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Solutions are described for arbitrary main\u2010arm layouts and for all possible cases of redundant (nine, eight, and seven sensors) and non\u2010redundant (six sensors) sensing of branch main\u2010arm joint displacements. It is demonstrated that closed\u2010form forward displacement solutions can be found for all cases of redundant sensing. Furthermore, it is shown that a closed\u2010form solution can be obtained for one of the two possible cases of non\u2010redundant sensing of the main\u2010arm joint displacements. The only case of joint displacement sensing not allowing a closed\u2010form forward displacement solution is two joints sensed per branch, a case that can be expressed as a 16th\u2010order polynomial of a single variable. Due to the importance of having efficient and failure\u2010safe solutions for the forward displacement problem, it is suggested that appropriate redundancy in displacement sensing should be an important consideration in the design of parallel manipulation devices. \u00a9 1994 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/rob.4620110603","type":"journal-article","created":{"date-parts":[[2007,7,6]],"date-time":"2007-07-06T15:18:04Z","timestamp":1183735084000},"page":"471-485","source":"Crossref","is-referenced-by-count":21,"title":["Complete forward displacement solutions for a class of three\u2010branch parallel manipulators"],"prefix":"10.1002","volume":"11","author":[{"given":"Leila Notash","family":"And","sequence":"first","affiliation":[]},{"given":"Ron P.","family":"Podhorodeski","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,27]]},"reference":[{"volume-title":"Kinematic Geometry of Mechanisms","year":"1978","author":"Hunt K. 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