Abstract Cable-driven serpentine manipulators have advantages in compact structure, light weight and superior dexterity. They are suitable for applications in unstructured environments. However, the flexibility of the driving cables reduces the manipulator’s stiffness and brings concerns on system performances. Therefore, stiffness is a key problem. This paper aims to establish a general framework for studying the stiffness of cable-driven serpentine manipulators. We firstly established the kinematic and static models, and then proposed the analytical and numerical methods to calculate the stiffness matrix. Simulation validations show that the relative difference of the stiffness matrices by the two methods is negligible. But traditional stiffness models that neglect Jocobian matrix’s variations and/or use pseudo-inverse calculations could cause large error. Further comparisons show that the analytical method has advantages in accuracy, calculating speed and real-time performance, but requires complex formula derivation. Based on these results, suggestions are given on how to choose the proper method. Lastly, discussions are made on the numerical model’s accuracy and the cable control model selection. The proposed methods are useful for the stiffness analyses of cable-driven serpentine manipulators, and could further provide a theoretical tool for structural optimization, deformation compensation, variable stiffness control, compliance control, etc.

中文翻译：

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缆索驱动蛇形机械手刚度建模的解析和数值方法

摘要 缆索驱动蛇形机械手具有结构紧凑、重量轻、灵巧性高等优点。它们适用于非结构化环境中的应用程序。然而，驱动电缆的灵活性降低了机械手的刚度，并带来了对系统性能的担忧。因此，刚度是一个关键问题。本文旨在建立一个研究电缆驱动蛇形机械手刚度的一般框架。我们首先建立了运动学和静态模型，然后提出了解析和数值方法来计算刚度矩阵。仿真验证表明，两种方法刚度矩阵的相对差异可以忽略不计。但是忽略约可比矩阵的变化和/或使用伪逆计算的传统刚度模型可能会导致很大的误差。进一步对比表明，该分析方法在准确度、计算速度和实时性方面具有优势，但需要复杂的公式推导。根据这些结果，就如何选择合适的方法给出了建议。最后，讨论了数值模型的精度和电缆控制模型的选择。所提出的方法可用于缆索驱动蛇形机械手的刚度分析，并可进一步为结构优化、变形补偿、变刚度控制、柔顺控制等提供理论工具。计算速度和实时性能，但需要复杂的公式推导。根据这些结果，就如何选择合适的方法给出了建议。最后，讨论了数值模型的精度和电缆控制模型的选择。所提出的方法可用于缆索驱动蛇形机械手的刚度分析，并可进一步为结构优化、变形补偿、变刚度控制、柔顺控制等提供理论工具。计算速度和实时性能，但需要复杂的公式推导。根据这些结果，就如何选择合适的方法给出了建议。最后，讨论了数值模型的精度和电缆控制模型的选择。所提出的方法可用于缆索驱动蛇形机械手的刚度分析，并可进一步为结构优化、变形补偿、变刚度控制、柔顺控制等提供理论工具。