{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T18:55:11Z","timestamp":1754160911853,"version":"3.41.2"},"reference-count":41,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T00:00:00Z","timestamp":1740009600000},"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":[[2025,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A more intuitive appreciation of spatial compliant behavior can be obtained through analysis and description of the behavior in terms of its <jats:italic>centers<\/jats:italic>, specifically the center of stiffness, the center of compliance, and the center of elasticity. This paper investigates the properties of each of these centers. Necessary and sufficient conditions for the coincidence of these centers are identified. A physical appreciation of those compliant behaviors that have coincident centers is obtained in terms of restrictions on the geometry of topologically simple mechanisms that realize those behaviors. The results can be used in the design of compliant mechanisms for robotic manipulation, especially when the compliance is characterized by the location of its center.<\/jats:p>","DOI":"10.1017\/s0263574725000190","type":"journal-article","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T03:02:56Z","timestamp":1740020576000},"page":"1171-1197","source":"Crossref","is-referenced-by-count":0,"title":["Unification of mathematical descriptions of compliant behavior centers with physical realizations of those behaviors"],"prefix":"10.1017","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6130-4433","authenticated-orcid":false,"given":"Shuguang","family":"Huang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-4286-6554","authenticated-orcid":false,"given":"Joseph M.","family":"Schimmels","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,2,20]]},"reference":[{"key":"S0263574725000190_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574722001448"},{"key":"S0263574725000190_ref29","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574798000058"},{"key":"S0263574725000190_ref8","doi-asserted-by":"publisher","DOI":"10.1115\/1.2919228"},{"key":"S0263574725000190_ref24","doi-asserted-by":"publisher","DOI":"10.1115\/1.1434273"},{"key":"S0263574725000190_ref30","doi-asserted-by":"publisher","DOI":"10.1002\/rob.10096"},{"key":"S0263574725000190_ref16","doi-asserted-by":"publisher","DOI":"10.1115\/1.4037019"},{"key":"S0263574725000190_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574715000363"},{"key":"S0263574725000190_ref13","doi-asserted-by":"publisher","DOI":"10.1115\/1.3211024"},{"key":"S0263574725000190_ref10","doi-asserted-by":"publisher","DOI":"10.1115\/1.2802402"},{"key":"S0263574725000190_ref31","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2018.12.021"},{"key":"S0263574725000190_ref38","unstructured":"[38] Ciblak, N. , Analysis of Cartesian Stiffness and Compliance with Applications Ph.D thesis (Georgia Institute of Technology, Atlanta, GA, USA, 1998."},{"key":"S0263574725000190_ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2021.104565"},{"key":"S0263574725000190_ref21","doi-asserted-by":"publisher","DOI":"10.1109\/70.795799"},{"key":"S0263574725000190_ref37","doi-asserted-by":"publisher","DOI":"10.1115\/DETC1992-0214"},{"key":"S0263574725000190_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0094-114X(97)00040-2"},{"key":"S0263574725000190_ref41","doi-asserted-by":"publisher","DOI":"10.1109\/70.88036"},{"key":"S0263574725000190_ref25","doi-asserted-by":"publisher","DOI":"10.1115\/1.2829309"},{"key":"S0263574725000190_ref34","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574710000743"},{"key":"S0263574725000190_ref2","first-page":"305","volume-title":"Robot Motion: Planning and Control","author":"Mason","year":"1983"},{"key":"S0263574725000190_ref20","doi-asserted-by":"publisher","DOI":"10.1109\/70.833197"},{"key":"S0263574725000190_ref1","doi-asserted-by":"publisher","DOI":"10.1115\/1.3149634"},{"key":"S0263574725000190_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2021.104636"},{"key":"S0263574725000190_ref3","doi-asserted-by":"publisher","DOI":"10.1109\/JRA.1987.1087148"},{"key":"S0263574725000190_ref9","doi-asserted-by":"publisher","DOI":"10.1115\/1.2919229"},{"key":"S0263574725000190_ref36","doi-asserted-by":"publisher","DOI":"10.1109\/LRA.2022.3214052"},{"volume-title":"The Screw Calculus and its Applications in Mechanics","year":"1965","author":"Dimentberg","key":"S0263574725000190_ref6"},{"key":"S0263574725000190_ref12","doi-asserted-by":"publisher","DOI":"10.1177\/02783640022067201"},{"key":"S0263574725000190_ref35","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574714000575"},{"key":"S0263574725000190_ref22","unstructured":"[22] Ciblak, N. and Lipkin, H. . \u201cSynthesis of Cartesian Stiffness for Robotic Applications.\u201d In: Proceedings of the IEEE International Conference on Robotics and Automation, Detroit, MI, USA (May 1999)."},{"key":"S0263574725000190_ref28","unstructured":"[28] Whitney, D. E. and Nevins, J. L. . \u201cWhat is the Remote Center Compliance (RCC) and What Can it Do.\u201d In: Proceeding of the 9th International Symposium and Exposition on Industrial Robots, Washington, DC, USA (March 1979) pp. 135\u2013152."},{"key":"S0263574725000190_ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574724000675"},{"key":"S0263574725000190_ref39","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-9961-0_16"},{"key":"S0263574725000190_ref32","doi-asserted-by":"publisher","DOI":"10.1002\/rob.1011"},{"key":"S0263574725000190_ref4","unstructured":"[4] Ciblak, N. and Lipkin, H. . \u201cCenters of Stiffness, Compliance and Elasticity in the Modelling of Robotic Systems.\u201d In: Proceedings of the ASME Design Technical Conference, Minneapolis, MN, USA (September 1994) pp. 185\u2013195."},{"key":"S0263574725000190_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574709990403"},{"key":"S0263574725000190_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(93)90088-D"},{"key":"S0263574725000190_ref26","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2018.2805315"},{"volume-title":"A Treatise on the Theory of Screws","year":"1900","author":"Ball","key":"S0263574725000190_ref5"},{"key":"S0263574725000190_ref23","first-page":"264","article-title":"Spatial stiffness realization with parallel springs using geometric parameters","volume":"18","author":"Choi","year":"2002","journal-title":"IEEE Trans. Robot. Autom."},{"key":"S0263574725000190_ref40","doi-asserted-by":"publisher","DOI":"10.1109\/70.843170"},{"key":"S0263574725000190_ref19","doi-asserted-by":"publisher","DOI":"10.1109\/70.678455"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574725000190","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T07:50:58Z","timestamp":1753689058000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574725000190\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,20]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,3]]}},"alternative-id":["S0263574725000190"],"URL":"https:\/\/doi.org\/10.1017\/s0263574725000190","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"type":"print","value":"0263-5747"},{"type":"electronic","value":"1469-8668"}],"subject":[],"published":{"date-parts":[[2025,2,20]]}}}