Modelling is a widely used teaching tool, especially in fields related to the development and analysis of systems. Today, these models are essentially in digital forms, but there is also a renewed interest in physical models that can help in learning concepts and functions with direct physical experience and can facilitate and complete the introduction and explanation of their related problems and solutions, even with historical perspectives ( Ceccarelli & Cocconcelli, 2022a ). In particular, since the early days of modern time mechanical engineering have been interested in physical models of mechanisms, both for educational purposes as well as for research activities in the field of classification and cataloguing of the structural possibilities of mechanisms ( Kerle, Mauersberger, & Ceccarelli, 2011 ; Ceccarelli, 2004 ; Ceccarelli, 2020 ), such as, for example, in the pioneering works ( Lanz & Betancourt, 1808 ; Borgnis, 1818-1821 ; Willis, 1841 ; Giulio, 1846 ; Reuleaux, 1875 ). The study of physical models of mechanisms and their re-evaluation, both at historical and educational levels, has attracted recent interest primarily for museum purposes, as reported in ( Ceccarelli & Cocconcelli, 2022b ; Franco, Trivella, & Quaglia, 2020 ; Shiroshita, 2009 ; Kerle, Mauersberger, & Ceccarelli, 2011 ). Recently, the use of mechanism models is re-evaluated also for modern educational purposes in combination with digital models that can be developed with CAD simulation procedures ( Ceccarelli, 2020 ).

In this work, we present specific aspects of the development and production of mechanisms’ physical models in the Italian context with a tradition started mainly from the early second half of the 19^th century and continued until the 1960s, with their use for educational purposes ( Ceccarelli, 2021 ; Ceccarelli & Cocconcelli, 2022 ). Today many of these models that were forgotten for a long time, are rediscovered and re-evaluated mainly for technical-historical valorization which still requires attention and research to properly define their characteristics and their history. This paper focuses also on the specific experience of Giovanni Blotto, an Italian manufacturer ( Blotto, 1879 ), who was very successful in the production of mechanism models since the early mid of the 19^th century, as proved by the presence of his wooden mechanism models in many universities in Italy. The successful dissemination of the Blotto models seems to have anticipated the German mechanism models as in ( Schroder, 1899 ) that were successfully disseminated by the Voigt company with catalogue ( Voigt, 1907 ), that is linked to the works of Franz Reuleaux ( Reuleaux, 1875 ).

A preliminary version of this paper was presented at HMM2024, the 8^th International Symposium on History of Machines and Mechanisms in Ankara, Turkey, 18-20 April 2024 ( Cocconcelli & Ceccarelli, 2024 ). In this extended revised version, mechanism models from most of the Italian universities of the time are shown and discussed. A special attention is addressed by referring to a comparison between the first (1869) and second (1879) edition of the Blotto’s catalogue. The proposed examination is an attempt to provide an overview of this experience with mechanism models in Italian frames as well as to suggest a stimulus for more in-depth research and valorisation of historical-technical aspects on mechanism models also at Italian local frames.

Models of mechanism were developed in two ways, namely by drawing schemes and physical models ( Ceccarelli, 2020 ; Traetta & Ceccarelli, 2022 ). The first type was used since the early day of the mechanism technologies for several aims, such as primarily to explain and formulate design solutions and but even to teach. Within this activity investigations were carried out to summarize the mechanism possibilities with catalogues. Catalogues were a first attempt of classification of mechanism’s that become a theoretical problem to search for unification principle of the large variety of mechanism designs. Indeed, classifications of mechanisms were developed also for practical purposes of cataloguing of the variety of mechanisms available under different viewpoints for design or applications attempting also to find new solutions as pointed out for example ( Ceccarelli, 2004 ). In the modern era, a first classification with those aims is due to Gaspard Monge, who was a co-founder of the Ecole Polytechnique in Paris teaching a first modern academic course on Mechanism Design. Following those lectures his collaborators-students Augustin Betancourt and Josè Maria Lanz published in the pioneering ‘Essai sur la composition des machines’ ( Lanz & Betancourt, 1808 ), a treatise for analysing and designing the input-output movement relations depending on the structure of the mechanism categories, Figure 1(a) . Monge’s successor, Jean Nicole Hachette made such an approach a textbook in ( Hachette, 1811 ) Figure 1(b) .

Figure 1. Monge classification of mechanisms in: (a) Essai sur la composition des machines ( Lanz & Betancourt, 1808 ); (b) Traite elementaire des Machines of 1811 ( Hachette, 1811 ).

This treatise was considered a reference for long time as per the later proposals of classifications and catalogues of mechanisms when searching for generality and topological possibilities of mechanisms, even those not yet invented or designed. In these catalogues, the models of the mechanisms were represented by drawings or schemes that were also used to produce physical examples of the structures of mechanisms, by starting to the teaching tradition with the use of models ( Ceccarelli, 1998 ).

