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Then, a wrench graph is obtained in order to represent some points at infinity on the Pl\u00fccker lines of the Jacobian matrix. Using Grassmann\u2013Cayley algebra, the rank deficiency of the Jacobian matrix amounts to the vanishing condition of the superbracket. Accordingly, the parallel singularities are expressed in three different forms involving superbrackets, meet and join operators, and vector cross and dot products, respectively. The approach is explained through the singularity analysis of the <jats:italic>H<\/jats:italic>4 robot. All the parallel singularity conditions of this robot are enumerated and the motions associated with these singularities are characterized.<\/jats:p>","DOI":"10.1017\/s0263574711001330","type":"journal-article","created":{"date-parts":[[2012,1,12]],"date-time":"2012-01-12T10:49:53Z","timestamp":1326365393000},"page":"1109-1118","source":"Crossref","is-referenced-by-count":14,"title":["Singularity analysis of the H4 robot using Grassmann\u2013Cayley algebra"],"prefix":"10.1017","volume":"30","author":[{"given":"Semaan","family":"Amine","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"St\u00e9phane","family":"Caro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philippe","family":"Wenger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Kanaan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2012,1,12]]},"reference":[{"key":"S0263574711001330_ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2009.2017132"},{"key":"S0263574711001330_ref4","first-page":"1179","volume-title":"Proceedings of the IEEE International Conference on Robotics and Automation","author":"Li","year":"2003"},{"key":"S0263574711001330_ref9","volume-title":"Kinematic Geometry of Mechanisms","author":"Hunt","year":"1978"},{"key":"S0263574711001330_ref30","unstructured":"S. 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