Article Leonardo da Vinci’s Contributions from a Design Perspective

Ernesto Cerveró-Meliá, Salvador F. Capuz-Rizo * and Pablo Ferrer-Gisbert Department of Engineering Projects, Universitat Politècnica de València, Camino de Vera, s/n, E-46022 Valencia, Spain; [email protected] (E.C.-M.); [email protected] (P.F.-G.) * Correspondence: [email protected]



Received: 29 June 2020; Accepted: 9 September 2020; Published: 18 September 2020


Abstract: The figure of Leonardo da Vinci has been extensively studied. In fact, the Leonardiana Library brings together tens of thousands of titles on Leonardo and his work. During the second half of the 20th century, various treaties were published focusing on Leonardo’s activity as an engineer, and more recently, an increasing number of scientific articles that focus on certain aspects of the prolific work of the genius such as construction, mechanics, strength of materials, etc. have been published. This article analyses the main contributions of the Tuscan genius in the field of design focusing on his processes for generating new solutions, his developments regarding graphic representation techniques, his improvements in plotting and measuring instruments, and how some of his devices were implemented and continue to maintain their usefulness.

Keywords: Leonardo da Vinci; design techniques and tools; artifacts and inventions

1. Introduction Leonardo (Vinci 1452–Amboise 1519), although better known as an artist and painter, was a multidisciplinary genius capable of standing out in most areas of knowledge; engineering, architecture, zoology, medicine, botany, etc. Even music did not escape his voracious interest in dominating everything known. In the field of product engineering, he was capable of designing or projecting ships with armoured hulls and moved by paddles, movable bridges, bronze sculptures over 7 m high, diving suits and submarines, bicycles, self-propelled vehicles predecessors of the automobile, musical instruments, etc., even humanoid automatons. In the architecture and civil engineering field, he designed fortresses and defences for cities, sanitation channels, diversions of rivers, and even projected an “ideal city”. Only a few of those designs or projects were actually executed back then, so some of his contemporaries did not take several of his works seriously. For this reason, a large number of them stayed in what we now call the Conceptual Design phase, others reached Preliminary Design, while only a few reached the Detailed Design phase, using the usual nomenclature in the technical systems design literature [1]. Today, the bridge that Leonardo designed conceptually in 1502 for the Ottoman Sultan Beyazid II in the Golden Horn (Istanbul) is a similar reality in the city of Aas (Norway). The 7.30 m tall Sforcesco Horse, which he designed in detail, can be seen in the square of the Milan racecourse (“Il Cavallo”), and in the city of Grand Rapids, Michigan (“American Horse”). His detailed design of the Paddle Boat was copied and materialised in the 18th century by Engineer Robert Fulton on his steamboats. For all this, Leonardo should be considered a visionary designer ahead of his time. This article aims to answer the following questions. What did Leonardo contribute to the design methods and tools of his time beyond the achievements represented in his works? Or being more specific, what were the sources of inspiration for the generation of new solutions to the objects designed

Designs 2020, 4, 38; doi:10.3390/designs4030038 www.mdpi.com/journal/designs Designs 2020, 4, 38 2 of 20 by Leonardo, to what extent did his designs rely on pre-existing knowledge, and how did he use experimentation to improve them? What improvements did it make in terms of the way of representing these objects and in the drawing and measurement tools he developed?

2. Materials and Methods Leonardo was and is known as one of the best painters of all time, although as a result of the rediscovery and study in detail of his great manuscript production, which comprises 23 notebooks, most of them in the 19th century (Codex Atlanticus, Arundel Codex, Leicester Codex, French manuscripts A-M-12 volumes-, Forster Codex-3 volumes-, Codex of the “Flight of Birds” or the Turin Codex, Codex Trivulziano and Windsor Royal Collection Manuscripts) and others in the middle of the 20th century (Madrid Codices I and II) [2–6], has gained fame in other disciplines such as engineering, urban planning, anatomy, botany, or even as a scientist and inventor. As a result of the studies published by the French art historian and curator of the Louvre museum, Charles Ravaisson-Mollien (1848–1919), “Les Manuscrites de Léonard de Vinci” (1881–1891) [7], a new interest has arisen in the scientific-technical work of Leonardo. Since then, countless scientists and science historians have studied many of the different aspects of Leonardo’s scientific-technical work [8,9]. According to the researcher in physics at the University of California at Berkeley Fritjof Capra (Vienna, 1939) “Good designers are capable of systematic thinking and synthesis. They excel in visualising things, in organising known elements into new configurations, in creating new relationships; and they are able to transmit these mental processes in the form of drawings almost as quickly as they occur. Leonardo, of course, had all these capabilities to a very high degree. Furthermore, he had a mysterious natural talent for perceiving and solving technical problems—another key characteristic of a good designer—to the point that, in his case, it was almost second nature” [10].

