{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T07:58:20Z","timestamp":1782547100946,"version":"3.54.5"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,2,21]],"date-time":"2017-02-21T00:00:00Z","timestamp":1487635200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2018,4]]},"DOI":"10.1007\/s10208-017-9348-x","type":"journal-article","created":{"date-parts":[[2017,2,21]],"date-time":"2017-02-21T13:03:20Z","timestamp":1487682200000},"page":"509-536","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Kempe\u2019s Universality Theorem for Rational Space Curves"],"prefix":"10.1007","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8734-4396","authenticated-orcid":false,"given":"Zijia","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5556-4001","authenticated-orcid":false,"given":"Josef","family":"Schicho","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2601-6695","authenticated-orcid":false,"given":"Hans-Peter","family":"Schr\u00f6cker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,2,21]]},"reference":[{"key":"9348_CR1","unstructured":"T.\u00a0G. Abbott, Generalizations of Kempe\u2019s Universality Theorem, Master\u2019s thesis, Massachusetts Institute of Technology, Cambridge 2008."},{"key":"9348_CR2","doi-asserted-by":"publisher","unstructured":"K.\u00a0Abdul-Sater, M.\u00a0M. Winkler, F.\u00a0Irlinger and T.\u00a0C. Lueth, Three-position synthesis of origami-evolved, spherically constrained spatial revolute\u2013revolute chains, ASME J. Mechanisms Robotics 8 (2016), no.\u00a01, doi: 10.1115\/1.4030370 .","DOI":"10.1115\/1.4030370"},{"key":"9348_CR3","volume-title":"Mechanisms for the generation of plane curves","author":"II Artobolevskii","year":"1964","unstructured":"I.\u00a0I. Artobolevskii, Mechanisms for the generation of plane curves, Pergamon Press, Oxford, 1964."},{"key":"9348_CR4","unstructured":"J.\u00a0E. Baker, On the motion geometry of the Bennett linkage, In Proceedings of the 8th International Conference on Engineering Computer Graphics and Descriptive Geometry, Austin, 1998, 433\u2013437."},{"key":"9348_CR5","first-page":"777","volume":"76","author":"GT Bennett","year":"1903","unstructured":"G.\u00a0T. Bennett, A new mechanism, Engineering 76 (1903), 777\u2013778.","journal-title":"Engineering"},{"key":"9348_CR6","doi-asserted-by":"crossref","unstructured":"G.\u00a0T. Bennett, The skew isogramm-mechanism, Proc. London Math. Soc. s2\u201313 (1914), 151\u2013173.","DOI":"10.1112\/plms\/s2-13.1.151"},{"key":"9348_CR7","volume-title":"Ebene Kinematik","author":"W Blaschke","year":"1956","unstructured":"W.\u00a0Blaschke and H.\u00a0R. M\u00fcller, Ebene Kinematik, Oldenbourg, M\u00fcnchen, 1956."},{"key":"9348_CR8","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.jsc.2015.08.005","volume":"74","author":"CC-A Cheng","year":"2016","unstructured":"C.\u00a0C.-A. Cheng and T.\u00a0Sakkalis, On new types of rational rotation-minimizing frame space curves, J. Symb. Comput. 74 (2016), 400\u2013407.","journal-title":"J. Symb. Comput."},{"key":"9348_CR9","doi-asserted-by":"crossref","first-page":"3394","DOI":"10.1109\/TSP.2004.837413","volume":"52","author":"RM Corless","year":"2004","unstructured":"R.\u00a0M. Corless, S.\u00a0M. Watt and L.\u00a0Zhi, QR factoring to compute the gcd of univariate approximate polynomials, IEEE Transactions on Signal Processing 52 (2004), 3394\u20133402.","journal-title":"IEEE Transactions on Signal Processing"},{"key":"9348_CR10","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511735172","volume-title":"Geometric Folding Algorithms: Linkages","author":"ED Demaine","year":"2007","unstructured":"E.