{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T19:18:12Z","timestamp":1648581492440},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2005,6,14]],"date-time":"2005-06-14T00:00:00Z","timestamp":1118707200000},"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":[[2005,7]]},"abstract":"<jats:p>The determination of the assembly modes of the parallel structures with three legs of type PS or SP (P and S stand for prismatic pair and spherical pair, respectively) consists of solving the direct position analysis of all the three-legged parallel manipulators which have, in each leg, one not actuated prismatic pair, one not actuated spherical pair and one or two one-dof actuated pairs of any type, placed along the leg in any order. There are two types of such structures: (i) 3PS structures and (ii) SP-2PS structures. The procedure to determine the assembly modes of the SP-2PS structures has not been presented yet, in the literature. This paper presents the analytic form determination of the assembly modes of the SP-2PS structures. In particular, the closure equations of a generic SP-2PS structure will be written and their solution will be reduced to the solution of an eight-degree univariate polynomial equation with real coefficients. Finally, the proposed algorithm will be applied to a real case. The result of this study is that the assembly modes of any SP-2PS structure are at most eight, and the end-effector poses, which solve the direct position analysis of the parallel manipulators that generate those structures, are also eight.<\/jats:p>","DOI":"10.1017\/s0263574704001109","type":"journal-article","created":{"date-parts":[[2005,6,14]],"date-time":"2005-06-14T06:22:22Z","timestamp":1118730142000},"page":"521-526","source":"Crossref","is-referenced-by-count":2,"title":["Direct position analysis of parallel manipulators which generate SP-2PS structures"],"prefix":"10.1017","volume":"23","author":[{"given":"Raffaele","family":"Di Gregorio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2005,6,14]]},"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574704001109","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,4]],"date-time":"2019-04-04T16:28:27Z","timestamp":1554395307000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574704001109\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6,14]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,7]]}},"alternative-id":["S0263574704001109"],"URL":"https:\/\/doi.org\/10.1017\/s0263574704001109","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6,14]]}}}