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A very useful simplification for kinematic chain, mechanism and manipulator enumeration is their representation through graphs. The method is based on group theory where abstract structures are used to capture the internal symmetry of a structure in the form of automorphisms of a group. The concept used is orbits of the group of automorphisms of a colored vertex graph. The theory and some examples are presented to illustrate the method.<\/jats:p>","DOI":"10.1017\/s0263574708004979","type":"journal-article","created":{"date-parts":[[2008,8,11]],"date-time":"2008-08-11T09:54:08Z","timestamp":1218448448000},"page":"589-597","source":"Crossref","is-referenced-by-count":9,"title":["Enumeration of parallel manipulators"],"prefix":"10.1017","volume":"27","author":[{"given":"Roberto","family":"Simoni","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea Piga","family":"Carboni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Martins","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,7,1]]},"reference":[{"key":"S0263574708004979_ref22","volume-title":"Proceedings of the 15th Jornadas de J\u00f3venes Investigadores da Asociaci\u00f3n de Universidades Grupo Montevideo","author":"Simoni","year":"2007"},{"key":"S0263574708004979_ref8","doi-asserted-by":"publisher","DOI":"10.1115\/1.3259028"},{"key":"S0263574708004979_ref6","article-title":"Variety and connectivity in kinematic chains","author":"Martins","journal-title":"Mech. 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Simoni R. and Martins D. , \u201cCriteria for Structural Synthesis and Classification of Mechanism,\u201d Proceedings of the 19th International Congress of Mechanical Engineering \u2013 COBEM, Bras\u00edlia - DF (2007)."}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574708004979","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,5]],"date-time":"2019-04-05T19:32:55Z","timestamp":1554492775000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574708004979\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["S0263574708004979"],"URL":"https:\/\/doi.org\/10.1017\/s0263574708004979","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,7]]}}}