Abstract The superposition principle, when applicable in the kinematic analysis of a mechanism, makes it possible to relate the studied mechanism with its component structures, and reduces the computation burden by exploiting the relationships among different data sets. Acceleration and higher-order analyses of holonomic or first-order non-holonomic mechanisms, and the velocity analysis of mechanisms with time-dependent (rheonomic) constraints need the solution of linear and non-homogeneous equation systems. The non-homogeneity of these problems forbids the use of the superposition principle to solve them. In this work, a novel kinematic-analysis technique (Incipient Motion Technique) that fully exploits the properties of linear and non–homogeneous equation systems is proposed. This solution technique has advantages similar to the ones of the superposition principle, holds for rheonomus systems, too, is efficient enough to use it in general purpose programs for multibody dynamics analysis, and is simple enough to present it in courses for graduate students.

中文翻译：

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通过扩展叠加原理解决的加速度和高阶分析：初始运动技术

摘要 叠加原理适用于机构的运动学分析时，可以将所研究的机构与其组件结构联系起来，并通过利用不同数据集之间的关系来减少计算负担。完整或一阶非完整机制的加速和高阶分析，以及具有时间相关（流变）约束的机制的速度分析需要线性和非齐次方程系统的解。这些问题的非同质性禁止使用叠加原理来解决它们。在这项工作中，提出了一种新的运动学分析技术（初始运动技术），它充分利用了线性和非齐次方程系统的特性。