Parallel continuum manipulators (PCMs) have increasingly attracted attentions in the field of mechanism and robotics, owing to their inherent merits, such as compliance in structure, reduction of backlash, and easiness in implementation. This paper presents a general approach for the kinetostatics modeling and analysis of spatial PCMs. A discretization-based technique is employed for the nonlinear large-deflection problems of the coupled slender flexible links in these flexible parallel manipulators. Benefiting from the mechanism approximation to the force-deflection characteristics of the flexible links, the kinetostatics models of the PCMs can be established analytically in the realm of robot kinematics/statics, rather than continuum mechanics. Moreover, a closed-form solution to the gradient of these nonlinear algebraic equations can be derived, such that gradient-based searching algorithms can be implemented to efficiently determine the equilibrium configurations in a variety of given conditions. A prototype of a three-limb 6-DOF PCM is developed, on which validation experiments are conducted. And the results verify the effectiveness of the proposed method for the kinetostatics modeling and analysis of parallel continuum manipulators.

并联连续机械手（PCM）由于其固有的优点（例如结构顺从，减少反冲，易于实施）而在机械和机器人领域引起了越来越多的关注。本文提出了一种用于空间PCM运动静力学建模和分析的通用方法。基于离散化的技术用于这些柔性并联机械手中耦合细长弹性连杆的非线性大挠度问题。得益于柔性连杆的力-挠度特性的近似机制，可以在机器人运动学/静力学领域而不是在连续力学领域中分析地建立PCM的运动静力学模型。而且，可以得出这些非线性代数方程的梯度的封闭形式解，这样就可以实施基于梯度的搜索算法，以有效地确定各种给定条件下的平衡构型。开发了三臂6-DOF PCM的原型，并在其上进行了验证实验。实验结果验证了该方法对并联连续机械手的动静力学建模和分析的有效性。