Abstract A singularity analysis of multi-platform parallel mechanisms is presented. If the mechanism can be decomposed into minimal mechanisms, the decomposition is performed and its singularity is determined through the singularity of its components. In contrast, if the mechanism is already a minimal mechanism, its singularity is determined through reduction of the original mechanism to a simpler mechanism using the reciprocality relation. The analysis of general two-platform and three-platform minimal mechanisms is presented, while examples of reduction to a simpler mechanism are shown on two actual two-platform mechanisms. It is found that for three-platform mechanisms, there are irreducible cases.

中文翻译：

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基于分解互易的多平台机制奇异性分析

摘要 提出了多平台并联机构的奇异性分析。如果机制可以分解为最小机制，则进行分解并通过其组件的奇异性确定其奇异性。相反，如果该机制已经是最小机制，则通过使用互易关系将原始机制简化为更简单的机制来确定其奇异性。介绍了一般两平台和三平台最小机制的分析，同时在两个实际的两平台机制上展示了简化为更简单机制的示例。发现对于三平台机制，存在不可约的情况。