3. Leonardo Designer

3.1. Design, Engineering and Engineering Design According to Braha and Maimon, “Design as problem-solving is a natural and the most ubiquitous of human activities” [11]. Design begins with the acknowledgment of needs and dissatisfaction with the current state of affairs, and realization that some action must take place in order to solve the problem. USA’s Accreditation Board for Engineering and Technology (ABET) defines Engineering Design “as a process of devising a system, component, or process to meet desired needs and specifications within constraints. It is an iterative, creative, decision-making process in which the basic sciences, mathematics, and engineering sciences are applied to convert resources into solutions. Engineering sciences are based on mathematics and basic sciences but require further knowledge to apply the creativity needed to solve engineering problems. These studies provide a bridge between mathematics and basic sciences on the one hand and engineering practice on the other” [12]. Under these premises, there is no doubt that Leonardo was, among other things, a prolific and multifaceted designer, both in the fields of engineering and architecture and in industrial design [9,13]. Although modest, he was also very conscious of being special, and it is not by accident that the general public remembers him and not the names of his contemporaries [14]. As stated by Blessing [15], design is a complex activity, involving artefacts, people, tools, processes, organisations and the micro- and macro-economic environment (market, legislation, society) in which it takes place. According to Nigel Cross [16], “any identifiable way of working, within the context of designing, can be considered to be a design method. Design methods can, therefore, be any procedures, techniques, aids or ‘tools’ for designing”. From these definitions, it is interesting to highlight the importance of methods, devices, instruments, and tools for designing artefacts, since these concepts will be used frequently in this work. To ensure proper use of terminology relating to technical methods and design tools, the following definitions are Designs 2020, 4, 38 3 of 20 attached, selected from the different options provided by the Oxford Dictionary and the Merrian-Webster Dictionary. An artifact is usually a simple object showing human workmanship or modification as distinguished from a natural object. A device is a piece of equipment or a mechanism designed to serve a special purpose or perform a special function. A technique is a way of carrying out a particular task, especially the execution or performance of an artistic work or a scientific procedure. A tool is a device or implement, especially one held in the hand, used to carry out a particular function. An instrument is a tool or device used for a particular task, especially for specialist or scientific work.

