In order to weaken the strict geometric constraint relationship between the axes of joints so as to reduce manufacturing/assembling errors of overconstrained mechanism, a configuration design methodology for single-loop non-overconstrained mechanism with inactive joints is proposed in this paper based on the screw theory. After completing analysis of degrees of freedom, the design principle and corresponding process of single-loop non-overconstrained mechanism with inactive joints are presented. By introducing two inactive R (R: single-degree-of-freedom revolute joint) joints to an active R joint of Goldberg overconstrained mechanism, the corresponding Goldberg non-overconstrained mechanism is obtained. It is verified that the velocities of two inactive joints in the Goldberg non-overconstrained mechanism are zero via investigating motion screws of branches. By further solving input and output kinematic parameters of Goldberg non-overconstrained mechanism, it is discovered that the overconstrained mechanism and corresponding non-overconstrained mechanism have the identical input–output relationship. Above results confirm that the overconstrained mechanism and its non-overconstrained counterpart with inactive joints are completely equivalent kinematically, which thereby demonstrate fully correctness of the configuration design principle and method of single-loop non-overconstrained mechanism proposed in this paper.

中文翻译：

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带非活动关节的单回路无过约束机构的配置设计

为弱化关节轴间严格的几何约束关系，减少过约束机构的制造/装配误差，提出了一种基于螺钉的无活动关节单环非过约束机构的构型设计方法。理论。在完成自由度分析后，给出了具有非活动关节的单回路非过约束机构的设计原理和相应过程。通过将两个非活动R（R：单自由度旋转关节）关节引入Goldberg过约束机构的一个活动R关节，得到相应的Goldberg非过约束机构。通过研究分支的运动螺杆，验证了Goldberg非过约束机构中两个非活动关节的速度为零。通过进一步求解 Goldberg 非过约束机构的输入输出运动学参数，发现过约束机构与对应的非过约束机构具有相同的输入输出关系。以上结果证实了过约束机构与其具有非活动关节的非过约束机构在运动学上是完全等效的，从而证明了本文提出的单回路无过约束机构构型设计原理和方法的完全正确性。发现过约束机制和对应的非过约束机制具有相同的输入输出关系。以上结果证实了过约束机构与其具有非活动关节的非过约束机构在运动学上是完全等效的，从而证明了本文提出的单回路无过约束机构构型设计原理和方法的完全正确性。发现过约束机制和对应的非过约束机制具有相同的输入输出关系。以上结果证实了过约束机构与其具有非活动关节的非过约束机构在运动学上是完全等效的，从而证明了本文提出的单回路无过约束机构构型设计原理和方法的完全正确性。