{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T09:47:47Z","timestamp":1726048067477},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T00:00:00Z","timestamp":1576540800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T00:00:00Z","timestamp":1576540800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math.Comput.Sci."],"published-print":{"date-parts":[[2020,6]]},"DOI":"10.1007\/s11786-019-00428-1","type":"journal-article","created":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T17:02:51Z","timestamp":1576602171000},"page":"375-389","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Using a CAS\/DGS to Analyze Computationally the Configuration of Planar Bar Linkage Mechanisms Based on Partial Latin Squares"],"prefix":"10.1007","volume":"14","author":[{"given":"Ra\u00fal M.","family":"Falc\u00f3n","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,12,17]]},"reference":[{"key":"428_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0002-9947-1974-0350629-3","volume":"193","author":"R Alexander","year":"1974","unstructured":"Alexander, R., Stolarsky, K.B.: Extremal problems of distance geometry related to energy integrals. Trans. Am. Math. Soc. 193, 1\u201331 (1974)","journal-title":"Trans. Am. Math. Soc."},{"key":"428_CR2","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/978-94-6091-618-2_9","volume-title":"Model-Centered Learning. Modeling and Simulations for Learning and Instruction","author":"JM Arranz","year":"2011","unstructured":"Arranz, J.M., Losada, R., Mora, J.A., Recio, T., Sada, M.: Modeling the cube using Geogebra. In: Bu, L., Schoen, R. (eds.) Model-Centered Learning. Modeling and Simulations for Learning and Instruction, pp. 119\u2013131. SensePublishers, Rotterdam (2011)"},{"key":"428_CR3","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1002\/cae.20346","volume":"19","author":"F Botana","year":"2011","unstructured":"Botana, F., Ab\u00e1nades, M.\u00c1., Escribano, J.: Exact internet accessible computation of paths of points in planar linkages and diagrams. Comput. Appl. Eng. Educ. 19, 835\u2013841 (2011)","journal-title":"Comput. Appl. Eng. Educ."},{"key":"428_CR4","volume-title":"Theory and Applications of Distance Geometry","author":"L Blumenthal","year":"1953","unstructured":"Blumenthal, L.: Theory and Applications of Distance Geometry. Oxford University Press, Oxford (1953)"},{"key":"428_CR5","unstructured":"Corves, B., H\u00fcsing, M., Riedel, M.: Descriptive and Intuitive Mechanism Design and Synthesis Using Geometry-Based Computer-Aided Methods. In: Thirteenth World Congress in Mechanism and Machine Science. Curran Associates, Inc., Guanajuato, Mexico (2011)"},{"key":"428_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6911-1","volume-title":"Using Algebraic Geometry","author":"DA Cox","year":"1998","unstructured":"Cox, D.A., Little, J.B., OShea, D.: Using Algebraic Geometry. Springer, New York (1998)"},{"key":"428_CR7","volume-title":"Distance Geometry and Molecular Conformation","author":"GM Crippen","year":"1988","unstructured":"Crippen, G.M., Havel, T.F.: Distance Geometry and Molecular Conformation. Wiley, New York (1988)"},{"key":"428_CR8","doi-asserted-by":"crossref","unstructured":"Crippen, G.M.: Distance geometry for realistic molecular conformations. In: Distance Geometry, pp. 315\u2013328. Springer, New York (2013)","DOI":"10.1007\/978-1-4614-5128-0_15"},{"key":"428_CR9","unstructured":"Decker, W. Greuel, G.M., Pfister, G., Sch\u00f6nemann, H.: Singular 4-1-2\u2013a computer algebra system for polynomial computations. http:\/\/www.singular.uni-kl.de (2018). Accessed 8 Nov 2019"},{"key":"428_CR10","volume-title":"Latin Squares and their Applications","author":"J D\u00e9nes","year":"1974","unstructured":"D\u00e9nes, J., Keedwell, A.D.: Latin Squares and their Applications. Academic Press, New York (1974)"},{"key":"428_CR11","first-page":"186","volume":"18","author":"MA Dokuchaev","year":"2014","unstructured":"Dokuchaev, M.A., Kasyanuk, M.V., Khibina, M.A., Kirichenko, V.V.: Exponent matrices and Frobenius rings. Algebra Discrete Math. 18, 186\u2013202 (2014)","journal-title":"Algebra Discrete Math."