Flexible manipulators become widely used in industrial and medical fields due to their high dexterity compared with traditional discrete manipulators. However, in existing kinematics models of flexible manipulators without extension ability, the inverse kinematic (IK) analytical solution including the end-effector position and pose cannot be obtained. In this paper, a design example of a class of n-tendon continuum manipulators is presented. Based on the constant curvature hypothesis, a unified solution for solving the coupling relationship among tendons is derived. Combined with the Denavit-Hartenberg (D-H) method, the Taylor Series and the quaternion, the forward and inverse models are established, and an approximate analytical solution to the IK is derived. Simulations show the proposed IK solution has a good performance in accuracy and efficiency. A two-dimensional plane experiment and a three-dimensional space experiment are implemented. The average position errors of the two validation experiments respectively account for less than 2.0% and 3.5% of the total manipulator length, and the average pose errors are respectively no more than 0.8° and 2.5°. GRAPHICAL ABSTRACT

中文翻译：

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一类n-腱连续体机械手的运动学建模

柔性机械手与传统的离散机械手相比，由于其灵活性高，在工业和医疗领域得到了广泛的应用。然而，在现有的不具有扩展能力的柔性机械手运动学模型中，无法获得包括末端执行器位置和姿态的逆运动学 (IK) 解析解。在本文中，介绍了一类 n 腱连续体机械手的设计实例。基于常曲率假设，推导出求解肌腱间耦合关系的统一解。结合Denavit-Hartenberg(DH)方法、泰勒级数和四元数，建立正反模型，推导出IK的近似解析解。仿真表明，所提出的 IK 解决方案在准确性和效率方面具有良好的性能。进行了二维平面实验和三维空间实验。两次验证实验的平均位置误差分别占机械臂总长度的不到2.0%和3.5%，平均位姿误差分别不超过0.8°和2.5°。图形概要