This paper presents the dynamic model and analytical modal analysis for robotic manipulators with rigid links and flexible joints. Dynamic equations of general robots with both prismatic and revolute joints are firstly developed using the Lagrangian formulation in minimal joint and motor coordinates. Next, linearized dynamic equations taking into account the influence of gravity forces, external forces, and control parameters are formulated based on the Taylor series. Therefore, the robot’s modal parameters can be computed for any configuration based on a state–space matrix derived from the linearization model. To illustrate the proposed method, modal parameters of a flexible joint robot with six degrees of freedom are computed using the analytical method and estimated using the operational modal technique based on the vector autoregression model. Results obtained by both methods agree very well with each other.

本文介绍了具有刚性连杆和柔性关节的机器人机械手的动力学模型和解析模态分析。首次使用拉格朗日公式在最小关节和电机坐标系中开发了具有棱柱和旋转关节的通用机器人的动力学方程。接下来，基于泰勒级数制定了考虑重力、外力和控制参数影响的线性化动力学方程。因此，可以基于从线性化模型导出的状态空间矩阵，针对任何配置计算机器人的模态参数。为了说明所提出的方法，使用解析方法计算具有六个自由度的柔性关节机器人的模态参数，并使用基于矢量自回归模型的操作模态技术进行估计。