3.2. Design Approaches in Leonardo. From Nature Observation to Analogies In technical systems projects (equipment, machines, artefacts, etc.), because they are considered complex, the parts cannot be designed individually without taking into account the influence of other parts in their surroundings; that is, they are systemic. Therefore, it is necessary to observe the relationship of each of the parts with the whole, that is, the overall objective to be achieved (target system), as well as the relationship between them. Hence the convenience, when studying the object, to consider its division into subsystems and components, taking advantage of areas with less interference. That is, they must be studied at the same time with an interdisciplinary vision, at least in the initial stages. Leonardo was not only able to create complex systems such as clocks, mechanisms, and machines, but also by taking advantage of the knowledge gained in all these fields, and in that of human physiognomy (acquired as a young man in the workshop of the Florentine sculptor and painter Andrea Verrocchio) and forensic anatomy (carried out with Marcantonio della Torre, professor of anatomy at the University of Pavia), he relates them all and observes them from a global and interdependence perspective. Thus, he identifies the human body as a complex system (he considers that this is how Nature works) and is able to extrapolate this metabolic and organic knowledge to his designs. He even projects and operates a humanoid automaton. Thus, his work constitutes a clear precursor of current design strategies, starting from the consideration of its object as a global and interdependent system. And also, of the principles of sustainable or ecological design, aware of the influences on the climate, the landscape, the living beings and the whole of Nature. In relation to this, he writes: “An invention will be never found, more beautiful, simpler, or more economical than those of nature, since nothing is lacking in its inventions and nothing is superfluous”; “The world is ruled, not by God, but by the incessant creativity of nature” [17]. Leonardo admired and mastered geometry, but for him the complexity of nature could not be reduced to figures and mechanical analysis. His special attention to qualities, dynamism, and overall view is an essential part of his science, present today in current systemic approaches and in the complexity theory [18]. Martin Kemp, professor of Art History at Oxford University and one of the highest authorities alive on Leonardo’s science and art, considers that Leonardo is the father of Topology. He also emphasizes that “analogy” is the main technique used by Leonardo to explain the behaviour of things. Nature displays its functions and human ingenuity must imitate them, but all things designed (devices, elements, machines) must follow the “Necessity Principle” as Nature does, where all designed forms perform some function: although wood exists, “Nature has not created bows to shoot arrows” [19]. The use of analogies was also a technique used by Leonardo in many of his projects. In the manuscripts of Figure1, he analyses the movement of a human arm under stress, draws it, and generates an artificial mechanism that emulates it. A clear analogy is given between Nature, which was its main source of inspiration, and the projected machine. This mechanism is supposed to have been used in the construction of his “Automata” project. Designs 2020, 4, 38 4 of 20 Designs 2020, 4, x FOR PEER REVIEW 4 of 20

Figure 1. Study of mechanisms for the arm of an automaton.automaton. Madrid Codex I, f. 90 v, 91 r. National Library of Spain [[4].4]. Note: f. f. is is the the abbreviation abbreviation for for sheet sheet (fo (foglio);glio); r r is is the the abbreviation abbreviation of of front front (recto) and v is short for reverse (verso).

He alsoalso mademade analogiesanalogies for for his his devices devices with with which which he he intended intended to to make make man man fly, fly, assimilating assimilating the wingsthe wings of his of prototypes his prototypes to those to those of his detailedof his detailed “Studies “Studies on the flighton the of flight birds” of existing birds” inexisting the Codex in the of Turin,Codex asof wellTurin, as as of well bats. as of bats.

