Abstract This paper systematically deals with the synthesis of multi-mode single-loop 6R, 7R and 8R Bennett-based mechanisms from an algebraic viewpoint. Based on the factorization of motion polynomials over dual quaternions, an algebraic method is proposed to synthesize multi-mode single-loop 6R, 7R and 8R Bennett-based mechanisms. Using this method, several multi-mode single-loop Bennett-based mechanisms with different number of joints are constructed depending on explicit poses of joint axes. Then motion mode analysis of the 7R mechanism is carried out by formulating and solving a set of kinematic loop equations using tools from algebraic geometry. The analysis demonstrates that this multi-mode 7R mechanism has four motion modes, including a two degree-of-freedom (DOF) double Bennett mode, a 2-DOF hybrid mode, a 1-DOF rotation mode and a 1-DOF spatial 7R mode. Meanwhile, multimode characteristics of the single-loop 6R and 8R mechanisms also are concisely demonstrated in light of reconfiguration analysis. This work provides an algebraic representation framework for further investigation on multi-mode mechanisms that composed of two or more single-loop overconstraint mechanisms.

中文翻译：

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使用运动多项式分解的多模式单环 Bennett 机制的综合

摘要 本文从代数的角度系统地讨论了多模单环 6R、7R 和 8R Bennett 机制的综合。基于对双四元数的运动多项式分解，提出了一种代数方法来合成多模单环6R、7R和8R Bennett机制。使用这种方法，根据关节轴的显式姿势构建了几种具有不同关节数​​量的基于多模式单回路 Bennett 的机构。然后，通过使用代数几何工具制定和求解一组运动学回路方程，对 7R 机构进行运动模式分析。分析表明，这种多模 7R 机构具有四种运动模式，包括两自由度 (DOF) 双贝内特模式、2-DOF 混合模式、1-DOF 旋转模式和 1-DOF 空间 7R 模式。同时，根据重配置分析，也简明地展示了单回路 6R 和 8R 机制的多模特性。这项工作为进一步研究由两个或多个单环过约束机制组成的多模式机制提供了一个代数表示框架。