Abstract A mechanism not only bears loads on the output but also endures loads from gravity, inertia, and other types of stresses from the environment on all rigid bodies (or links). These loads are collectively called external wrenches. Internal wrenches, which include the constraint loads of joints and the driving loads of actuators, resist external wrenches. Mapping from internal to external wrenches can provide an extensive evaluation of the mechanism considering all the constraint loads of the joints, the driving loads of the actuators, and all the possible loads of each rigid body. This paper proposes a novel index that can evaluate a mechanism by considering both the internal and external wrenches. First, the whole wrench mapping matrix from the internal to the external wrenches is built based on the digraph connections of the rigid bodies. Second, with the condition number of the matrix, the whole wrench index is obtained to evaluate the mapping from internal to external wrenches, and its physical interpretation is studied. Finally, two kinds of parallel mechanisms are analyzed to indicate the significance and universality of the novel index.

中文翻译：

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一种评估并行机构从内部到外部扳手的映射的新指标

摘要 机构不仅在输出端承受载荷，而且在所有刚体（或连杆）上承受来自重力、惯性和来自环境的其他类型应力的载荷。这些负载统称为外部扳手。内部扳手，包括关节的约束载荷和执行器的驱动载荷，抵抗外部扳手。考虑到关节的所有约束载荷、致动器的驱动载荷以及每个刚体的所有可能载荷，从内部到外部扳手的映射可以提供对机构的广泛评估。本文提出了一种新的指标，可以通过考虑内部和外部扳手来评估机构。首先，从内部到外部扳手的整个扳手映射矩阵是基于刚体的有向图连接构建的。其次，利用矩阵的条件数，得到全扳手指数，评价内扳手到外扳手的映射，并研究其物理解释。最后，通过分析两种并行机制来说明新指标的意义和普遍性。