\u00a0D. Demaine and J.\u00a0O\u2019Rourke, Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Cambridge University Press, Cambridge, 2007."},{"key":"9348_CR11","unstructured":"P.\u00a0Dietmaier, Einfach \u00fcbergeschlossene Mechanismen mit Drehgelenken, Habilitation thesis, Graz University of Technology, Graz, 1995."},{"key":"9348_CR12","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1090\/mcom\/3120","volume":"86","author":"M Gallet","year":"2016","unstructured":"M.\u00a0Gallet, C.\u00a0Koutschan, Z.\u00a0Li, G.\u00a0Regensburger, J.\u00a0Schicho and N.\u00a0Villamizar, Planar linkages following a prescribed motion, Math. Comput. 86 (2016), 473-506.","journal-title":"Math. Comput."},{"key":"9348_CR13","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1016\/S0094-114X(01)00040-4","volume":"36","author":"X-S Gao","year":"2001","unstructured":"X.-S. Gao, C.-C. Zhu, S.-C. Chou and J.-X. Ge, Automated generation of Kempe linkages for algebraic curves and surfaces, Mech. Machine Theory 36 (2001), 1019\u20131033.","journal-title":"Mech. Machine Theory"},{"key":"9348_CR14","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.mechmachtheory.2013.05.010","volume":"69","author":"G Heged\u00fcs","year":"2013","unstructured":"G.\u00a0Heged\u00fcs, J.\u00a0Schicho and H.-P. Schr\u00f6cker, Factorization of rational curves in the Study quadric and revolute linkages, Mech. Machine Theory 69 (2013), 142\u2013152.","journal-title":"Mech. Machine Theory"},{"key":"9348_CR15","doi-asserted-by":"publisher","unstructured":"G.\u00a0Heged\u00fcs, J.\u00a0Schicho and H.-P. Schr\u00f6cker, Four-pose synthesis of angle-symmetric 6R linkages, J. Mechanisms Robotics 7 (2015), no.\u00a04. doi: 10.1115\/1.4029186 .","DOI":"10.1115\/1.4029186"},{"key":"9348_CR16","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/S0893-9659(02)80003-9","volume":"15","author":"L Huang","year":"2002","unstructured":"L.\u00a0Huang and W.\u00a0So, Quadratic formulas for quaternions, Appl. Math. Lett. 15 (2002), 533\u2013540.","journal-title":"Appl. Math. Lett."},{"key":"9348_CR17","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/978-1-4419-0999-2_4","volume-title":"Nonlinear Computational Geometry (I","author":"M Husty","year":"2009","unstructured":"M.\u00a0Husty and H.-P. Schr\u00f6cker, Algebraic geometry and kinematics, In Nonlinear Computational Geometry (I.\u00a0Z. Emiris, F.\u00a0Sottile and T.\u00a0Theobald, eds.), Springer, New York, 2009, pp.\u00a085\u2013107."},{"issue":"202","key":"9348_CR18","first-page":"117","volume":"II","author":"B J\u00fcttler","year":"1993","unstructured":"B.\u00a0J\u00fcttler, \u00dcber zwangl\u00e4ufige rationale Bewegungsvorg\u00e4nge, \u00d6sterreich. Akad. Wiss. Math.-Natur. Kl. S.-B. II 202 (1993), 117\u2013232.","journal-title":"\u00d6sterreich. Akad. Wiss. Math.-Natur. Kl. S.-B."},{"key":"9348_CR19","doi-asserted-by":"crossref","unstructured":"E. Kaltofen, Z. Yang and L.\u00a0Zhi, Approximate Greatest Common Divisors of Several Polynomials with Linearly Constrained Coefficients and Singular Polynomials, In Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation (J.-G. Dumas, eds.), ACM, New York, 2006, pp.\u00a0169\u2013176.","DOI":"10.1145\/1145768.1145799"},{"key":"9348_CR20","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1016\/S0040-9383(01)00034-9","volume":"41","author":"M Kapovich","year":"2002","unstructured":"M.