Mechanical linkages: Dynamic Geometry and Kinematics on a STEM Educational environment


  • Fco. Javier Manzano Mozo IES Delicias (Valladolid) Spain
  • Melchor Gómez García Universidad Autónoma de Madrid Spain
  • Jorge Mozo Fernández Universidad de Valladolid Spain





A concrete proposal for using a Dynamic Geometry System at an educational setting in a STEM environment (Science, Technology, Engineering and Mathematics) and, particularly, in the subject of Mathematics, consists on the generation and handling of digital simulations of mechanical linkages.

Herein, in this article we collect proposals arguing for the teaching of mechanical models or articulated mechanisms and curve drawing devices in particular, as a path to apply complex mathematical ideas and notions which are based on Dynamic Geometry. In addition, this perspective constitute a powerful resource for the iniciation and reproduction of historical contexts of scientific experience in the classroom.

We present two digital repositories of articulated mechanisms, the Kinematics Models For Design Digital Library and the Laboratorio delle Macchine Matematiche together with a review of educative proposals dealing with these mechanisms.


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Abánades, M.Á., et al. (2014). An algebraic taxonomy for locus computation in dynamic geometry. Computer-Aided Design 56 22–33.

American Association for the Advancement of Science AAAS. (1993). Benchmarks for science literacy. New York: Oxford Press.

Artobolevskii, I. I. (1964). Mechanisms for the generation of plane curves. Pergamon.

Banks, F., & Barlex, D. (2014). Teaching STEM in the secondary school: Helping teachers meet the challenge. Routledge.

Bolt, B. (1992). Matemáquinas: la matemática que hay en la tecnología (1ª ed.) Barcelona: Labor.

Bryant, J., & Sangwin, C. (2011). How round is your circle?: where engineering and mathematics meet. Princeton University Press.

Bussi, M. G. B. (1998). Drawing instruments: Theories and practices from history to didactics. In Proceedings of the International Congress of Mathematicians (pp. 735-746).

Bussi, M. G. B. et al. (2004, July). Learning Mathematics with tools. Paper presented at the 10th International Congress on Mathematical Education (ICME-10), Copenhagen, Denmark.

Bybee, R. W. (August 26, 2010) What Is STEM Education? Science 329 (5995), 996. [doi: 10.1126/science.1194998].

Bybee, R. W. (2013). The case for STEM education: Challenges and opportunities. National Science Teachers Association.

Cortés, J. C.; Soto Rodríguez, H. A. (2012). Uso de Artefactos Concretos en Actividades de Geometría Analítica: Una Experiencia con la Elipse. Journal of Research in Mathematics Education, 1(2), 159-193. doi: 10.4471/redimat.2012.09

De Villiers, M. (1998). An alternative approach to proof in Dynamic Geometry. In R. Lehrer and D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space. Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 369–393.

Dennis, D. (1995). Historical perspectives for the reform of mathematics curriculum: Geometric curve drawing devices and their role in the transition to an algebraic description of functions. Cornell University, May.

Dennis, D. (2000). The role of historical studies in mathematics and science educational research. Handbook of research design in mathematics and science education, 799-813.

European Parliament. (2015). Encouraging STEM Studies for the Labour Market. Recuperado de:

Farouki, R. T. (2000). Curves from motion, motion from curves. CALIFORNIA UNIV DAVIS DEPT OF MECHANICAL AND AERONAUTICAL ENGINEERING.

Flórez, M., Carbonell, M. V., & Martínez, E. (2011). Design of Cycloids, Hypocycloids and Epicycloids Curves with Dynamic Geometry Software. Engineering Applications. EDULEARN11 Proceedings, 1011-1016.

Fontes, F. L. (2012). Instrumentos virtuais de desenho e a argumentação em Geometria. (Dissertação de Mestrado em Ensino de Matemática). Universidade Federal do Rio Grande do Sul. Porto Alegre. Brasil.

Gonzalez, H. B., & Kuenzi, J. J. (2012, August). Science, Technology, Engineering, and Mathematics (STEM) Education: A primer. Congressional Research Service, Library of Congress.

