{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T10:16:09Z","timestamp":1768644969840,"version":"3.49.0"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[1997,7,1]],"date-time":"1997-07-01T00:00:00Z","timestamp":867715200000},"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":[[1997,7]]},"abstract":"<jats:p>In this paper we present a technique for designing planar parallel\nmanipulators with platforms capable of reaching any number of desired poses. The\nmanipulator consists of a platform connected to ground by RPR chains. The set of\npositions and orientations available to the end-effector of a general RPR chain\nis mapped into the space of planar quaternions to obtain a quadratic manifold.\nThe coefficients of this <jats:italic>constraint manifold<\/jats:italic> are functions of the\nlocations of the base and platform <jats:italic>R<\/jats:italic> joints and the distance between\nthem. Evaluating the constraint manifold at each desired pose and defining the\nlimits on the extension of the <jats:italic>P<\/jats:italic> joint yields a set of equations.\nSolutions of these equations determine chains that contain the desired poses as\npart of their workspaces. Parallel manipulators that can reach the prescribed\nworkspace are assembled from these chains. An example shows the determination of\nthree RPR chains that form a manipulator able to reach a prescribed\nworkspace.<\/jats:p>","DOI":"10.1017\/s0263574797000441","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T13:36:08Z","timestamp":1027776968000},"page":"361-365","source":"Crossref","is-referenced-by-count":23,"title":["A planar quaternion\napproach to the kinematic synthesis of a parallel manipulator"],"prefix":"10.1017","volume":"15","author":[{"given":"Andrew P.","family":"Murray","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7ois","family":"Pierrot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierre","family":"Dauchez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.\nMichael","family":"McCarthy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[1997,7,1]]},"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574797000441","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T20:38:13Z","timestamp":1557607093000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574797000441\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,7]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1997,7]]}},"alternative-id":["S0263574797000441"],"URL":"https:\/\/doi.org\/10.1017\/s0263574797000441","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,7]]}}}