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On the elastostatic analysis of mechanical systems

机译：关于机械系统的弹力分析

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摘要

The subject of this paper is the elastostatic analysis of robot structures. The method of analysis is based on the concept of generalized spring, in which each flexible link is replaced with a six-dimensional generalized spring. The stiffness matrix of this spring, when the link complexity so requires, should be obtained numerically, via finite element analysis (FEA). In this study, a novel formulation for the modeling of all six lower kinematic pairs (LKP), when connecting two flexible links, is introduced. By resorting to this formulation, a compact formula for the stiffness matrix of a parallelogram with flexible linkages, what is called a Π-joint, is obtained. As an illustrative example, the procedure is applied to a Schonflies motion generator that features Π joints. In order to illustrate the online feasibility of the computations involved, the minimum eigenvalues of a dimensionless factor of the stiffness matrix, used as stiffness performance index, are plotted along a standard trajectory adopted by the industry.
机译：本文的主题是机器人结构的弹力分析。分析方法基于广义弹簧的概念，其中每个柔性链节均由六维广义弹簧代替。当需要连杆复杂性时，应通过有限元分析（FEA）以数值方式获得该弹簧的刚度矩阵。在这项研究中，介绍了一种新颖的公式，用于在连接两个柔性链环时对所有六个下部运动对（LKP）进行建模。通过采用这种公式，可以获得具有柔性连接的平行四边形的刚度矩阵的紧凑公式，即所谓的join接头。作为说明性示例，该过程应用于具有Π关节的Schonflies运动生成器。为了说明所涉及计算的在线可行性，沿着行业采用的标准轨迹绘制了用作刚度性能指标的刚度矩阵的无量纲因子的最小特征值。

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