{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:28:06Z","timestamp":1763468886114,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,9,11]],"date-time":"2023-09-11T00:00:00Z","timestamp":1694390400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52275442","51975319"],"award-info":[{"award-number":["52275442","51975319"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotics"],"abstract":"<jats:p>Geometric errors are the main factors affecting the output accuracy of the parallel spindle head, and it is necessary to perform a sensitivity analysis to extract the critical geometric errors. The traditional sensitivity analysis method analyzes the output position and orientation errors independently, defining multiple sensitivity indices and making it difficult to determine critical geometric errors. In this paper, we propose sensitivity indices that can comprehensively consider position and orientation errors. First, the configuration of the hybrid machine tool is introduced, and the TCP position error model is derived. Then, the tool radius and the effective cutting length are introduced, and the sensitivity indices are defined. After that, the sensitivity analysis of the 3-DOF parallel spindle head is performed using the proposed sensitivity indices, and six critical geometric errors are extracted. The machining accuracy of the parallel spindle head can be greatly improved by improving the critical geometric errors. The proposed sensitivity analysis method can provide important guidance for machine tool accuracy design.<\/jats:p>","DOI":"10.3390\/robotics12050129","type":"journal-article","created":{"date-parts":[[2023,9,12]],"date-time":"2023-09-12T04:38:48Z","timestamp":1694493528000},"page":"129","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Novel Error Sensitivity Analysis Method for a Parallel Spindle Head"],"prefix":"10.3390","volume":"12","author":[{"given":"Liping","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Key Laboratory of Precision\/Ultra-Precision Manufacturing Equipment and Control, Beijing 100084, China"}]},{"given":"Mengyu","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Key Laboratory of Precision\/Ultra-Precision Manufacturing Equipment and Control, Beijing 100084, China"}]},{"given":"Guang","family":"Yu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing Key Laboratory of Precision\/Ultra-Precision Manufacturing Equipment and Control, Beijing 100084, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1007\/s00170-010-2584-8","article-title":"Dynamic and geometric error assessment of an XYC axis subset on five-axis high-speed machine tools using programmed end point constraint measurements","volume":"50","author":"Slamani","year":"2010","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"658","DOI":"10.1007\/BF01350824","article-title":"Developing a postprocessor for three types of five-axis machine tools","volume":"13","author":"Lee","year":"1997","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/S0890-6955(98)00039-X","article-title":"Computation of stiffness and stiffness bounds for parallel link manipulators","volume":"39","author":"Ferreira","year":"1999","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/j.mechmachtheory.2007.04.002","article-title":"Accuracy analysis of 3-DOF planar parallel robots","volume":"43","author":"Briot","year":"2008","journal-title":"Mech. Mach. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1109\/3516.809515","article-title":"Static balancing of 3-DOF planar parallel mechanisms","volume":"4","author":"Gosselin","year":"1999","journal-title":"IEEE-ASME Trans. Mechatron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1007\/s11223-017-9903-3","article-title":"Experimental study of Inconel 718 surface treatment by edge robotic deburring with force control","volume":"49","author":"Burghardt","year":"2017","journal-title":"Strength Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1007\/s12666-015-0525-9","article-title":"Optimization of micro-milling parameters regarding burr size minimization via RSM and simulated annealing algorithm","volume":"68","author":"Khanghah","year":"2015","journal-title":"Trans. Indian Inst. Met."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1515\/ijame-2016-0060","article-title":"Optimization of process parameters of edge robotic deburring with force control","volume":"21","author":"Burghardt","year":"2016","journal-title":"Int. J. Appl. Mech. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1016\/S0890-6955(00)00009-2","article-title":"Error compensation in machine tools\u2014A review: Part I: Geometric, cutting-force induced and fixture-dependent errors","volume":"40","author":"Ramesh","year":"2000","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1016\/S0890-6955(00)00010-9","article-title":"Error compensation in machine tools\u2014A review: Part II: Thermal errors","volume":"40","author":"Ramesh","year":"2000","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1007\/s00170-010-2848-3","article-title":"A methodology for systematic geometric error compensation in five-axis machine tools","volume":"53","author":"Khan","year":"2011","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1151","DOI":"10.1016\/j.ijmachtools.2006.09.006","article-title":"A new approach for the geometrical calibration of parallel kinematics machines tools based on the machining of a dedicated part","volume":"47","author":"Chanal","year":"2007","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10256","DOI":"10.3390\/s101110256","article-title":"An overview of kinematic and calibration models using internal\/external sensors or constraints to improve the behavior of spatial parallel mechanisms","volume":"10","author":"Majarena","year":"2010","journal-title":"Sensors"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1007\/s00170-018-2322-1","article-title":"A sensitivity method to analyze the volumetric error of five-axis machine tool","volume":"98","author":"Li","year":"2018","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/s00170-015-7034-1","article-title":"Active precision design for complex machine tools: Methodology and case study","volume":"80","author":"Xu","year":"2015","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"109582","DOI":"10.1016\/j.measurement.2021.109582","article-title":"A new calibration method for hybrid machine tools using virtual tool center point position constraint","volume":"181","author":"Li","year":"2021","journal-title":"Measurement"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"102480","DOI":"10.1016\/j.rcim.2022.102480","article-title":"A