Abstract A new non-symmetric 5R-SPM is introduced and a geometrical approach is developed to analyze its configurations and singularities. The proposed methodology determines the type of configuration of a 5R-SPM, i.e. regular, singular, or out-of-workspace and also the type of singularity, i.e. instantaneous or finite, only based on geometric parameters and without solving verbose kinematic equations. It also provides insights into the workspace and singularities of 5R-SPMs, in the preliminary stage of design. The mechanism was analyzed by both the new geometrical approach and conventional methods for comparison. The geometrical approach could intuitively detect all the singularities observed by the Jacobian matrix and the kinematic analysis, with more details on the type and characteristics of each singularity. The dimensional synthesis for the designed mechanism was also performed based on the type and existence of singularities. The proposed methodology might be further developed to specify the configurations and singularities of general SPMs and also to introduce a geometrical measure for singularity closeness.

中文翻译：

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一种新型非对称 2DOF 5R 球面平行机械臂的配置和奇异性分析的几何方法

摘要 介绍了一种新的非对称 5R-SPM，并开发了一种几何方法来分析其配置和奇异性。所提出的方法确定 5R-SPM 的配置类型，即规则的、奇异的或工作空间外的以及奇异的类型，即瞬时或有限，仅基于几何参数而无需求解冗长的运动学方程。它还在设计的初步阶段提供了对 5R-SPM 的工作空间和奇异性的见解。通过新的几何方法和传统的比较方法来分析该机制。几何方法可以直观地检测到雅可比矩阵和运动学分析观察到的所有奇点，并详细说明每个奇点的类型和特征。设计机构的维度综合也是基于奇点的类型和存在性进行的。所提出的方法可能会进一步发展以指定一般 SPM 的配置和奇点，并引入奇点接近度的几何度量。