真实机构运动分析综合与机床精度测评理论基础

doi:10.3901/JME.2025.21.075

摘要/Abstract

摘要： 构建了真实机构运动分析与综合的理论基础架构，定义了真实机构及其真实构件、真实运动副，研究真实机构运动分析与综合方法。首先，基于真实回转副/移动副的实测运动数据，分析了其约束几何要素的离散运动轨迹性质，获得五个全局运动不变量参数——最小准线点的平动位移区域和最小球面像方向的角位移区域，揭示了真实运动副不存在理想轴线，而是由真实运动整体性质确定近似动/定准轴线，由此确定真实构件的尺度。其次，将真实运动副约束两真实构件间的运动分解为随动准轴线的牵连运动和相对动准轴线的运动，而牵连运动参数恰为动准轴线的五个运动不变量参数，提出了真实运动副不变量运动精度。再次，由真实构件连接真实运动副动-定准轴线形成真实机构，建立了真实机构运动学基本方程，揭示了真实机构结构、尺度与真实运动的内在联系。同时，构建了真实机构运动分析与综合初步架构——由真实机构求解实际输出运动、由实际测试数据辨识真实机构。最后，将机床运动精度测量与分析转化为真实机构运动分析与综合问题，为机床运动精度分析设计和误差辨识提供理论基础。据此，将机构运动分析与综合理论由刚体机构发展到真实机构，拓展了机构学应用领域，为丰富和发展机构学理论提供了新路径。

关键词: 真实机构, 不变量, 运动分析, 机构综合, 数控机床, 精度

Abstract: This research establishes the theoretical framework for the kinematic analysis and synthesis of real mechanisms, defines the concepts of real mechanisms, real links, and real kinematic pairs, and develops methodologies for the kinematic analysis and synthesis of real mechanisms. Firstly, based on measured motion data from real revolute/prismatic pairs, the discrete trajectory properties of their constrained geometric elements are analyzed. This reveals five global motion invariant parameters: the translational displacement region of the minimum quasi-line point and the angular displacement region of the minimum spherical image orientation. It is shown that real kinematic pairs do not possess ideal axes; instead, approximate moving and fixed quasi-axes are determined by the overall motion properties, thereby defining the dimensions of real links. Secondly, the motion of real kinematic pairs is decomposed into the transport motion of the moving quasi-axis and the relative motion about this axis. Crucially, the transport motion parameters correspond to the motion invariants of the moving quasi-axis. This leads to the proposal of the invariant motion accuracy for real kinematic pairs. Thirdly, a real mechanism is formed by connecting the moving and fixed quasi-axes of real kinematic pairs via real links. Fundamental kinematic equations for real mechanisms are established, revealing the intrinsic relationships between the mechanism’s structure, link dimensions, and its real motion. Finally, a framework is constructed encompassing two processes: kinematic analysis, which solves for the output motion patterns given the mechanism’s structure, dimensional parameters, and motion invariants; and kinematic synthesis, which identifies or estimates the structural parameters and motion invariants from experimental test data. These methods provide the theoretical basis and methodology for analyzing, designing, and compensating for motion accuracy and errors in machine tools. Consequently, this work extends mechanism kinematics theory from rigid-body mechanisms to real mechanisms, broadening the application scope of mechanism science and offering novel pathways for enriching and advancing mechanism theory.

Key words: real mechanisms, invariants, kinematic analysis, kinematic synthesis, machine tools, accuracy

中图分类号:

TG156

唐首臣, 钟祾充, 郭彩玲, 王智, 刘辉, 刘喜平, 王德伦. 真实机构运动分析综合与机床精度测评理论基础[J]. 机械工程学报, 2025, 61(21): 75-99.

TANG Shouchen, ZHONG Lingchong, GUO Cailing, WANG Zhi, LIU Hui, LIU Xiping, WANG Delun. Kinematic Analysis and Synthesis of Real Mechanisms and Theoretical Basis in Machine Tool Accuracy Measurements and Evaluations[J]. Journal of Mechanical Engineering, 2025, 61(21): 75-99.

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