Kinematic Analysis and Synthesis of Real Mechanisms and Theoretical Basis in Machine Tool Accuracy Measurements and Evaluations

doi:10.3901/JME.2025.21.075

Abstract

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

CLC Number:

TG156

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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http://www.cjmenet.com.cn/EN/Y2025/V61/I21/75

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