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First, the Cartesian stiffness model based on the Jacobian matrix was established for a robot, and then the displacement error model of deformations caused by external force was established based on Cartesian stiffness. Second, the transmission system of the robot\u2019s joint was analyzed, and an equivalent method for joint stiffness was presented based on a series spring system. Meanwhile, the stiffness of the key components including the servo motor, harmonic reducer, and timing belt was deduced in detail. Finally, a compared simulation and a measurement experiment were conducted on a 6-joint series robot. It was found that the FPM-CSES could calculate any configuration among the robot\u2019s workspace. Compared with the finite element analysis (FEA) method, the presented method is feasible and more efficient. The experimental results showed that the prediction accuracy of the FPM-CSES is rather high, with an average rate of more than 83.72%. Hence, the prediction method presented in this study is simple, fast, and reliable, and could be used to predict and analyze the displacement errors caused by the cutting force, and provide the basis for trajectory planning and error compensation, enhancing the robot\u2019s machining performance.<\/jats:p>","DOI":"10.3390\/s22165963","type":"journal-article","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T04:20:32Z","timestamp":1660105232000},"page":"5963","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A New Prediction Method of Displacement Errors Caused by Low Stiffness for Industrial Robot"],"prefix":"10.3390","volume":"22","author":[{"given":"Zhenya","family":"He","sequence":"first","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China"},{"name":"State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingjing","family":"Song","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9472-3151","authenticated-orcid":false,"given":"Xianmin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guojian","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Guangdong Mechanical and Electrical Polytechnic, Guangzhou 510515, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.rcim.2018.07.001","article-title":"Stiffness-based pose optimization of an industrial robot for five-axis milling","volume":"55","author":"Xiong","year":"2019","journal-title":"Robot. 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