发表时间：
2006-07
影响因子：
3.3
通讯作者：
H. Su;J. Michael McCarthy
中科院分区：
文献类型：
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作者：
H. Su;J. Michael McCarthy
本文以多项式形式制定了平面柔顺机构的逆静态分析。目标是找到系统响应施加到机构的已知力/力矩的平衡配置。连杆的几何约束定义了一组运动学方程，这些方程与从势能函数的偏导数获得的平衡方程相结合。为了将多项式同伦求解器应用于这些方程，我们使用正弦和余弦函数来近似每个关节处的线性扭转弹簧扭矩。然后使用牛顿-拉夫森迭代对同伦求解器获得的结果进行细化。为了演示分析步骤，我们研究了两个示例平面柔顺机构、带有两个扭转弹簧的四杆连杆机构以及由三个线性弹簧支撑的平行平台。提供了数值示例以及在选定的平衡位置之间移动期间的势能图。
This paper formulates the inverse static analysis of planar compliant mechanisms in polynomial form. The goal is to find the equilibrium configurations of the system in response to a known force/moment applied to the mechanism. The geometric constraint of the linkage defines a set of kinematics equations which are combined with equilibrium equations obtained from partial derivatives of the potential-energy function. In order to apply polynomial homotopy solver to these equations, we approximate the linear torsion spring torque at each joint by using sine and cosine functions. The results obtained from the homotopy solver are then refined using Newton-Raphson iteration. To demonstrate the analysis steps, we study two example planar compliant mechanisms, a four-bar linkage with two torsional springs, and a parallel platform supported by three linear springs. Numerical examples are provided together with plots of the potential energy during a movement between selected equilibrium positions.