3.3. Leonardo’s Design Principles from the Point of View of Current DesignDesign TheoriesTheories In the evolution of design theories in the last 50 years, it is possible to highlight the influenceinfluence of the SystemsSystems Theory, Theory, the the scientific scientific method, method, and and the usethe of use analogies, of analogies, as well as as well other as projective other projective methods andmethods techniques. and techniques. The next The section next includes section includes the analysis the analysis of the way of the in which way in Leonardo which Leonardo already appliedalready theapplied scientific the methodscientific and method the systemic and approachthe systemic in his work,approach while in considering his work, environmental while considering factors, introducingenvironmental ecological factors, andintroducing ergonomic ecological principles. and ergonomic principles. According to the Technical SystemsSystems Theory [[20],20], objects, artefacts or products are seen as technical systems that transform energy, material,material, andand information.information. The functional behaviour of a technical system is fully determined by physical principles and and can can be be described by by physical physical laws. laws. The engineeringengineering designdesign problem problem is is to to find find and and define defin thee the geometry geometry and and materials materials of the of systemthe system in such in asuch way a that way the that required the required prescribed prescribed physical physical behaviour behaviour is realised is in realised the most in eff theective most and effective efficient way.and efficientTaking way. this approach, the conclusion that the form (of the artefact) is created to fulfill a function, that is,Taking the functionthis approach, creates the the conclusion organ, can that also the be form derived (of the from artefact) the statementis created to of fulfill the principle a function, of necessitythat is, the observed function in creates nature bythe Leonardo.organ, can This also approach be derived can from be observed the statement in the currentof the engineeringprinciple of designnecessity proposals. observed Forin nature example, by Leonardo. the Standard This VDI approach 2221 [21 can] structures be observed the in design the current process engineering in 7 steps, generatingdesign proposals. the Function For example, Structure the Standard in the second VDI 2221 stage, [21] while structures the Module the design structure process is generatedin 7 steps, ingenerating the fourth. the Function The Theory Structure of Technical in the second Systems stag proposese, while the a designModule process structure in is 5 generated steps (Purpose, in the Processfourth. The Model, Theory Function of Technical Model, Systems Organ Modelproposes and a Componentdesign process Model) in 5 steps [22]. (Purpose, Suh’s Axiomatic Process DesignModel, Function [23,24] sees Model, designing Organ as Model a mapping and Componen process fromt Model) the “functional [22]. Suh’s space”Axiomatic into Design the “physical [23,24] space”,sees designing or, more as specifically: a mapping process mapping from a given the “funct set ofional functional space” requirements into the “physical (FRs, space”, “what weor, more want tospecifically: achieve”) mapping into a defined a given set set of of design functional parameters requirements (DPs, description (FRs, “what of we “how want we to wantachieve”) to achieve into a it”)defined [20]. set of design parameters (DPs, description of “how we want to achieve it”) [20]. According to Professor Plinio Innocenci, “sometimes Leonardo seems to approach the modern concept ofof design.design. However,However, wewe mustmust not not make make the the mistake mistake of of using using a contemporarya contemporary point point of of view view to defineto define an an artist-engineer artist-engineer who who lived lived 500 500 years years ago. ago. Leonardo Leonardo is still is still the the son son of his of time,his time, and and heis he not is thenot onlythe only one toone use to technical use technical design, design, and perhaps and perhaps he is not he even is not the even best. Somethe best. projects Some by projects Francesco by Francesco di Giorgio or Bonaccorso Ghiberti reach a level of technical precision that rivals that of Designs 2020, 4, 38 5 of 20 di Giorgio or Bonaccorso Ghiberti reach a level of technical precision that rivals that of Leonardo. However, his machine repertoire represents something unique and, in this sense, extremely original for the variety of solutions and innovations” [25]. He obviously was not the only engineer of his time, but he was the best and exceeded by far the achievements of his contemporaries and predecessors. For example, he improved Roberto Valturio’s (1405–1475, Rimini) and Francesco di Giorgio Martini’s (1439–1501, Siena) machine designs and the hydraulic contraptions of Mariano di Iacopo’s (1382–1453, Siena), known as “Il Taccola”. He also complemented and surpassed Brunelleschi’s crane designs for his project for the diversion of the Arno River. In fact, in his technical designs more than 500 years ago, he already included most of the documents which make up a Project. According to Sara Taglialagamba, [26], the definition “Leonardo industrial designer” was first introduced by Carlo Pedretti in his book Leonardo Architetto [27].

3.4. Leonardo and the Scientific Method The influence of Leonardo da Vinci’s work in the history of science is of fundamental importance [28,29]. Although he obviously learned from his predecessors, his contributions to scientific development have not been established until recently. In the architectural field, Filippo Brunelleschi (1377–1446) and his disciple Leon Alberti (1404–1472) influenced his work. In the mechanical field, it has been established that he read Ponderibus’s Tratactus and the Treatise on Weights by Biagio Pelacani, also known as Blasius de Parma (1365–1416). He was also influenced by the school of Giordano de Nemore and by Albert of Saxony (1320–1390), to whom we owe a theory of weight which influenced the development of mechanics by solving many difficulties of Aristotelian physics. His friend, the mathematician, philosopher and professor at the University of Pavia, Facio Cardano (1444–1524), gave him access to the treatise “Perspectiva Communis” by the theologian, professor at the University of Oxford and archbishop, Jhon Peckham (1220/1225–1290), while in optics and mathematics he studied the texts of the Polish friar, theologian, and mathematician Witelo (Erazm Ciolek) (1230–1280/1290) and of the Arab physicist, astronomer, and mathematician Alhacen (Ibn Al-Haitam) (965–1040) [30,31]. The scientific method is based on observing a phenomenon, developing hypotheses, and carrying out the corresponding experiments to confirm or discard said hypothesis. If the experiments confirm the hypotheses, the link of certainty (law) is established, and if they do not confirm it, it returns to the beginning. Leonardo, as its precursor, did it in a similar way, opting in his investigations for the experimental or investigatory system of Aristotelian roots. Thus, he writes: “Mathematics gives us the supreme certainty”; “No human investigation can be called true science if it does not go through mathematical proof” or “no certainty exists where any of the mathematical sciences or those connected with them cannot be applied” [32]. Or also [17]: “Before proceeding with an investigation, I will do some experiment, because my intention is to invoke the experience first and then demonstrate, with reasoning, why such experience must operate in such a way.” “And this is the true rule according to which observers of natural effects must proceed. As much as nature begins with reason and ends in experience, we must follow the opposite course, that is, begin, as I said before, with experience, and with it investigate the reason.” “Experience is never wrong, only your judgements are wrong, promising strange results to personal experimentation” [28]. Thus, for example, he was concerned with the strength of beams and made mathematical formulations about their bending strength. He managed to define laws, although imperfect, regarding beams’ elastic line for different sections (for square, horizontal and end-supported beams), coming to observe that the strength varies in relation to the square of its length. Unlike most of those who later came to be at the forefront of the construction of the scientific method (Galileo, Descartes, Newton, and Leibniz), Leonardo da Vinci was not a mathematician. Designs 2020,, 4,, 38x FOR PEER REVIEW 6 of 20