\u00a0Kapovich and J.\u00a0J. Millson, Universality theorems for configuration spaces of planar linkages, Topology 41 (2002), 1051\u20131107.","journal-title":"Topology"},{"key":"9348_CR21","doi-asserted-by":"crossref","unstructured":"A.\u00a0B. Kempe, On a general method of describing plane curves of the nth degree by linkwork, Proc. London Math. Soc. s1\u20137 (1876), 213\u2013216.","DOI":"10.1112\/plms\/s1-7.1.213"},{"key":"9348_CR22","unstructured":"A.\u00a0Kobel, Automated generation of Kempe linkages for algebraic curves in a dynamic geometry system, Bachelor\u2019s thesis, Saarland University, 2008."},{"key":"9348_CR23","doi-asserted-by":"crossref","unstructured":"Z.\u00a0Li, Sharp linkages, In Advances in Robot Kinematics (J.\u00a0Lenar\u010di\u010d and O.\u00a0Khatib, eds.), Springer, Cham, 2014, pp.\u00a0131\u2013138.","DOI":"10.1007\/978-3-319-06698-1_15"},{"key":"9348_CR24","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1016\/j.mechmachtheory.2013.08.002","volume":"70","author":"Z Li","year":"2013","unstructured":"Z.\u00a0Li and J.\u00a0Schicho, Classification of angle-symmetric 6R linkages, Mech. Machine Theory 70 (2013), 372\u2013379.","journal-title":"Mech. Machine Theory"},{"key":"9348_CR25","doi-asserted-by":"crossref","unstructured":"Z.\u00a0Li and J.\u00a0Schicho, Three types of parallel 6R linkages, In Computational Kinematics: Proceedings of the 6th International Workshop on Computational Kinematics (CK2013) (F.\u00a0Thomas and A.\u00a0Perez\u00a0Gracia, eds.), Springer, Dordrecht, 2014, pp.\u00a0111\u2013119.","DOI":"10.1007\/978-94-007-7214-4_13"},{"key":"9348_CR26","doi-asserted-by":"publisher","unstructured":"Z.\u00a0Li, J.\u00a0Schicho and H.-P. Schr\u00f6cker, 7R Darboux linkages by factorization of motion polynomials, In Proceedings of the 14th IFToMM World Congress (S.-H. Chang, ed.), 2015, doi: 10.6567\/IFToMM.14TH.WC.OS2.014","DOI":"10.6567\/IFToMM.14TH.WC.OS2.014"},{"key":"9348_CR27","unstructured":"Z.\u00a0Li, J.\u00a0Schicho and H.-P. Schr\u00f6cker, Factorization of motion polynomials, arXiv:1502.07600 , 2015."},{"key":"9348_CR28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cagd.2015.10.002","volume":"41","author":"Z Li","year":"2016","unstructured":"Z.\u00a0Li, J.\u00a0Schicho and H.-P. Schr\u00f6cker, The rational motion of minimal dual quaternion degree with prescribed trajectory, Comput. Aided Geom. Design 41 (2016), 1\u20139.","journal-title":"Comput. Aided Geom. Design"},{"key":"9348_CR29","unstructured":"A.\u00a0J. Perez, Analysis and Design of Bennett Linkages, Ph.D. thesis, University of California, Irvine, 2004."},{"key":"9348_CR30","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1007\/s12045-011-0028-x","volume":"16","author":"A Saxena","year":"2011","unstructured":"A.\u00a0Saxena, Kempe\u2019s linkages and the universality theorem, Resonance 16 (2011), 220\u2013237.","journal-title":"Resonance"}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-017-9348-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-017-9348-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-017-9348-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,18]],"date-time":"2019-09-18T19:10:38Z","timestamp":1568833838000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-017-9348-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,21]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["9348"],"URL":"https:\/\/doi.org\/10.1007\/s10208-017-9348-x","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,21]]}}}