{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T23:11:58Z","timestamp":1762297918023,"version":"3.40.4"},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2012,11,19]],"date-time":"2012-11-19T00:00:00Z","timestamp":1353283200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[2013,7]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>This work presents a methodology using image analysis to estimate the experimental stiffness of a parallel robot, Parallix LKF-2040, a 3-degree-of-freedom manipulator. The proposed methodology has a simple implementation and can be applied to different architectures of parallel robots. This methodology uses image analysis and camera calibration techniques to estimate compliant displacements of mobile platform produced by several loads at the end effector level, and calculate stiffness in a specific position of mobile platform. Experimental results are presented for different positions within the workspace.<\/jats:p>","DOI":"10.1017\/s0263574712000641","type":"journal-article","created":{"date-parts":[[2012,11,19]],"date-time":"2012-11-19T10:25:42Z","timestamp":1353320742000},"page":"657-667","source":"Crossref","is-referenced-by-count":6,"title":["Stiffness estimation of a parallel manipulator using image analysis and camera calibration techniques"],"prefix":"10.1017","volume":"31","author":[{"given":"Abraham","family":"Gonzalez-Hernandez","sequence":"first","affiliation":[]},{"given":"Eduardo","family":"Castillo-Castaneda","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2012,11,19]]},"reference":[{"key":"S0263574712000641_ref21","doi-asserted-by":"crossref","unstructured":"Z. Zhang , \u201cA flexible new technique for camera calibration,\u201d IEEE Trans. Pattern Anal. Mach. Intell. 22 (11), 1330\u20131334 (2000).","DOI":"10.1109\/34.888718"},{"key":"S0263574712000641_ref20","unstructured":"International Organization for Standardization, \u201cISO 5725-1:1994. Accuracy (Trueness and Precision) of Measurement Methods and Results \u2013 Part 1: General Principles and Definitions,\u201d (ISO, Geneva, Switzerland, 1994)."},{"key":"S0263574712000641_ref19","unstructured":"J. Y. Bouguet , \u201cCamera calibration toolbox for Matlab,\u201d Available at: http:\/\/www.vision.caltech.edu\/bouguetj\/calib_doc\/ (2010). (Accessed 26 October 2012)."},{"key":"S0263574712000641_ref16","unstructured":"A. Pashkevich , D. Chablat and P. Wenger , \u201cStiffness analysis of overconstrained parallel manipulators,\u201d Mech. Mach. Theory 44, 966\u2013982 (2009)."},{"key":"S0263574712000641_ref15","unstructured":"R. S. Goncalves and J. C. Mendes Carvalho , \u201cStiffness Analysis of Parallel Manipulator Using Matrix Structural Analysis,\u201d In: Proceedings of the Second European Conference on Mechanism Science (EUCOMES 08) (2008) pp. 255\u2013262."},{"key":"S0263574712000641_ref14","unstructured":"F. Majou et al., \u201cParametric stiffness analysis of the Orthoglide,\u201d Mech. Mach. Theory 42, 296\u2013311 (2007)."},{"key":"S0263574712000641_ref13","unstructured":"D. Deblaise , X. Hernot and P. Maurine , \u201cA systematic analytical method of PKM stiffness matrix calculation,\u201d Proceedings of the 2006 IEEE International Conference on Robotics and Automation, Orlando, Florida, USA (2006)."},{"key":"S0263574712000641_ref12","unstructured":"C. Corradini , J. C. Fauroux , S. Krut and O. Company , \u201cEvaluation of a 4 Degree of Freedom Parallel Manipulator Stiffness,\u201d Proceedings of the 11th World Congress in Mechanism and Machine Science, Tianjin, China (2004)."},{"key":"S0263574712000641_ref11","unstructured":"O. Company , F. Pierrot and J. C. Fauroux , \u201cA Method for Modeling Analytical Stiffness of a Lower Mobility Parallel Manipulator,\u201d Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005)."