{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T22:23:58Z","timestamp":1778538238837,"version":"3.51.4"},"reference-count":15,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2007,3,13]],"date-time":"2007-03-13T00:00:00Z","timestamp":1173744000000},"content-version":"vor","delay-in-days":7042,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Robotic Syst."],"published-print":{"date-parts":[[1987,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In general, the manipulator's end\u2010effector can be located in a desired position and orientation in its work\u2010space through angular and\/or linear displacements of its joints. These joint coordinates can be obtained by solving the loop\u2010closure equation of the manipulator's kinematic model. The most common method for obtaining this equation is based on the point coordinates 4\u00d74 homogeneous transformation matrix. This method uses a special set of frames which are adapted to the manipulator's configuration. Within the last few years there has been some interest in the use of screw operators (line transformations) to model the kinematic configuration of manipulators and to form the loop\u2010closure equation. In this article, a kinematic model of a general (6 DOF) manipulator is obtained through the application of a screw operator (dual\u2010unit quaternion) to represent the screw displacements of the line coordinates of the manipulator link and joint axes. The loop\u2010closure equation of the closed kinematic chain is obtained by introducing a hypothetical link\/joint at the manipulator's end\u2010effector location. The resultant non\u2010linear loop\u2010closure equation is then solved for the joint coordinates using a numerical technique. The method is illustrated with an example.<\/jats:p>","DOI":"10.1002\/rob.4620040605","type":"journal-article","created":{"date-parts":[[2007,7,6]],"date-time":"2007-07-06T06:21:00Z","timestamp":1183702860000},"page":"771-797","source":"Crossref","is-referenced-by-count":7,"title":["Formulation of the kinematic model of a general (6 DOF) robot manipulator using a screw operator"],"prefix":"10.1002","volume":"4","author":[{"given":"S.","family":"Payandeh","sequence":"first","affiliation":[]},{"given":"A. A.","family":"Goldenberg","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Robot Manipulators: Mathematics, Programming and Control","author":"Paul R. P.","year":"1981"},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1115\/1.4011045","article-title":"A Kinematic Notation for Lower\u2010pair Mechanisms Based on Matrices","volume":"22","author":"Denavit J.","year":"1955","journal-title":"ASME J. Applied Mechanics"},{"key":"e_1_2_1_4_2","first-page":"159","article-title":"The Kinematics of Manipulators Under Computer Control","volume":"2","author":"Pieper D. L.","year":"1969","journal-title":"Proceeding Hnd. Inter. Congress of the Theory of Mechanics and Mechanisms"},{"key":"e_1_2_1_5_2","volume-title":"Analysis of Mechanisms and Robot Manipulators","author":"Duffy J.","year":"1980"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498300200203"},{"key":"e_1_2_1_7_2","unstructured":"G. R.Pennock andA. T.Yang \u201cApplication of Dual\u2010Number Matrices to the Inverse Kinematics Problem of Robot Manipulators \u201d ASME 84\u2010DET\u201033 1984."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1068\/b050045"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498600500205"},{"key":"e_1_2_1_10_2","volume-title":"A Solution to the Generalized Inverse Kinematics Problem of Robot Manipulators Using Screw Axis Theory and Dual Quantities","author":"Payandeh S.","year":"1986"},{"key":"e_1_2_1_11_2","volume-title":"Vectors and Tensor Analysis","author":"Brand L.","year":"1957"},{"key":"e_1_2_1_12_2","first-page":"47","volume-title":"Interactive Kinematics Simulation of Robot Manipulators","author":"Rakhsha F.","year":"1985"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1145\/363790.363830"},{"key":"e_1_2_1_14_2","volume-title":"The Theory of Screws: A Study in the Dynamics of a Rigid Body","author":"Ball R. S.","year":"1876"},{"key":"e_1_2_1_15_2","volume-title":"Geometry and Imagination","author":"Hilbert D.","year":"1952"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3629601"}],"container-title":["Journal of Robotic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frob.4620040605","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rob.4620040605","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T22:13:20Z","timestamp":1697926400000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rob.4620040605"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,12]]},"references-count":15,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1987,12]]}},"alternative-id":["10.1002\/rob.4620040605"],"URL":"https:\/\/doi.org\/10.1002\/rob.4620040605","archive":["Portico"],"relation":{},"ISSN":["0741-2223","1097-4563"],"issn-type":[{"value":"0741-2223","type":"print"},{"value":"1097-4563","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,12]]}}}