{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,9]],"date-time":"2025-02-09T05:06:08Z","timestamp":1739077568574,"version":"3.37.0"},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,3,9]],"date-time":"2009-03-09T00:00:00Z","timestamp":1236556800000},"content-version":"unspecified","delay-in-days":7007,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[1990,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>Velocity similarity principle V(\u03b8.,<jats:italic>\u1e61<\/jats:italic>, u<jats:sub><jats:italic>b<\/jats:italic><\/jats:sub>, Q<jats:sub><jats:italic>b<\/jats:italic><\/jats:sub>) = D<jats:sub><jats:italic>ab<\/jats:italic><\/jats:sub>V (\u03b8.,<jats:italic>\u1e61<\/jats:italic>, u<jats:sub><jats:italic>a<\/jats:italic><\/jats:sub>, Q<jats:sub><jats:italic>a<\/jats:italic><\/jats:sub>)D<jats:sub><jats:italic>ab<\/jats:italic><\/jats:sub><jats:sup>\u20131<\/jats:sup>is presented and used to derive several useful forms of the Jacobian matrix for the manipulator from its basic kinematic equations in 4 X 4 matrix form. The zero reference position representation is used and, therefore, the base system is the only coordinate system utilized in the derivations. For manipulators with a spherical wrist, a modified form of the Jacobian is presented in which the Jacobian columns corresponding to the regional structure are completely decoupled from those corresponding to the wrist structure.<\/jats:p>","DOI":"10.1017\/s0263574700007359","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T13:20:09Z","timestamp":1236691209000},"page":"81-84","source":"Crossref","is-referenced-by-count":5,"title":["Formulation of manipulator Jacobian using the velocity similarity principle"],"prefix":"10.1017","volume":"8","author":[{"given":"K. C.","family":"Gupta","sequence":"first","affiliation":[]},{"given":"R.","family":"Ma","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"key":"S0263574700007359_ref014","unstructured":"14. Ma R. \u201cKinematics of Robots with Oblique Bevel \u2013 Geared Wrists\u201d MS Thesis (University of Illinois at Chicago, Chicago, 1988)."},{"key":"S0263574700007359_ref013","doi-asserted-by":"publisher","DOI":"10.1177\/027836498600500202"},{"key":"S0263574700007359_ref011","first-page":"42","article-title":"Robot Kinematics \u2013 A Compact Analytic Inverse Solution for Velocities","volume":"109","author":"Hunt","year":"1987","journal-title":"ASME J. Mechanisms"},{"volume-title":"Robotics \u2013 Basic Analysis and Design","year":"1987","author":"Wolovich","key":"S0263574700007359_ref009"},{"key":"S0263574700007359_ref008","doi-asserted-by":"publisher","DOI":"10.1177\/027836498300200203"},{"key":"S0263574700007359_ref002","doi-asserted-by":"crossref","unstructured":"2. Whitney D. \u201cThe Mathematics of Coordinated Control of Prosthetic Arms and Manipulators\u201d ASME J. Dynamic Systems, Measurement, and Control 303\u2013309 (1972).","DOI":"10.1115\/1.3426611"},{"key":"S0263574700007359_ref001","unstructured":"1. Pieper D.L. , \u201cThe Kinematics of Manipulators under Computer Control Doctoral Dissertation. (Stanford University, Stanford, 1968)."},{"key":"S0263574700007359_ref005","first-page":"237","article-title":"Discussion for \u201cA Study of the Jacobian Matrix of Serial Manipulators","volume":"107","author":"Gupta","year":"1985","journal-title":"ASME J. Mechanisms"},{"volume-title":"Robot Manipulators","year":"1981","author":"Paul","key":"S0263574700007359_ref003"},{"key":"S0263574700007359_ref004","first-page":"230","article-title":"A Study of the Jacobian Matrix of Serial Manipulators","volume":"107","author":"Waldron","year":"1985","journal-title":"ASME J. Mechanisms"},{"key":"S0263574700007359_ref007","doi-asserted-by":"publisher","DOI":"10.1177\/027836498600500206"},{"key":"S0263574700007359_ref010","unstructured":"10. Pieper D.L. and Roth B. , \u201cThe Kinematics of Manipulators under Computer Control\u201d Proc. 2nd IFToMM Intl. Cong. Theory of Machines and Mechanisms Warsaw, 2 159\u2013168 (1969)."},{"key":"S0263574700007359_ref006","doi-asserted-by":"crossref","unstructured":"6. Gupta K.C. and Kazerounian S.M.K. , \u201cImproved Numerical Solutions of Inverse Kinematics of Robots\u201d Proc. IEEE Int. Conf. Robotics and Automation St. Louis, 743\u2013748 (1985).","DOI":"10.1109\/ROBOT.1985.1087237"},{"key":"#cr-split#-S0263574700007359_ref012.1","unstructured":"12. Gupta K.C. , \"A Note on Position Analysis of Manipulators\" Proc. 7th Applied Mechanisms Conf. Kansas City, 3.1-3.3 (1981)"},{"key":"#cr-split#-S0263574700007359_ref012.2","unstructured":"also Mechanism and Machine Theory, 195-8 (1984)."}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574700007359","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T04:56:45Z","timestamp":1738990605000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574700007359\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1990,1]]}},"alternative-id":["S0263574700007359"],"URL":"https:\/\/doi.org\/10.1017\/s0263574700007359","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"type":"print","value":"0263-5747"},{"type":"electronic","value":"1469-8668"}],"subject":[],"published":{"date-parts":[[1990,1]]}}}