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In number synthesis, kinematic chains are represented by graphs, and thus the symmetry of a kinematic chain is the same as the symmetry of its graph. We present a formal definition of symmetry in kinematic chains based on the automorphism group of its associated graph. The symmetry group of the graph is associated with the graph symmetry. By using the group structure induced by the symmetry of the kinematic chain, we prove that degrees-of-control, connectivity and redundancy are invariants by the action of the automorphism group of the graph. Consequently, it is shown that it is possible to reduce the size of these matrices and thus reduce the complexity of the kinematic analysis of mechanisms and parallel manipulators in early stages of mechanisms design.<\/jats:p>","DOI":"10.1017\/s0263574712000057","type":"journal-article","created":{"date-parts":[[2012,3,22]],"date-time":"2012-03-22T20:57:16Z","timestamp":1332449836000},"page":"61-70","source":"Crossref","is-referenced-by-count":10,"title":["Symmetry and invariants of kinematic chains and parallel manipulators"],"prefix":"10.1017","volume":"31","author":[{"given":"Roberto","family":"Simoni","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Celso Melchiades","family":"Doria","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":[[2012,3,21]]},"reference":[{"key":"S0263574712000057_ref49","doi-asserted-by":"publisher","DOI":"10.1177\/027836499801700907"},{"key":"S0263574712000057_ref46","doi-asserted-by":"publisher","DOI":"10.1007\/s10601-008-9044-1"},{"key":"S0263574712000057_ref41","unstructured":"SAGE. 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