• CN：11-2187/TH
• ISSN：0577-6686

• 仪器科学与技术 •

### 回转精度测评的运动几何学原理与不变量方法

1. 大连理工大学机械工程学院 大连 116024
• 收稿日期:2019-03-01 修回日期:2019-10-01 出版日期:2020-02-20 发布日期:2020-04-23
• 通讯作者: 王德伦(通信作者),男,1958年出生,博士,教授,博士研究生导师。主要研究方向为机构学及机械装备数字化设计。E-mail:dlunwang@dlut.edu
• 作者简介:王智,男,1986年出生,博士。主要研究方向为机构学与精密装备的设计与测量理论。E-mail:wangzhi@mail.dlut.edu.cn
• 基金资助:
国家自然科学基金资助项目（51775079）。

### Kinematic Geometry Principles and Invariants Method for Rotational Accuracy Measurements and Evaluations

WANG Zhi, DONG Huimin, WANG Delun

1. School of Mechanical Engineering, Dalian University of Technology, Dalian 116024
• Received:2019-03-01 Revised:2019-10-01 Online:2020-02-20 Published:2020-04-23

Abstract: The error-included kinematic geometry principles for rotational accuracy measurements and evaluations of revolute pairs are presented for the first time, which are represented by the kinematic geometry models and the basic closed-loop vector equations formed by three basic elements, including the error motion of the rotor, the geometric elements tested and the measuring parameters of the sensors. The completeness conditions for measuring rotational accuracy are derived according to the error-included kinematic geometry principles. The integrality of the measured kinematic parameters of the rotational error motion is discussed based on the existence of solutions of the basic equations, whose evolution forms are tied to the measuring methods and used to clarify the kinematic and geometric meanings of the measured data and their accuracy indexes. The invariants theorem of rotational error motion are given by considering the kinematic geometry properties of the error motion; the minimal spherical image curve and the minimal striction curve of the rotational error motion are obtained, which separates the rotational error motion of the rotor into angular error motion and translational error motion. The relationships between the current accuracy indexes and the invariants, such as the angular error and the translational error, are set up; these help to develop a new invariants method for rotational accuracy evaluation, which can avoid the influences of different geometric elements tested. It provides a theoretical basis for measuring and evaluating rotational accuracy of revolute pairs.