Giuseppe Antonio Borgnis, ( Ceccarelli, 2014 ), extended Monge classification in his milestone work ( Borgnis, 1818-1821 ) by including a description of machine components in terms of “receptors, modificators, frames, regulators, and operators”, as summarized in the textbook index in Figure 2 .

Then he catalogued the existing machines by referring to practical applications up to include 1200 mechanical devices with drawing schemes in his encyclopaedic mechanism handbook of 9 volumes ( Borgnis, 1818-1821 ). This milestone work was of practical reference during the whole 19^th century and was also source of further developments, whose the most significative ones can be considered those by Robert Willis (1841) and Carlo Ignazio Giulio (1846) . In 1841, Willis classified mechanisms as function of the transmission ratio (constant as constant or varying with constant or changing direction of the motion) in five divisions depending on the type of contacts among basic components as “rolling contact, sliding contact, wrapping connectors, linkwork, reduplication”. In the same time Carlo Ignazio Giulio (1803-1859), who was professor of Pure and Applied Mathematics as cofounder of the School of Engineering in Turin, in 1846 published a textbook ( Giulio, 1846 ) from lectures started in 1841 for the students at the Royal School od Application for Engineers in Turin. In his textbook ( Giulio, 1846 ), he included a classification of mechanisms based on the motion of the input and output elements that he classified according to three characteristics, namely the shape (rectilinear, circular or curvilinear motion), the type (continuous or alternative), the direction (input and output of the mechanism can be input exchanged with each other). Based on these characteristics the possible 21 categories are identified as summarized in Figure 3 . Each mechanism category is discussed with mechanism examples that are analysed in detail with drawing models in tables at the end of the book. This started the Italian modern tradition on Mechanism Design.

The specific interest on mechanism classification attracted Francesco Masi, ( Ceccarelli, 2010 ) at the University of Bologna. With his works he extended the previous mechanisms analyses and proposed a classification procedure using the mechanism modelling of Reuleaux up to elaborate his own algorithm in ( Masi, 1883 ), which classifies up to 10,362,600 mechanisms including quaternary ones (composed of quaternary links) ( Figure 4 ).

Figure 4. Classification with numbering of mechanisms by Francesco Masi ( Masi, 1883 ): (a) the summary table; (b) examples of graphical models of catalogued mechanisms.

Also, in this classification graphical models of mechanisms are used to explain the mechanism catalogue and to prove the algorithm efficiency in describing design and operation features of each type of mechanisms. These graphical models are treated as mechanism models in combination with those physical models that started to circulate for teaching purposes. Masi work well established an Italian tradition up nowadays in teaching Mechanism Design by looking at the variety of mechanisms combined with experiencing models (graphical, physical, or virtual ones) ( Ceccarelli, 2020 ; Ceccarelli & Cocconcelli, 2022 ), with practical details in design and applications.

Figure 5 shows the Italian figures who were pioneers mainly but not only, in Italian frames in developing approaches in design and teaching Mechanism Design both with theoretical (graphical) and practical models.

The value of mechanism classifications can be recognized in teaching purposes to give the students a methodology to approach the design of mechanisms or machines considering the variety of available solutions. Once a student has a clear understanding of the input-output motion relationship (as a constraint of a problem or not), she/he can select a topological solution among available mechanisms by applying further design and performance criteria. The mechanism models, either in graphical representations or physical products, can clearly explain the design and operation that are formulated by equations and discussions in a textbook or handbook, helping students with practical examples. Physical models can represent a further step even in today computer-based teaching activity, since they permit the students to touch what today we call 3D-model of a mechanism.

In the early days of 19^th century, both theoretical and practical courses in engineering schools in Italy and Europe were included as important parts of the teaching activities for engineering formation. This was emphasised also by the name of the schools, like in Italy where the engineering schools were named “School of Application for Engineers” (Scuola di Applicazione per Ingegneri). The laboratory activity was planned for students to manage objects and tools for a direct experience on what a professor explained in classrooms, for a better understanding of the theoretical subjects. Mechanism models were widely used for teaching purposes in university engineering curricula throughout the 19^th century ( Ceccarelli & Cocconcelli, 2022b ). The main advantage of mechanisms models consists in the fact they can provide a three-dimensional representation of mechanisms and machines, which cannot be fully represented by two-dimensional drawings in textbooks and in research design results. The diffusion of teaching mechanism models was so successful that the most important schools were organized with their own official workshops, and their models were often sold to other research centres and universities through commercial sales supported by catalogues. Two emblematic examples of the 19^th-century market activity of mechanism models can be indicated in Gustav Voigt in Germany ( Voigt, 1907 ) and Giovanni Blotto (1842-1932) in Italy ( Blotto, 1879 ).