},{"key":"428_CR12","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1023\/A:1013857218127","volume":"22","author":"Q Dong","year":"2002","unstructured":"Dong, Q., Wu, Z.: A linear-time algorithm for solving the molecular distance geometry problem with exact inter-atomic distance. J. Global Optim. 22, 365\u2013375 (2002)","journal-title":"J. Global Optim."},{"key":"428_CR13","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.endm.2018.06.010","volume":"68","author":"D Eiran","year":"2018","unstructured":"Eiran, D., Falc\u00f3n, R.M., Kotlar, D., Marbach, T.G., Stones, R.J.: Two-line graphs of partial Latin rectangles. Electron. Notes Discrete Math. 68, 53\u201358 (2018)","journal-title":"Electron. Notes Discrete Math."},{"key":"428_CR14","volume-title":"Mechanism Design: Analysis and Synthesis","author":"AG Erdman","year":"1984","unstructured":"Erdman, A.G., Sandor, G.N.: Mechanism Design: Analysis and Synthesis. N.J. Prentice Hall, Englewood Cliffs (1984)"},{"key":"428_CR15","doi-asserted-by":"publisher","first-page":"1150","DOI":"10.1016\/j.disc.2011.11.013","volume":"313","author":"RM Falc\u00f3n","year":"2013","unstructured":"Falc\u00f3n, R.M.: The set of autotopisms of partial Latin squares. Discrete Math. 313, 1150\u20131161 (2013)","journal-title":"Discrete Math."},{"key":"428_CR16","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/j.ejc.2015.02.022","volume":"48","author":"RM Falc\u00f3n","year":"2015","unstructured":"Falc\u00f3n, R.M.: Enumeration and classification of self-orthogonal partial Latin rectangles by using the polynomial method. Eur. J. Comb. 48, 215\u2013223 (2015)","journal-title":"Eur. J. Comb."},{"key":"428_CR17","doi-asserted-by":"publisher","first-page":"1769","DOI":"10.1007\/s10444-018-9654-0","volume":"45","author":"RM Falc\u00f3n","year":"2019","unstructured":"Falc\u00f3n, R.M., \u00c1lvarez, V., Gudiel, F.: A computational algebraic geometry approach to analyze pseudo-random sequences based on Latin squares. Adv. Comput. Math. 45, 1769\u20131792 (2019)","journal-title":"Adv. Comput. Math."},{"key":"428_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3390\/sym10080322","volume":"10","author":"RM Falc\u00f3n","year":"2018","unstructured":"Falc\u00f3n, R.M., Falc\u00f3n, O.J., N\u00fa\u00f1ez, J.: A historical perspective of the theory of isotopisms. Symmetry 10, 1\u201321 (2018)","journal-title":"Symmetry"},{"key":"428_CR19","doi-asserted-by":"publisher","first-page":"765","DOI":"10.1016\/j.endm.2015.06.103","volume":"49","author":"RM Falc\u00f3n","year":"2015","unstructured":"Falc\u00f3n, R.M., Stones, R.J.: Classifying partial Latin rectangles. Electron. Notes Discrete Math. 49, 765\u2013771 (2015)","journal-title":"Electron. Notes Discrete Math."},{"key":"428_CR20","doi-asserted-by":"publisher","first-page":"1242","DOI":"10.1016\/j.disc.2017.01.002","volume":"340","author":"RM Falc\u00f3n","year":"2017","unstructured":"Falc\u00f3n, R.M., Stones, R.J.: Partial Latin rectangle graphs and autoparatopism groups of partial Latin rectangles with trivial autotopism groups. Discrete Math. 340, 1242\u20131260 (2017)","journal-title":"Discrete Math."