用Sylvester的透析消去法求解三自由度柔顺机构的平衡公式

Mustafa M. Mustafa, C. Crane, I. Hamad
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引用次数: 0

摘要

研究了三自由度平面柔顺平台机构在环境中与固体接触时的平衡表达式。该机构包括两个平台,它们由三个线性弹簧并联连接。操纵两个平台的变形能力使问题异常复杂。分析的目的是确定两种不同情况下的所有平衡构型:第一种情况下,所有三个弹簧的自由长度为零,第二种情况下,只有两个弹簧的自由长度为零。该方法首先计算顶平台在不接触表面时的姿态,然后检测顶平台是否接触以确定平衡构型。采用Sylvester消去法求解该机构的几何方程。该方法分别得到了第一种和第二种情况下的4次和48次多项式方程。数值算例验证了分析过程。利用Maple软件进行了数值计算,结果证明了分析的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Equilibrium Formulation of a 3-DOF Compliant Mechanism using Sylvester’s Dialytic Method of Elimination
This paper studies the equilibrium formulation of a three degree of freedom planar compliant platform mechanism, which is in contact with a solid body in its environment. The mechanism includes two platforms, which are connected in parallel by three linear springs. The capability of deformation by manipulating both platforms exceptionally complicates the problem. The analysis aims to determine all equilibrium configurations for two different cases: FIRST CASE all three springs have zero free lengths and SECOND CASE only two of the springs have zero free lengths. The proposed procedure calculates the pose of the top platform when it is not in contact with the surface, and then detects if the top platform is in contact to determine the equilibrium configurations. To solve the geometric equations of the mechanism, we use Sylvester’s method of elimination. The approach obtains 4th and 48th-degree polynomial equations for the first and second cases, respectively. Numerical examples have been applied to verify the process of analysis. The results, which are numerically calculated by software Maple, prove the validity of the analysis.
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