{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T01:10:43Z","timestamp":1782177043239,"version":"3.54.5"},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,3,9]],"date-time":"2009-03-09T00:00:00Z","timestamp":1236556800000},"content-version":"unspecified","delay-in-days":4634,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[1996,7]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>We present a method for kinematic calibration of open chain mechanisms based on the product of exponentials (POE) formula. The POE formula represents the forward kinematics of an open chain as a product of matrix exponentials, and is based on a modern geometric interpretation of classical screw theory. Unlike the kinematic representations based on the Denavit- Hartenberg (D-H) parameters, the kinematic parameters in the POE formula vary smoothly with changes in the joint axes, <jats:italic>ad hoc<\/jats:italic> methods designed to address the inherent singularities in the D-H parameters are therefore unnecessary. Another important advantage is that simple closed-form expressions can be obtained for the derivatives of the forward kinematic equations with respect to the kinematic parameters. After introducing the POE formula, we derive a least-squares kinematic calibration algorithm for general open chain mechanisms. Simulation results with a 6-axis open chain are presented.<\/jats:p>","DOI":"10.1017\/s0263574700019810","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T13:09:54Z","timestamp":1236690594000},"page":"415-421","source":"Crossref","is-referenced-by-count":180,"title":["Kinematic calibration using the product of exponentials formula"],"prefix":"10.1017","volume":"14","author":[{"given":"Koichiro","family":"Okamura","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"F.C.","family":"Park","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"key":"S0263574700019810_ref007","doi-asserted-by":"publisher","DOI":"10.1109\/9.280779"},{"key":"S0263574700019810_ref001","doi-asserted-by":"publisher","DOI":"10.1115\/1.3143737"},{"key":"S0263574700019810_ref011","volume-title":"Robot Manipulators: Mathematics, Programming and Control","author":"Paul","year":"1982"},{"key":"S0263574700019810_ref006","first-page":"120","volume-title":"Proc. Int. Symp. Math. Theory of Networks and Systems","author":"Brockett","year":"1983"},{"key":"S0263574700019810_ref012","first-page":"13","volume-title":"Proc. 3rd Int. Workshop on Advanced Motion Control","author":"Park","year":"1994"},{"key":"S0263574700019810_ref002","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.1983.269783"},{"key":"S0263574700019810_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-1999-3"},{"key":"S0263574700019810_ref004","doi-asserted-by":"publisher","DOI":"10.1109\/70.149944"},{"key":"S0263574700019810_ref005","first-page":"79","volume-title":"Proc. Int. Comput. in Eng. Conf. Exhibit","author":"Mooring","year":"1984"},{"key":"S0263574700019810_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5286-3"},{"key":"S0263574700019810_ref009","unstructured":"9. Park F.C. , \u201cThe Optimal Kinematic Design of Mechanisms\u201d, Ph.D. Thesis (Harvard University, 1991)."},{"key":"S0263574700019810_ref010","doi-asserted-by":"publisher","DOI":"10.1177\/027836498800700204"},{"key":"S0263574700019810_ref013","volume-title":"The Robotics Review I","author":"Hollerbach","year":"1989"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574700019810","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T21:09:18Z","timestamp":1557695358000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574700019810\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,7]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,7]]}},"alternative-id":["S0263574700019810"],"URL":"https:\/\/doi.org\/10.1017\/s0263574700019810","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,7]]}}}