{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T15:27:22Z","timestamp":1766503642877,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2019,8,30]],"date-time":"2019-08-30T00:00:00Z","timestamp":1567123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research &amp; Development Program of China","award":["2017YFB1300700"],"award-info":[{"award-number":["2017YFB1300700"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>For systems of measurement, geometric errors such as manufacturing and assembly errors could have a significant impact on the accuracy of the angle encoders of the system. In this study, an error model of angular measurement with geometric errors of a torsional characteristic measurement system was developed based on multibody system theory, the aim of which was to reveal the impact of geometric errors on angular measurement and to compensate the measurement error. According to the principle of spatial error transfer, the decomposition of geometric errors is illustrated and the error matrix of geometric errors is constructed by the Denavit\u2013Hartenberg (DH) method. Subsequently, an error compensation function can be obtained and the impact of geometric error on angular measurement is discussed. Finally, we demonstrate by the experimental results of an ultra-autocollimator that the proposed error compensation method reduced the angular measurement error from 3.7% to 0.7%, which shows that the proposed error model can effectively predict the angular measurement error. In addition, it can be seen from the measurement results of the RV reducer that the error of the torsional characteristic measurement system decreased significantly.<\/jats:p>","DOI":"10.3390\/s19173772","type":"journal-article","created":{"date-parts":[[2019,8,30]],"date-time":"2019-08-30T10:31:17Z","timestamp":1567161077000},"page":"3772","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A New Error Model and Compensation Strategy of Angle Encoder in Torsional Characteristic Measurement System"],"prefix":"10.3390","volume":"19","author":[{"given":"Bingkui","family":"Chen","sequence":"first","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3152-5948","authenticated-orcid":false,"given":"Changyan","family":"Peng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"}]},{"given":"Jian","family":"Huang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1299\/kikaic.55.216","article-title":"Torsional Stiffness of Harmonic Drive Reducers","volume":"55","author":"Yanabe","year":"1989","journal-title":"Trans. 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Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"398","DOI":"10.3901\/CJME.2012.02.398","article-title":"Multifunctional Measurement System for High Precision Planetary Servo Gearhead","volume":"25","author":"Fan","year":"2012","journal-title":"Chin. J. Mech. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/j.mechatronics.2014.02.009","article-title":"Modeling, Observation, and Control of Hysteresis Torsion in Elastic Robot Joints","volume":"24","author":"Michael","year":"2014","journal-title":"Mechatronics"},{"key":"ref_7","first-page":"536","article-title":"The Design of Test Bed for RV Reducer Dynamic Characteristics Comprehensive Testing","volume":"15","author":"Zheng","year":"2017","journal-title":"Chin. J. Const. Mach."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.mechmachtheory.2017.09.019","article-title":"Lost Motion Analysis of CBR Reducer","volume":"120","author":"Sun","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.3788\/OPE.20122011.2479","article-title":"Eccentric Testing of Benchmark Circular Grating and Compensation of Angular Error","volume":"20","author":"Ai","year":"2012","journal-title":"Opt. Precis. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lou, Z.F., Hao, X.P., and Cai, Y.D. (2019). An Embedded Sensor System for Real-Time Detecting 5-DOF Error Motions of Rotary Stages. 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Res."},{"key":"ref_14","first-page":"360","article-title":"A New Method for Circular Grating\u2019s Eccentricity Identification and Error Compensation","volume":"83","author":"Su","year":"2015","journal-title":"IMCCC"},{"key":"ref_15","first-page":"9","article-title":"Effect of Eccentric of Circular Gratings on Angular Position Accuracy of Simulator","volume":"37","author":"Mi","year":"2014","journal-title":"J. Changchun Univ. Sci. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"31428","DOI":"10.3390\/s151229863","article-title":"A Novel Error Model of Optical Systems and an On-Orbit Calibration Method for Star Sensors","volume":"15","author":"Wang","year":"2015","journal-title":"Sensors"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1367","DOI":"10.1016\/j.measurement.2011.05.004","article-title":"Analysis of Optical Linear Encoders\u2019 Errors under Vibration at Different Mounting Conditions","volume":"44","author":"Lopez","year":"2011","journal-title":"Measurement"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.measurement.2017.07.048","article-title":"Non-uniform Flank Rolling Measurement for Shaped Noncircular Gears","volume":"116","author":"Zheng","year":"2018","journal-title":"Measurement"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.ijmachtools.2015.11.006","article-title":"Modeling and compensation of volumetric errors for five-axis machine tools","volume":"101","author":"Xiang","year":"2016","journal-title":"Int. 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