Iriarte, X., Aginaga, J., & Ros, J. (2014). Teaching Mechanism and Machine Theory with GeoGebra. In New Trends in Educational Activity in the Field of Mechanism and Machine Theory (pp. 211-219). Springer International Publishing.

Jahnke, H. N., Arcavi, A., Barbin, E., Bekken, O., Furinghetti, F., El Idrissi, A., ... & Weeks, C. (2002). The use of original sources in the mathematics classroom. In History in mathematics education (pp. 291-328). Springer Netherlands.

Laborde, C. et al. (2006) Teaching and learning Geometry with Technology. Handbook of research on the psychology of mathematics education: Past, present and future, p. 275-304.

Manzano, F. J. (2016) Conicógrafos del Siglo XVII para la Educación Matemática del Siglo XXI. Revista TRIM, 10, pp. 47-60. Centro Tordesillas de Relaciones con Iberoamérica. Universidad de Valladolid.

Marginson, S., Tytler, R., Freeman, B., & Roberts, K. (2013). STEM: country comparisons: international comparisons of Science, Technology, Engineering and Mathematics (STEM) Education. Final Report.

Moon, F. C. (2003). Franz Reuleaux: Contributions to 19th century kinematics and theory of machines. Applied Mechanics Reviews, 56(2), 261-285.

Mora Sánchez, J. A. (2007). Geometría Dinámica en Secundaria. Recuperado de

OECD, (2007). PISA 2006: Science Competencies for Tomorrow’s World, Vol. 1.

OECD Publishing. (2012). Strengthening education for innovation . In OECD Science, Technology and Industry Outlook 2012 (pp. 206-208). OECD Pub.

Peron, G. C., de Cássia Silva, R., de Araújo Nunes, M. A., & Oliveira, A. B. S. (2011). Dynamical Simulation of a Valvetrain Mechanism: an Engineering Education Approach. Proceedings of COBEM 2011.

Quevedo, J. (2005). Informales e interactivas: Theatrum Machinarum. Matemáquinas en el Museo Universitario de Módena. Suma: Revista sobre Enseñanza y Aprendizaje de las Matemáticas, (48), 81-90.

Reuleaux, F. (1885). The influence of the Technical Sciences upon General Culture. Columbia University, Henry Krumb School of Mines.

Rothwell, J. (2013). The hidden STEM Economy. Washington: Brookings Institution.

Sanchis, G. R. (2014). Historical Activities for the Calculus Classroom. - Module 1: Curve Drawing Then and Now," Convergence. June

Soto Rodríguez, H. A. (2010). Experimentación con un grupo de estudiantes de Bachillerato con hojas de trabajo relacionadas con la parábola y elipse usando artefactos concretos. (Tesis para obtener el título de Licenciado en Ciencias Físico Matemáticas). Universidad Michoacana San Nicolás de Hidalgo. Morelia, México.

Taimina, D., Pan, B., Gay, G., Saylor, J., Hembrooke, H., Henderson, D., ... & Paventi, C. (2007). Historical mechanisms for drawing curves. Hands On History: A Resource for Teaching Mathematics, 89-104.

Vincent, J., & McCrae, B. (2000). Mechanical Linkages, Dynamic Geometry Software and Mathematical Proof. In Proceedings of the International Conference on Technology in Mathematics Education (pp. 280-288). Auckland Inst. of Tech.

Vincent, J. (2003). Mathematical reasoning in a technological environment. Informatics in Education-An International Journal, (Vol 2_1), 139-150.

Yates, R. C. (1941) Geometrical Tools: A Mathematical Sketch and Model Book. Educational Publishers.

Zavala, J. C. C., & Rodríguez, H. A. S. (2012). Uso de artefactos concretos en actividades de Geometría Analítica: una experiencia con la elipse. REDIMAT, 1(2), 159-193.

Zimmermann, W., & Cunningham, S. (1991). Editor’s introduction: What is mathematical visualization. Visualization in teaching and learning mathematics, 1-7.



How to Cite

Manzano Mozo, F. J., García, M. G., & Fernández, J. M. (2017). Mechanical linkages: Dynamic Geometry and Kinematics on a STEM Educational environment. Innoeduca. International Journal of Technology and Educational Innovation, 3(1), 15–27.