Leonardo would use abstraction by replacing time with a succession of drawings, each representing Hea certain took instant. mathematics classes with Luca Pacioli [29]; however, his relationship with mathematics was mainlySoledad based Álvarez, on geometry, Professor due of toArt his History great interest at the inUniversity studying theof lawsOviedo of linearstated perspective. that “The Leonardomultifaceted would and usemasterful abstraction creative by replacing activity of time Leonardo with a successionis the origin of of drawings, the scientific each representingillustration in a certainwhich image instant. outweighs theoretical reflection in thoroughness and accuracy” [33]. Soledad Álvarez, Professor of Art History at the University of Oviedo stated that “The multifaceted and3.5. The masterful Scientific creative Method activity in Action: of LeonardoTests and Experiments is the origin of the scientific illustration in which image outweighsFor his theoretical projects and reflection designs, in Leonardo thoroughness needed and to accuracy” know the [ 33efforts]. that both the material meant to be used and the human resources employed could make. For this reason, he carries out his own 3.5. The Scientific Method in Action: Tests and Experiments studies on strength of materials and human nature. Thus, he studies the buckling behaviour in beams as loadsFor are his projectsapplied at and their designs, centre Leonardo. He also does needed it with to know ropes the and eff cablesorts that when both they the are material subjected meant to tostresses, be used both and directly the human and through resources pulleys employed [34]. He could also make. studies For friction this reason, between he different carries out bodies his ownand studieson rolling on strengthelements of on materials different and surfaces. human All nature. this Thus,to establish he studies possible the buckling transferable behaviour estimates in beams after aseach loads of his are projects. applied at their centre. He also does it with ropes and cables when they are subjected to stresses,The bothMadrid directly Codices and through I and II pulleys (Figure [34 ].2) Heare also resp studiesectively friction entitled between “Treatise different on bodiesStatic and onMechanics” rolling elements and “Treatise on different on Fortification, surfaces. All thisStatic to and establish Geometry” possible [35]. transferable Among estimatesManuscripts after at each the ofFrench his projects. Institute in Paris, Manuscript “E” is a treatise on physics and mechanics, and Manuscript “M” is oneThe on Madrid geometry. Codices In the I and London II (Figure Forster2) are Codex respectively, there entitledare themes “Treatise of geometry, on Static andhydraulics, Mechanics” and andphysics. “Treatise Finally, on Fortification,the Codex Atlanticus Static and (Ambrosian Geometry” [Library35]. Among of Milan) Manuscripts also has at pages the French with topics Institute of inmechanics, Paris, Manuscript physics, and “E” mathematics. is a treatise on physics and mechanics, and Manuscript “M” is one on geometry.Although In the his London studies Forster in mechanics Codex, have there some are themes errors, of he geometry, is also recognised hydraulics, for and some physics. contributions Finally, theto the Codex science Atlanticus and strength (Ambrosian of materials, Library such of Milan)as being also the has first pages one to with draw topics the ofcatenary mechanics, and propose physics, andits study mathematics. using a discrete model still in use today [36].

