A modular approach to the kinematics of planar linkages is based on a structural analysis of the mechanisms. Kinematic chains that can be synthesized according to Assur principle are well classified by their structure. Such a classification allows the development of general methods of the kinematics of subchains that can be algorithmized and used for computer-aided design. The paper introduces a new method of the position analysis of Assur dyads based on vector algebra tools. Obtained in unified vector form formulas give the opportunity to calculate the radius-vectors of all points of the dyads in the standard basis for the three-dimensional space. The method can be applied to the position, complete kinematic and kinetostatic analyses of planar linkages of the 2nd class according to Artobolevsky.

中文翻译：

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Assur 二元位置分析的直接向量方法

平面连杆运动学的模块化方法基于机构的结构分析。可根据 Assur 原理合成的运动链按其结构进行了很好的分类。这种分类允许开发子链运动学的通用方法，这些方法可以进行算法化并用于计算机辅助设计。介绍了一种基于向量代数工具的Assur二元位置分析新方法。以统一向量形式公式获得的结果使得有机会在三维空间的标准基础上计算二元组的所有点的半径向量。该方法可应用于 Artobolevsky 提出的第二类平面连杆机构的位置、完整运动学和静动学分析。