摘 要
机械臂作为现代工业自动化的核心技术之一，在智能制造、医疗手术、航空航天等领域具有广泛应用，其运动学与动力学性能直接影响任务执行的精度与效率。为深入研究机械臂的运动特性及其控制策略，本文以六自由度机械臂为研究对象，系统开展了运动学正解与逆解分析、动力学建模以及仿真验证工作。研究中采用D-H参数法建立了机械臂的运动学模型，并通过雅可比矩阵推导实现了末端位姿与关节变量之间的映射关系；同时基于拉格朗日方法构建了机械臂的动力学方程，全面描述了其惯性力、重力、科氏力及离心力等作用机制。为进一步提升模型准确性，引入数值优化算法对运动学逆解进行求解，并结合实际工况调整动力学参数。通过MATLAB与Simulink平台搭建了虚拟仿真环境，验证了所建立模型的有效性与可靠性。结果表明，该方法能够精确描述机械臂在复杂运动条件下的动态响应特性，且显著提高了路径规划与轨迹跟踪的精度。本文的主要创新点在于提出了一种改进的雅可比迭代算法以解决运动学逆解的多解问题，并将动力学参数辨识与仿真验证相结合，为机械臂的实际应用提供了理论支持和技术保障。研究成果不仅深化了对机械臂运动规律的理解，还为后续的控制器设计与优化奠定了坚实基础。
关键词：六自由度机械臂；运动学建模；动力学分析；雅可比迭代算法；数值优化
Abstract
As one of the core technologies in modern industrial automation, robotic arms have extensive applications in intelligent manufacturing, medical surgery, aerospace, and other fields. Their kinematic and dynamic performance directly affects the accuracy and efficiency of task execution. To further investigate the motion characteristics and control strategies of robotic arms, this study focuses on a six-degree-of-freedom robotic arm and systematically conducts analyses of forward and inverse kinematics, dynamic modeling, and simulation verification. The Denavit-Hartenberg (D-H) parameter method is employed to establish the kinematic model of the robotic arm, and the mapping relationship between the end-effector pose and joint variables is realized through the derivation of the Jacobian matrix. Meanwhile, the Lagrangian method is used to construct the dynamic equations of the robotic arm, comprehensively describing the mechanisms of inertial forces, gravitational forces, Coriolis forces, and centrifugal forces. To enhance the accuracy of the model, a numerical optimization algorithm is introduced for solving the inverse kinematics problem, and the dynamic parameters are adjusted according to actual working conditions. A virtual simulation environment is built using MATLAB and Simulink platforms to verify the effectiveness and reliability of the established model. The results show that this method can accurately describe the dynamic response characteristics of the robotic arm under complex motion conditions and significantly improves the precision of path planning and trajectory tracking. The main innovation of this study lies in proposing an improved Jacobian iterative algorithm to address the multi-solution issue of inverse kinematics and integrating dynamic parameter identification with simulation verification, providing theoretical support and technical guarantees for the practical application of robotic arms. The research not only deepens the understanding of the motion laws of robotic arms but also lays a solid foundation for subsequent controller design and optimization.
Keywords: Six Degrees Of Freedom Manipulator; Kinematics Modeling; Dynamics Analysis; Jacobian Iterative Algorithm; Numerical Optimization
目 录
1绪论 1
1.1机械臂运动学与动力学研究背景 1
1.2机械臂运动学与动力学分析的意义 1
1.3国内外研究现状综述 1
1.4本文研究方法与技术路线 2
2机械臂运动学分析 2
2.1运动学基础理论概述 2
2.2正向运动学建模与求解 3
2.3逆向运动学分析方法 3
2.4关节空间与操作空间的关系 4
2.5运动学仿真验证 4
3机械臂动力学分析 5
3.1动力学基本原理与公式推导 5
3.2拉格朗日方法在动力学中的应用 5
3.3牛顿-欧拉方法的动力学建模 6
3.4动力学参数辨识与优化 6
3.5动力学仿真与结果分析 7
4机械臂运动学与动力学联合仿真 7
4.1联合仿真的必要性与意义 7
4.2仿真平台与工具的选择 8
4.3运动学与动力学模型的集成 8
4.4仿真案例设计与实现 9
4.5仿真结果分析与讨论 9
结论 10
参考文献 11
致 谢 12
