This paper studies the dynamics of a space manipulator. The space manipulator is designed for precise on-orbit servicing missions in a highly constrained environment. The concerned manipulator has hyper-redundant degrees of freedom and moves with a piecewise constant curvature, which enhances the flexibility and controllability. Such manipulator consists of a large number of links and a complex rope network. When the manipulator is driven, the interacting forces between the links and ropes introduce complexity into the dynamic behavior. In terms of dynamic modeling, the manipulator is a very complex system. This paper proposes a dynamic model of the manipulator based on methods of multibody dynamics. The ropes are assumed to be massless and linear elastic. The equations of motion are derived using space operator algebra. The vibration of the manipulator is investigated. The governing equations of the vibration are derived by applying the perturbation method to the proposed dynamic model. The values of the natural frequencies are investigated for the elasticities of the ropes. The proposed dynamic model is also applied in numerical simulation. The explicit fourth-order Runge-Kutta method is utilized to solve the equations of motion numerically. In numerical simulation, an upper bound of the time step is encountered. The value of upper bound is found to be related to the elasticities of the ropes. Such phenomena are studied by analyzing the stability region of the Runge-Kutta methods. Besides, the computational efficiency of the numerical simulation is also limited by the value of upper bound. Two modifications of the dynamic model are introduced to relax the upper bound of the time step. The effects of the modifications are demonstrated by numerical results.

本文研究了空间操纵器的动力学。空间操纵器设计用于在高度受限的环境中进行精确的在轨维修任务。所关注的机械手具有超冗余的自由度，并且以分段恒定的曲率运动，从而增强了灵活性和可控性。这种操纵器由大量的链接和复杂的绳索网络组成。当驱动机械手时，链节和绳索之间的相互作用力将复杂性引入动态行为。就动态建模而言，操纵器是一个非常复杂的系统。本文提出了一种基于多体动力学方法的机械手动力学模型。假设绳索是无质量且线性弹性的。运动方程是使用空间算子代数导出的。研究了机械手的振动。通过将扰动方法应用于所提出的动力学模型，得出了振动的控制方程。研究了固有频率的值以了解绳索的弹性。所提出的动力学模型也被应用于数值模拟。显式四阶Runge-Kutta方法用于数值求解运动方程。在数值模拟中，会遇到时间步长的上限。发现上限值与绳索的弹性有关。通过分析Runge-Kutta方法的稳定性区域来研究此类现象。此外，数值模拟的计算效率也受到上限值的限制。引入了两个动态模型修改，以放松时间步长的上限。数值结果证明了修改的效果。