Labels and symbolic notations are the basis for modelling and analysis of mechanical designs, particularly of mechanisms with features that have been proposed since the beginning of the nineteenth century, even for design purposes. They were proposed in several forms and solutions, starting with pioneer applications in catalogs and classifications of machines and mechanisms. Early symbolic notations of mechanisms, mainly due to Babbage, Reuleaux, and Masi, are presented and discussed in this paper with the aim of giving merit to those pioneer works and of tracing a historical evolution of the matter that is still fundamental for modern developments both in teaching and research. Modern symbolic notations have evolved from these early attempts with new mathematical features for design and analysis algorithms, with an increased interest in broader classifications and more efficient analysis and synthesis procedures.
References
[1]
Artobolevsky, I. I. (1975-1980). Mechanisms in Modern Engineering (5 Vols). Mir Publ.
[2]
Babbage, C. (1826). XVIII. On a Method of Expressing by Signs the Action of Machinery. Philosophical Transactions of the Royal Society of London, 116, 250-265. https://doi.org/10.1098/rstl.1826.0022
[3]
Babbage, C. (1830). Notation. In D. Brewster (Ed.), The Edinburgh Encyclopaedia (Vol. 15, pp. 394-399). William Blackwood.
[4]
Babbage, C. (1851). Laws of Mechanical Notation (for Consideration). https://archive.org/details/TO01157442_TO0324_62167_000000
[5]
Borgnis, J. A. (1818-1823). Traitè complet de mecanique appliqee aux arts (10 Vols). éditeur Bachelier 1818-1823.
[6]
Ceccarelli, M. (2004). Classifications of Mechanisms over Time. In Proceedings ofInternational Symposium on History of Machines and Mechanisms HMM2004 (pp. 285-302). Kluwer.
[7]
Chondros, T. G. (2021). Razvoj mehanike i in？enjerskog dizajna i teorije ma？ine od perioda renesanse. FME Transactions, 49, 291-307. https://doi.org/10.5937/fme2102291c
[8]
Dickinson, H. W. (2010). James Watt: Craftsman and Engineer. Cambridge University Press. https://doi.org/10.1017/cbo9780511708145
[9]
Dutz, J., & Schlimm, D. (2021). Babbage’s Guidelines for the Design of Mathematical Notations. Studies in History and Philosophy of Science, 88, 92-101. https://doi.org/10.1016/j.shpsa.2021.03.001
[10]
Gibbings, J. C. (2014). Dimensional Analysis (297 p.). Springer.
[11]
Giulio, C. I. (1846). Sunti delle Lezioni di Meccanica applicata alle arti. Tipografia Pomba, Torino.
[12]
Krylov, E., Devyaterikov, S., & Nazarov, A. (2024). Language of Kinematics as Analytical Tool for Junior TMM Students. In A. Tuleshov, Jomartov, A., & M. Ceccarelli (Eds.), Advances in Asian Mechanism and Machine Science (Vol. 167, pp. 217-225). Springer. https://doi.org/10.1007/978-3-031-67569-0_25
[13]
Lanz, J. M., & Betancourt, A. (1808). Essai sur la composition des machines. L’Imprimerie Impe？riale.
[14]
Masi, F. (1883). Manuale di cinematica applicata: Nuova classificazione dei meccanismi. Zanichelli.
[15]
Masi, F. (1897). La Teoria dei Meccanismi. Zanichelli.
[16]
Moon, F. C. (2003). Franz Reuleaux: Contributions to 19th Century Kinematics and Theory of Machines. Applied Mechanics Reviews, 56, 261-285. https://doi.org/10.1115/1.1523427
[17]
Papadopoulos, E. (2007). Heron of Alexandria (c. 10-85 AD). In M. Ceccarelli (Ed.), Distinguished Figures in Mechanism and Machine Science: Their Contributions and Legacies (pp. 161-187). Springer.
[18]
Reuleaux, F. (1875). Theoretische Kinematic. F. Vieweg und Sohn Publs.
[19]
Willis, R. (1841). Principle of Mechanisms (2nd ed.). Cambridge University Press.
