{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T10:07:08Z","timestamp":1777716428463,"version":"3.51.4"},"reference-count":29,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[1989,10,1]],"date-time":"1989-10-01T00:00:00Z","timestamp":623203200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[1989,10]]},"abstract":"<jats:p>This paper sets forth an approach to robotic kinematics that brings together the use of matrix exponentiation and dual numbers. Working from first principles, it is shown that a screw displacement can be represented by the exponential of a dual skew-symmetric matrix; a product of two such matri ces will suffice to specify the relationship between a pair of link coordinate frames. An example problem, dealing with the kinematics of the Rhino XR-2, illustrates how the approach immediately identifies those groups of joint variables that tend to cluster together.<\/jats:p>","DOI":"10.1177\/027836498900800505","type":"journal-article","created":{"date-parts":[[2007,3,4]],"date-time":"2007-03-04T20:24:06Z","timestamp":1173039846000},"page":"57-66","source":"Crossref","is-referenced-by-count":28,"title":["On the Use of Dual- Matrix Exponentials in Robotic Kinematics"],"prefix":"10.1177","volume":"8","author":[{"given":"A.K.","family":"Pradeep","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering University of California Berkeley, California 94720"}]},{"given":"Paul J.","family":"Yoder","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Industrial Engineering Clarkson University Potsdam, New York 13676"}]},{"given":"Rangaswamy","family":"Mukundan","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering Clarkson University Potsdam, New York 13676"}]}],"member":"179","published-online":{"date-parts":[[1989,10,1]]},"reference":[{"key":"atypb1","volume-title":"Theoretical kinematics (see Appendix)","author":"Bottema, O.","year":"1979"},{"key":"atypb2","volume-title":"Vector and tensor analysis","author":"Brand, L.","year":"1957"},{"key":"atypb3","volume-title":"Introduction to robotics, mechanics and control","author":"Craig, J.J.","year":"1986"},{"issue":"2","key":"atypb4","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1115\/1.4011045","volume":"22","author":"Denavit, J.","year":"1955","journal-title":"ASME J. 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