Little is known about Giovanni Blotto’s life and his company. Born in Biella, Giovanni Blotto was employed at the Royal School of Application for Engineers (Reale Scuola di Applicazione per Ingegneri) of Turin since 1860. During works at Valentino in 1863-1864, among the 13 workers the name of Giovanni Blotto appears in the economic books, indicating that he was hired the following year as a trainer. With this job he was responsible for developing the collections of mechanics, constructions, geometry and crystallography with wooden objects coloured in oil and paint in imitation of real products, in the frame of a laboratory-workshop within the Royal School of Application for Engineers under the direction of Professor Curioni, teacher of Machine Design. He collaborated in the preparation of collections of solid geometry, models for elementary mechanics, construction of mechanical and steam machines, with a large sector dedicated to wood, iron and stone constructions for civil works and infrastructures. Since 1865 Blotto, as head of that laboratory-workshop at the Royal School of Application of Engineers of Turin, became the teachers’ point of reference for the development of teaching models for courses and for scientific experiments. Vittorio Canepa appeared later as his close collaborator with whom he will also share the direction of the laboratory. Already in 1861 Blotto participated with an exhibition of models of machines and mechanisms at the Italian Exhibition held in Florence with a citation in Volume 2 of the Proceedings. He was awarded a silver medal in 1884 for section VIII - INSTITUTES, BOOKS AND LIBRARIES of the Academy of Sciences of Turin. On 14 February 1876 he was appointed Knight of the Order of the Crown of Italy (Cavaliere dell’ordine della corona d’Italia) for technical-scientific merits linked to his activity as a trainer with the construction of teaching models, also exported to other training institutes in the Italian kingdom. Giovanni Blotto died in 1887 in Turin.

Today, few mechanisms models of Blotto productions remain. The main reference source is the catalogue of models, whose a copy of the second edition (1879), Figure 6(b) , is preserved in the Bologna University Historical Archive, while a digitalized version of the first edition in 1869 is available on Google Books ( Blotto, 1869 ) ( Figure 6(a) ). The catalogue of 1869 is a result of activity that was started since the early 1860s’ very likely following a tradition of the school with laboratory practices, by indicating the original activity against the later German activity with metal models.

The Blotto catalogue contains the list of all models for sale at a given price to other institutions. Figure 6 shows the title page of the first and second editions of the catalogues, which consist of 30 and 36 pages respectively. Unfortunately, the

Figure 6. Front pages of the Blotto catalogues: (a) 1^st edition published in ( Blotto, 1869 ); (b) 2^nd edition published in ( Blotto, 1879 ).

catalogue does not contain any figure of the models, but only the name of the model and the corresponding price in Italian pound ( Figure 8 ). The second edition of the Blotto catalogue consists of 871 increasing the 682 models of the first edition. The model offer is divided into three main categories: 345 (281 in the first edition) mechanical models, 326 (201) construction models, 200 (200) Crystallography models. Mechanical models are further divided into eight sub-categories: 4 (0) solid geometry models, 20 (17) elementary mechanics, 100 (80) kinematics, 85 (56) machine design, 62 (64) steam engines, 40 (36) Railways, 34 (28) Hydraulics. In addition, the catalogues include 200 crystallographic models, and 312 construction models divided into unions between woods (80), different wooden structures (54), iron constructions (40), masonry constructions and different vaults (30), common and hydraulic foundations (22), devices for the transport of earth and materials with appropriate hardware (14), retaining walls (22).

In 1879 Blotto’s new collection included 895 wooden models, among which Quintino Sella’s crystallographic models also appear as composed of geometric shapes combined with colours (e.g. yellow for primitive shape, white for octahedron, dark green for rhombododecahedron, etc.) to simplify the recognition of minerals.

Table 1 summarizes the list of items in the catalogues in the two editions.

The specific complete list of the mechanism models is reported in the Appendix. The mechanism models can be classified into 6 categories, namely cams, screws, friction devices, pulleys, gears, and cranks. The number in the table in Appendix refers to the sequential code number in the Blotto’s catalogue. Engraved on each wooden model there is the stamp of the manufacturer with the name and the city ( Figure 7 ), but unfortunately it is not indicated any date of the manufacturing nor the corresponding name of the catalogue nor the code of the mechanism. The catalogue books are the only documents available of the Blotto productions of models that very likely were purchased by many Italian universities at that time.

Recently we discovered similar wood models of mechanisms with the indication of “Costa - Grugliasco” and “G. Costa - E. Giraudo modellatori Torino” referring to a model production yet in Turin in a period after 1910. These workshops look to be the continuation of the Blotto activity, still linked to the Turin Royal School of Application for Engineer but located outside of it. This can indeed indicate a well-established production of mechanism models with a dissemination in the le territory of Italian Kingdom.