},{"key":"428_CR21","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1016\/S0747-7171(08)80120-4","volume":"11","author":"TF Havel","year":"1991","unstructured":"Havel, T.F.: Some examples of the use of distances as coordinates for euclidean geometry. J. Symb. Comp. 11, 579\u2013593 (1991)","journal-title":"J. Symb. Comp."},{"key":"428_CR22","unstructured":"Hohenwarter, M.: GeoGebra: Ein Softwaresystem f\u00fcr dynamische Geometrie und Algebra der Ebene. Ph.D. Thesis. Paris Lodron University, Salzburg, Austria (2002)"},{"key":"428_CR23","doi-asserted-by":"publisher","first-page":"1397","DOI":"10.1111\/evo.13208","volume":"71","author":"Y Hu","year":"2017","unstructured":"Hu, Y., Nelson-Maney, N., Anderson, P.S.L.: Common evolutionary trends underlie the four-bar linkage systems of sunfish and mantis shrimp. Evolution 71, 1397\u20131405 (2017)","journal-title":"Evolution"},{"key":"428_CR24","doi-asserted-by":"publisher","first-page":"1197","DOI":"10.1090\/S0025-5718-2010-02420-2","volume":"80","author":"A Hulpke","year":"2011","unstructured":"Hulpke, A., Kaski, P., \u00d6sterg\u00e5rd, P.R.J.: The number of Latin squares of order 11. Math. Comput. 80, 1197\u20131219 (2011)","journal-title":"Math. Comput."},{"key":"428_CR25","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/978-3-319-01836-2_23","volume-title":"New Trends in Educational Activity in the Field of Mechanism and Machine Theory","author":"X Iriarte","year":"2014","unstructured":"Iriarte, X., Aginaga, J., Ros, J.: Teaching mechanism and machine theory with GeoGebra. In: Garc\u00eda-Prada, J.C., Castej\u00f3n, C. (eds.) New Trends in Educational Activity in the Field of Mechanism and Machine Theory, pp. 211\u2013219. Springer International Publishing, Switzerland (2014)"},{"key":"428_CR26","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/0097-3165(90)90015-O","volume":"54","author":"G Kolesova","year":"1990","unstructured":"Kolesova, G., Lam, C.W.H., Thiel, L.: On the number of $$8\\times 8$$ Latin squares. J. Combin. Theory Ser. A 54, 143\u2013148 (1990)","journal-title":"J. Combin. Theory Ser. A"},{"key":"428_CR27","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.disc.2014.05.004","volume":"331","author":"D Kotlar","year":"2014","unstructured":"Kotlar, D.: Computing the autotopy group of a Latin square by cycle structure. Discrete Math. 331, 74\u201382 (2014)","journal-title":"Discrete Math."},{"key":"428_CR28","unstructured":"Kov\u00e1cs Z., Kov\u00e1cs, B.: A Compilation of LEGO Technic Parts to Support Learning Experiments on Linkages. Technical Report (2017) arXiv:1712.00440 [math.HO]"},{"key":"428_CR29","doi-asserted-by":"crossref","unstructured":"Kurita, K., Inoue, F., Furuya, N., Shiokawa T., Natori M.: Development of adaptive roof structure by variable geometry truss. In: Proceedings of the 18th International Symposium on Automation and Robotics in Construction, pp. 1\u20136. Krakow, Poland (2001)","DOI":"10.22260\/ISARC2001\/0012"},{"key":"428_CR30","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/978-3-319-01836-2_21","volume-title":"New Trends in Educational Activity in the Field of Mechanism and Machine Theory","author":"S Kurtenbach","year":"2014","unstructured":"Kurtenbach, S., Prause, I., Weigel, C., Corves, B.: Comparison of geometry software for the analysis in mechanism theory. In: Garc\u00eda-Prada, J.C., Castej\u00f3n, C. (eds.) New Trends in Educational Activity in the Field of Mechanism and Machine Theory, pp. 193\u2013201. Springer International Publishing, Switzerland (2014)"},{"key":"428_CR31","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1016\/j.ejor.2011.11.007","volume":"219","author":"C Lavor","year":"2012","unstructured":"Lavor, C., Liberti, L., Maculan, N., Mucherino, A.: Recent advances on the discretizable molecular distance geometry problem. Eur. J. Oper. Res. 219, 698\u2013706 (2012)","journal-title":"Eur. J. Oper. Res."