{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T03:06:17Z","timestamp":1648868777299},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[1997,7,1]],"date-time":"1997-07-01T00:00:00Z","timestamp":867715200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[1997,7]]},"abstract":"A method to determine the two parameter set of circular cylinders, whose\nsurfaces contain three given points, is presented in the context of an efficient\nalgorithm, based on the set of two parameter projections of the points onto\nplanar sections, to compute radius and a point where the axes intersect the\nplane of the given points. The geometry of the surface of points, whose position\nvectors represent cylinder radius, r<\/jats:italic>, and axial orientation, is\nrevealed and described in terms of symmetry and singularity inherent in the\ntriangle with vertices on the given points. This strongly suggests that, given\none constraint on the axial orientation of the cylinder, there are up to six\ncylinders of identical radius on the three given points. A bivariate function,\nin two of the three line direction Pl\u00fccker coordinates, is derived to prove\nthis. By specifying r<\/jats:italic> and an axis direction, say, perpendicular to a\ngiven direction, one obtains a sixth order univariate polynomial in one of the\nline coordinates which yields six axis directions. These ideas are needed in the\ndesign of parallel manipulators<\/jats:p>","DOI":"10.1017\/s026357479700043x","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T09:36:08Z","timestamp":1027762568000},"page":"355-360","source":"Crossref","is-referenced-by-count":0,"title":["Congruence of circular\ncylinders on three given points"],"prefix":"10.1017","volume":"15","author":[{"given":"P. J.","family":"Zsombor-Murray","sequence":"first","affiliation":[]},{"given":"P.","family":"Gervasi","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[1997,7,1]]},"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S026357479700043X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,11]],"date-time":"2019-05-11T16:38:09Z","timestamp":1557592689000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S026357479700043X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,7]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1997,7]]}},"alternative-id":["S026357479700043X"],"URL":"https:\/\/doi.org\/10.1017\/s026357479700043x","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"value":"0263-5747","type":"print"},{"value":"1469-8668","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,7]]}}}