Mechanism models are still available today in several Italian universities, as outlined in ( Ceccarelli & Cocconcelli, 2022b ; Ceccarelli, 2021 ). They can be found in teachers offices, archives, and museums of the oldest universities active with school of engineering in 19^th century, such as Bologna, Milan, Padua, Palermo, Pisa, Rome, Naples, and Turin. In the following, examples from each of these universities are proposed with short discussion also referring to different model producers and testifying the diffusion of mechanism models in education. It should be noted that most of these mechanisms’ models were inspired, if not even designed, referring to the graphical models in these treaties and manuals, such as ( Borgnis, 1818 ) Giulio ( Giulio, 1846 ) and Masi ( Masi, 1883 ), which contain a classification of mechanisms with catalogues and examples of mechanisms. The models of the mechanisms that remain in some Italian academic institutions where a group in the field of Theory of Machines and Mechanisms (TMM) (today Mechanisms and Machine Science (MMS)) is still active, have been preserved against dispersion and destruction in recent years due to a depreciation following activities based on the use of the computer, thanks to mainly individual interest of some colleagues who recognized historical and educational values. In some cases, it was possible to preserve a conspicuous collection with a dimension valid even for a museum exhibition as today can be appreciated at the Politecnico of Turin (in the Department of Mechanics) ( Franco, Trivella, & Quaglia, 2020 ), and the University of Palermo (at the museum University of Engines and Mechanisms) ( Genchi, 2024 ). Furthermore, it should be noted that in addition to what is described above in relation to the production of Italian models, the existence of wooden and metallic models can be found which were probably produced locally both in the academic laboratories and by a specially appointed craftsman. However, there is no information on many of these models which also remain of unknown dating. In the following overview with a few examples of these models, this variety of models and their manufacturing can be highlighted although there is evident a significant representation of the commercial ones made by Voigt and Blotto which seem to have also been an inspiration for these local productions. Another worthy observation is the originality of the Italian models of mechanisms, especially wooden ones, which were produced even before the marketing mentioned above. In the end, the modern models appear to have originated from these simple but functional designs, which were converted into real mechanisms by different manufacturers almost without any modifications, as educational tools within teaching courses in engineering schools. It is worth noting that the practice of final tables that collected all mechanical drawings in textbooks at the end of the 19th century was later quite common, and that remarkably similar tables are present in different books of this period and later.

Wooden and metal model of mechanisms has been developed in the modern era together with teaching on the analysis and design of mechanisms with particular reference to the proposals for classification and cataloguing of mechanisms since the beginning of the 16^th century in an Italian tradition well developed both with the start of engineering schools and with the work of classification and cataloguing of mechanisms by Italians such as Borgnis, Giulio, and Masi. This activity also determined an important teaching line for the training of engineers which is still persistent today. The production of mechanism models in Italy is characterized by two aspects, namely the creation of models based on local needs in local laboratories and the production of models corresponding to catalogues and classifications available from corporate entities also for sale to other educational institutions. The second category corresponds to the case of Giovanni Blotto who at the Turin school developed models of mechanisms that were spread throughout the Italian territory, first and then in competition with the more famous German manufacturer Voigt of educational models. Unfortunately, many of these models have been lost due to the modern teaching concept based on the use of computers which has diminished their usefulness even at the level of practical exercises. Recently, a new interest from a historical and technical point of view has seen these models of mechanisms being re-evaluated to the point of recognizing their museum value as well as considering their re-evaluation at an educational and training levels. The overview offered on what remains in many Italian locations allows us to clarify both the historical and technical-scientific values of these mechanism models, with the aim also of promoting greater attention and research into what could still be preserved in the archives and the warehouses of universities.

Table A1 lists the mechanism models that are proposed by Blotto in his catalogue. The first column shows the description of a mechanism as provided by Blotto, and the second and third columns list the corresponding enumeration in the first ( Blotto, 1869 ) and second ( Blotto, 1879 ) editions of the catalogue. The second edition differs from the first one by twenty new entries: some of them are completely new (e.g. the Oldham’s coupling (82)), some other are a revised version of previous mechanisms (e.g. circular (10), heart (11), triangular (12) and variable (13) cams with ring and rotational shaft were originally proposed as a unique model (10) in the first edition of the catalogue). Sometimes there are few changes (e.g. “four wheels with live axles moving by belts” (32) in 2^nd edition was “six wheels with live axles moving by belts” (25) in the 1^st edition.

Table A1. List of mechanism models proposed by Blotto in the 1^st ( Blotto, 1869 ) and 2^nd ( Blotto, 1879 ) edition of the catalogue. The numbers refer to the enumeration in the catalogue.