When using parallel manipulators as machine tools, the spherical joint has been widely used and replaced by a combination of a universal joint and a rotating unit, but the introduced differences and effects have not been studied in detail. In this paper, an approach to establish the mathematical models of the ideal and combined spherical joints is presented, and the differences between the two spherical joints are given from the perspective of constraints, workspace, clearance, and contact deformation. First, the non-interference workspace of a class universal joint is investigated by using a simple and clear projection method, where the constraint domain and workspace of two spherical joints are proposed. Next, the approximate clearance models of these two spherical joints are analyzed, and the corresponding contact deformation models are also given based on the Hertzian Contact theory. Finally, a 1PU + 3UPS parallel manipulator is used to verify the discrepant effects of two spherical joints on parallel manipulators. If the combined spherical joint is used, the results indicate that the improvement in the workspace is significant, but the drop in stiffness is also evident. Thus, this paper provides a theoretical basis for researchers to use combined spherical joints.

中文翻译：

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理想球关节与组合球关节的区别及其对并联机械手的影响

并联机械手作为机床使用时，球形关节已被广泛使用，并被万向节和旋转单元的组合所取代，但尚未详细研究引入的差异和影响。本文提出了一种建立理想和组合球关节数学模型的方法，并从约束、工作空间、间隙和接触变形的角度给出了两种球关节之间的差异。首先，采用简单明了的投影方法研究了类万向节的非干涉工作空间，提出了两个球形关节的约束域和工作空间。接下来分析这两个球关节的近似间隙模型，并基于赫兹接触理论给出了相应的接触变形模型。最后，使用1PU+3UPS并联机械手验证了两个球形关节对并联机械手的差异影响。如果使用组合球面关节，结果表明工作空间的改善是显着的，但刚度的下降也很明显。因此，本文为研究人员使用组合球关节提供了理论依据。