The robot kinematic model is the basis of motion control, calibration, error analysis, etc. Considering these factors, the kinematic model needs to meet the requirements of completeness, model continuity, and minimality. DH model as the most widely used method to build robot kinematic model still has problems in completeness, model continuity, and calculation, especially for robots with complex mechanisms such as closed chain mechanism and branch mechanism. In this paper, an improved kinematic modeling method is proposed based on the cooperation of the DH model and the Hayati and Mirmirani model and considering the Lie group concept. The improved model is complete and continuous, and when combining with Lie group to calculate, it avoids numbers of trigonometric functions and antitrigonometric functions in the process so as to optimize the algorithm. With this method, the kinematic model of the closed chain cascade manipulator developed in our laboratory is established, and a working process of it is numerically calculated. The results of the numerical calculation are basically consistent with those of virtual prototype simulation, which means the established kinematic model is correct and the numerical calculation method can solve the problem correctly. The kinematic model and the results of the kinematic analysis provide a theoretical basis for the subsequent motion control, calibration, and error analysis of the robot.

中文翻译：

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基于改进建模方法和李群理论的闭链机器人运动学分析

机器人运动学模型是运动控制，校准，误差分析等的基础。考虑到这些因素，运动学模型需要满足完整性，模型连续性和最小化的要求。DH模型作为建立机器人运动学模型最广泛使用的方法，在完整性，模型连续性和计算上仍然存在问题，特别是对于具有复杂机制（如闭链机构和分支机构）的机器人。本文基于DH模型与Hayati和Mirmirani模型的协作，并考虑了Lie群的概念，提出了一种改进的运动学建模方法。改进后的模型是完整而连续的，结合李群进行计算，它在处理过程中避免了三角函数和反三角函数的数量，从而优化了算法。利用该方法，建立了我所实验室开发的闭链叶栅机械手的运动学模型，并对其工作过程进行了数值计算。数值计算结果与虚拟样机仿真结果基本吻合，说明建立的运动学模型正确，数值计算方法可以正确解决问题。运动学模型和运动学分析的结果为机器人的后续运动控制，校准和误差分析提供了理论基础。并对其工作过程进行数值计算。数值计算结果与虚拟样机仿真基本吻合，说明建立的运动学模型正确，数值计算方法可以正确解决问题。运动学模型和运动学分析结果为机器人的后续运动控制，校准和误差分析提供了理论基础。并对其工作过程进行数值计算。数值计算结果与虚拟样机仿真结果基本吻合，说明建立的运动学模型正确，数值计算方法可以正确解决问题。运动学模型和运动学分析结果为机器人的后续运动控制，校准和误差分析提供了理论基础。