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Second, a complicated derivation of the DTG and an identification of an isomorphic DTG are transformed into a simple derivation of an array and an identification of an isomorphic array using a compiled program. Third, one or more spatial closed-loop chains in the derived DTGs are changed into the planar closed-loop chains by modifying digits marked in closed-loop chains, and the DTGs are transformed into the r-DTGs for the type synthesis of the spatial 3-DoF PMs with planar sub-chains. Finally, the 52 novel spatial 3-DoF PMs with the planar sub-chains are synthesized and verified by simulation mechanisms.<\/jats:p>","DOI":"10.1017\/s0263574715000557","type":"journal-article","created":{"date-parts":[[2015,7,10]],"date-time":"2015-07-10T07:55:42Z","timestamp":1436514942000},"page":"370-383","source":"Crossref","is-referenced-by-count":7,"title":["Type synthesis of spatial 3-DoF parallel mechanisms with planar sub-chains using revised digital topological graphs and arrays"],"prefix":"10.1017","volume":"35","author":[{"given":"Yi","family":"Lu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nijia","family":"Ye","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling","family":"Ding","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2015,7,10]]},"reference":[{"key":"S0263574715000557_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-4201-7"},{"key":"S0263574715000557_ref11","doi-asserted-by":"publisher","DOI":"10.1115\/1.1637662"},{"key":"S0263574715000557_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2012.07.008"},{"key":"S0263574715000557_ref12","article-title":"Analysis of kinematics and statics for a novel 6-DoF parallel mechanism with three planar mechanism limbs","author":"Lu","year":"2014","journal-title":"Robotica"},{"key":"S0263574715000557_ref22","doi-asserted-by":"publisher","DOI":"10.1115\/1.2829891"},{"key":"S0263574715000557_ref6","unstructured":"R. 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