},{"key":"S0263574712000641_ref10","unstructured":"M. Ceccarelli and G. Carbone , \u201cNumerical and Experimental Analysis of the Stiffness Performances of Parallel Manipulators,\u201d Proceedings of the 2nd International Colloquium \u201cCollaborative Research Centre 562,\u201d Braunschweig, Germany (2005)."},{"key":"S0263574712000641_ref9","unstructured":"W. K. Yoon , T. Suehiro , Y. Tsumaki and M. Uchiyama , \u201cStiffness analysis and design of a compact modified delta parallel mechanism,\u201d Robotica 22, 463\u2013475 (2004)."},{"key":"S0263574712000641_ref6","unstructured":"T. Huang , X. Zhao and D. J. Whitehouse , \u201cStiffness estimation of a tripod-based parallel kinematic machine,\u201d IEEE Trans. Robot Automat. 18, 50\u201358 (2002)."},{"key":"S0263574712000641_ref5","unstructured":"E. Rebeck and G. Zhang , \u201cA method for evaluating the stiffness of a Hexapod machine tool support structure,\u201d Int. J. Flexible Autom. Integr. Manuf. 7, 149\u2013165 (1999)."},{"key":"S0263574712000641_ref4","unstructured":"C. M. Clinton and Y G. Zhang , \u201cStiffness modeling of a Stewart platform-based milling machine,\u201d Trans. North Am. Manuf. Res. Inst. SME, 25, 335\u2013340 (1997)."},{"key":"S0263574712000641_ref1","unstructured":"E. Castillo , \u201cDevelopment of parallel robots for teaching Mechatronics and Robotics\u201d, Final report, project sponsored by ICTY-DF, Mexico (2008)."},{"key":"S0263574712000641_ref3","doi-asserted-by":"publisher","DOI":"10.1109\/70.56657"},{"key":"S0263574712000641_ref8","unstructured":"G. Carbone , M. Ceccarelli and M. Teolis , \u201cA Numerical Evaluation of the Stiffness of CaHyMan (Cassino Hybrid Manipulator),\u201d In: Proceedings of 2nd Workshop on Computational Kinematics (CK 2001), Seoul (2001) pp. 145\u2013154."},{"key":"S0263574712000641_ref17","unstructured":"J. Najera , J. Aginaga and I. Zabalza , \u201cAn\u00e1lisis de Rigidez de Manipuladores Paralelos Basado en el An\u00e1lisis de Sensibilidad. Aplicacion al 6-RUS,\u201d Proceedings of the 9 Congreso Iberoamericano de Ingenier\u00eda Mec\u00e1nica, Las Palmas de Gran Canaria, Spain (2009)."},{"key":"S0263574712000641_ref2","unstructured":"L.-W. Tsai , Robot Analysis: The Mechanics of Serial and Parallel Manipulators (Jonh Wiley, 1999)."},{"key":"S0263574712000641_ref7","unstructured":"M. Ceccarelli and G. Carbone , \u201cA stiffness analysis for CaPaMan (Cassino Parallel Manipulator),\u201d Mech. Mach. Theory 37, 427\u2013439 (2002)."},{"key":"S0263574712000641_ref18","unstructured":"J. Lang , D. K. Pai and R. J. Woodham , \u201cRobotic acquisition of deformable models,\u201d IEEE Int. Conf. Robot. Autom. 1, 933\u2013938 (2002)."},{"key":"S0263574712000641_ref22","doi-asserted-by":"crossref","unstructured":"J. Heikkila and O. Silven , \u201cA Four-Step Camera Calibration Procedure with Implicit Image Correction,\u201d In: Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Jun. 17\u201319, 1997) pp. 1106\u20131112.","DOI":"10.1109\/CVPR.1997.609468"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574712000641","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,21]],"date-time":"2025-04-21T03:54:01Z","timestamp":1745207641000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574712000641\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,19]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["S0263574712000641"],"URL":"https:\/\/doi.org\/10.1017\/s0263574712000641","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"type":"print","value":"0263-5747"},{"type":"electronic","value":"1469-8668"}],"subject":[],"published":{"date-parts":[[2012,11,19]]}}}