},{"key":"428_CR32","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/BF01448840","volume":"100","author":"K Menger","year":"1928","unstructured":"Menger, K.: Untersuchungen \u00fcber allgemeine Metrik. Mathematische Annalen 100, 75\u2013163 (1928)","journal-title":"Mathematische Annalen"},{"key":"428_CR33","doi-asserted-by":"publisher","first-page":"721","DOI":"10.2307\/2371222","volume":"53","author":"K Menger","year":"1931","unstructured":"Menger, K.: New foundation of Euclidean geometry. Am. J. Math. 53, 721\u2013745 (1931)","journal-title":"Am. J. Math."},{"key":"428_CR34","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1002\/jcd.20105","volume":"15","author":"BD McKay","year":"2007","unstructured":"McKay, B.D., Meynert, A., Myrvold, W.: Small Latin squares, quasigroups, and loops. J. Combin. Des. 15, 98\u2013119 (2007)","journal-title":"J. Combin. Des."},{"key":"428_CR35","unstructured":"Prause, I., Fauroux, J.C., H\u00fcsing, M., Corves, B.: Using Geometry Sketchers and CAD Tools for Mechanism Synthesis. In: Proceedings of IFToMM 2015, The 14th World Congress in Mechanism and Machine Science, paper OS3-032, 11 pp. International Federation for the Theory of Mechanisms and Machines, Taiwan (2015)"},{"key":"428_CR36","doi-asserted-by":"crossref","unstructured":"Porta, J.M., Rojas, N., Thomas, F.: Distance Geometry in Active Structures. In: Ottaviano E., Pelliccio A., Gattulli V. (eds.) Mechatronics for Cultural Heritage and Civil Engineering. Intelligent Systems, Control and Automation: Science and Engineering 92, pp. 115\u2013136. Springer, Cham (2018)","DOI":"10.1007\/978-3-319-68646-2_5"},{"key":"428_CR37","unstructured":"Rojas, N.: Distance-based formulations for the position analysis of kinematic chains. PhD thesis. Universitat Polit\u00e8cnica de Catalunya, Institut de Rob\u00f2tica i Inform\u00e0tica Industrial, Barcelona (2012)"},{"key":"428_CR38","unstructured":"Saxe, J.: Embeddability of weighted graphs in $$k$$-space is strongly NP-hard. In: Proceedings of 17th Allerton Conference in Communications, Control and Computing, pp. 480\u2013489. Monticello, IL (1979)"},{"key":"428_CR39","doi-asserted-by":"publisher","first-page":"1092","DOI":"10.1016\/j.ejc.2013.02.005","volume":"34","author":"DS Stones","year":"2013","unstructured":"Stones, D.S.: Symmetries of partial Latin squares. Eur. J. Combin. 34, 1092\u20131107 (2013)","journal-title":"Eur. J. Combin."}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-019-00428-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11786-019-00428-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-019-00428-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T00:38:21Z","timestamp":1608079101000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11786-019-00428-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,17]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["428"],"URL":"https:\/\/doi.org\/10.1007\/s11786-019-00428-1","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"value":"1661-8270","type":"print"},{"value":"1661-8289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,17]]},"assertion":[{"value":"30 November 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 March 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 December 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}