multiple test arbors-based calibration method for a hybrid machine tool","volume":"80","author":"Li","year":"2023","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.ijmachtools.2014.01.003","article-title":"A general approach for error modeling of machine tools","volume":"79","author":"Tian","year":"2014","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1319","DOI":"10.1007\/s00170-017-0590-9","article-title":"Error modeling for sensitivity analysis and calibration of the tri-pyramid parallel robot","volume":"93","author":"Lee","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.rcim.2004.07.018","article-title":"Kinematic analysis and error modeling of TAU parallel robot","volume":"21","author":"Cui","year":"2005","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.rcim.2019.05.016","article-title":"Kinematic calibration of a 5-DOF hybrid kinematic machine tool by considering the ill-posed identification problem using regularisation method","volume":"60","author":"Tian","year":"2019","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.rcim.2016.02.008","article-title":"Kinematic calibration of a 3-DoF rotational parallel manipulator using laser tracker","volume":"41","author":"Sun","year":"2016","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1017\/S0263574798000538","article-title":"Kinematic calibration of the parallel Delta robot","volume":"16","author":"Vischer","year":"1998","journal-title":"Robotica"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.ijmachtools.2010.11.009","article-title":"Kinematical calibration of a hybrid machine tool with regularization method","volume":"51","author":"Huang","year":"2011","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2873","DOI":"10.1007\/s00170-020-06565-3","article-title":"A machining accuracy improvement approach for a horizontal machining center based on analysis of geometric error characteristics","volume":"112","author":"Niu","year":"2021","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1109\/TMRB.2023.3237924","article-title":"Safe manipulation in robotic surgery using compliant constant-force mechanism","volume":"5","author":"Sun","year":"2023","journal-title":"IEEE Trans. Med. Robot. Bionics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2375","DOI":"10.1007\/s12541-020-00421-w","article-title":"Kinematic chain optimization design based on deformation sensitivity analysis of a five-axis machine tool","volume":"21","author":"Zhang","year":"2020","journal-title":"Int. J. Precis. Eng. Manuf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s00170-019-04030-4","article-title":"Geometric accuracy enhancement of five-axis machine tool based on error analysis","volume":"105","author":"Guo","year":"2019","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0007-8506(07)60827-0","article-title":"Volumetric error analysis of a Stewart platform-based machine tool","volume":"46","author":"Patel","year":"1997","journal-title":"CIRP Ann."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1561","DOI":"10.1016\/S0890-6955(03)00202-5","article-title":"Sensitivity analysis of the 3-PRS parallel kinematic spindle platform of a serial-parallel machine tool","volume":"43","author":"Fan","year":"2003","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"104532","DOI":"10.1016\/j.mechmachtheory.2021.104532","article-title":"A minimal-error-model based two-step kinematic calibration methodology for redundantly actuated parallel manipulators: An application to a 3-DOF spindle head","volume":"167","author":"Jiang","year":"2022","journal-title":"Mech. Mach. Theory"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Du, X., Wang, B., and Zheng, J. (2022). Geometric Error Analysis of a 2UPR-RPU Over-Constrained Parallel Manipulator. Machines, 10.","DOI":"10.3390\/machines10110990"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2525","DOI":"10.1007\/s00170-013-4874-4","article-title":"Volumetric error modeling and sensitivity analysis for designing a five-axis ultra-precision machine tool","volume":"68","author":"Chen","year":"2013","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s00170-014-6133-8","article-title":"An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis","volume":"75","author":"Cheng","year":"2014","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3369","DOI":"10.1007\/s00170-016-9609-x","article-title":"Key geometric error extraction of machine tool based on extended Fourier amplitude sensitivity test method","volume":"90","author":"Cheng","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1729881417715012","DOI":"10.1177\/1729881417715012","article-title":"Error modeling and sensitivity analysis of a 3-P (Pa) S parallel type spindle head with parallelogram structure","volume":"14","author":"Li","year":"2017","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_37","unstructured":"Bonev, I.A. (2002). Geometric Analysis of Parallel Mechanisms, Universit\u00e9 Laval."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1016\/j.rcim.2011.10.003","article-title":"A 3-DOF parallel manufacturing module and its kinematic optimization","volume":"28","author":"Xie","year":"2012","journal-title":"Robot. Comput.-Integr. Manuf."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3229","DOI":"10.1007\/s00170-017-0755-6","article-title":"Investigation of sensitivity analysis and compensation parameter optimization of geometric error for five-axis machine tool","volume":"93","author":"Guo","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2037","DOI":"10.1007\/s00170-015-7492-5","article-title":"Geometric error modeling and sensitivity analysis of a five-axis machine tool","volume":"82","author":"Li","year":"2016","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1166\/jctn.2013.2845","article-title":"Analysis of volumetric error of machine tool based on Monte Carlo method","volume":"10","author":"Liang","year":"2013","journal-title":"J. Comput. Theor. Nanosci."}],"container-title":["Robotics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2218-6581\/12\/5\/129\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:49:02Z","timestamp":1760129342000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2218-6581\/12\/5\/129"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,11]]},"references-count":41,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["robotics12050129"],"URL":"https:\/\/doi.org\/10.3390\/robotics12050129","relation":{},"ISSN":["2218-6581"],"issn-type":[{"type":"electronic","value":"2218-6581"}],"subject":[],"published":{"date-parts":[[2023,9,11]]}}}