{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T16:51:58Z","timestamp":1782406318365,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,9,29]],"date-time":"2017-09-29T00:00:00Z","timestamp":1506643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Foundation of PR China","award":["51105322"],"award-info":[{"award-number":["51105322"]}]},{"name":"the Natural Science Foundation of Hebei Province","award":["E2014203176"],"award-info":[{"award-number":["E2014203176"]}]},{"name":"the Natural Science Research Foundation of Higher Education of Hebei Province","award":["QN2015040"],"award-info":[{"award-number":["QN2015040"]}]},{"name":"China's Post-doctoral Science Fund","award":["2016M590212"],"award-info":[{"award-number":["2016M590212"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>By combining a parallel mechanism with integrated flexible joints, a large measurement range and high accuracy sensor is realized. However, the main errors of the sensor involve not only assembly errors, but also deformation errors of its flexible leg. Based on a flexible joint 6-UPUR (a kind of mechanism configuration where U-universal joint, P-prismatic joint, R-revolute joint) parallel six-axis force sensor developed during the prephase, assembly and deformation error modeling and analysis of the resulting sensors with a large measurement range and high accuracy are made in this paper. First, an assembly error model is established based on the imaginary kinematic joint method and the Denavit-Hartenberg (D-H) method. Next, a stiffness model is built to solve the stiffness matrix. The deformation error model of the sensor is obtained. Then, the first order kinematic influence coefficient matrix when the synthetic error is taken into account is solved. Finally, measurement and calibration experiments of the sensor composed of the hardware and software system are performed. Forced deformation of the force-measuring platform is detected by using laser interferometry and analyzed to verify the correctness of the synthetic error model. In addition, the first order kinematic influence coefficient matrix in actual circumstances is calculated. By comparing the condition numbers and square norms of the coefficient matrices, the conclusion is drawn theoretically that it is very important to take into account the synthetic error for design stage of the sensor and helpful to improve performance of the sensor in order to meet needs of actual working environments.<\/jats:p>","DOI":"10.3390\/s17102238","type":"journal-article","created":{"date-parts":[[2017,9,29]],"date-time":"2017-09-29T12:24:04Z","timestamp":1506687844000},"page":"2238","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Error Modeling and Experimental Study of a Flexible Joint 6-UPUR Parallel Six-Axis Force Sensor"],"prefix":"10.3390","volume":"17","author":[{"given":"Yanzhi","family":"Zhao","sequence":"first","affiliation":[{"name":"Key Laboratory of Parallel Robot and Mechatronic System of Hebei Province, Yanshan University, Qinhuangdao 066004, China"},{"name":"Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education of China, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yachao","family":"Cao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Parallel Robot and Mechatronic System of Hebei Province, Yanshan University, Qinhuangdao 066004, China"},{"name":"Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education of China, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Caifeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Parallel Robot and Mechatronic System of Hebei Province, Yanshan University, Qinhuangdao 066004, China"},{"name":"Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of Education of China, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dan","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Lassonde School of Engineering, York University, 4700 Keele Street, Toronto, ON M3J1P3, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Basic Teaching, LiRen College of Yanshan University, Qinhuangdao 066004, Hebei, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,29]]},"reference":[{"key":"ref_1","first-page":"151","article-title":"How to design flexture hinges","volume":"37","author":"Paros","year":"1965","journal-title":"Mach. 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