Figure 2. Study of weights. Madrid Madrid Codex Codex I, I, ff.ff. 76 76 v, v, 77 r. National Library of Spain [[4].4].

4. ContributionsAlthough his to studies Graphic in mechanicsRepresentation have some Techniques errors, hefor is Design also recognised for some contributions to theIn science the words and of strength the writers of materials, and historians such as Luca being Antoccia the first and one Carlo to draw Pedretti, the catenary “Leonardo and can propose boast itsof having study using had an a discrete indisputable model primacy, still in use which today pl [aces36]. him at the head of the beginnings of modern 4.scientific Contributions illustration. to Graphic Indeed, Representationno one before him Techniques had been forable Design to expose a complex technical project so effectively in a drawing” [37]. InHow, the words500 years of the ago, writers did Leonardo and historians da Vinci Luca manage Antoccia to and carry Carlo out Pedretti, such high-quality “Leonardo cantechnical boast ofdesigns having and had to anformulate indisputable his conceptual primacy, whichmodels places solelyhim through at the drawing? head of theLeonardo beginnings took ofadvantage modern of his great knowledge in drawing and painting, together with his spectacular creative capacity, to generate an important contribution of graphic techniques that can be used in technical designs. Designs 2020, 4, 38 7 of 20

Designs 2020, 4, x FOR PEER REVIEW 7 of 20 scientific illustration. Indeed, no one before him had been able to expose a complex technical project so effectivelyThis section in a drawing” will discuss [37]. three of the main contributions to graphical representation techniques developedHow, by 500 Leonardo years ago, da did Vinci, Leonardo explosion da Vincidiagrams manage, charts to of carry route out families, such high-quality path diagrams, technical and bird’sdesigns eye and maps. to formulate his conceptual models solely through drawing? Leonardo took advantage of his great knowledge in drawing and painting, together with his spectacular creative capacity, 4.1.to generate Explosion an or important Exploded Diagrams contribution of graphic techniques that can be used in technical designs. This section will discuss three of the main contributions to graphical representation techniques This object representation technique has been very useful for understanding the conformation developed by Leonardo da Vinci, explosion diagrams, charts of route families, path diagrams, and bird’s and operation of machines and products. But it was not until the middle of the 20th century that the eye maps. term emerged as a three-dimensional (isometric) illustration that shows the coupling relationship of parts,4.1. Explosion subsets, orand Exploded large assemblies. Diagrams It can also show the assembly or disassembly sequence of the detailed parts. It is still widely used today to capture joint interior views of drawings of mechanisms, mechanicalThis object or electrical representation elements, technique etc. Three-di has beenmensional very useful views forand understanding animation are thethe conformationnew heirs of thisand technique. operation of machines and products. But it was not until the middle of the 20th century that the termLeonardo, emerged aswho a three-dimensional dissected both human (isometric) bodies illustration (in his facet that as showsan anatomist), the coupling and relationshipmachines and of artefactsparts, subsets, (in his andengineering large assemblies. facet) into It individual can also show parts, the needed assembly to represent or disassembly them through sequence separate of the parts,detailed but parts. without It is losing still widely sight of used the today whole. to For capture this purpose, joint interior he used views this of drawingstechnique, of together mechanisms, with themechanical identification or electrical and description elements, of etc. the Three-dimensionalparts through letters views and short and animationtexts close areto the the views, new heirs which of isthis why technique. he can be considered the precursor of the use of explosion diagrams for anatomical studies and, togetherLeonardo, with who the dissected Italian engineer both human Mariano bodies di Jacopo (in his “Il facet Taccola”, as an anatomist), for machines and and machines artefacts. and artefactsAs an (in example, his engineering in the Codex facet) Atlanticus, into individual f. 30 v parts, at the needed Ambrosian to represent Library themof Milan, through he draws separate his assembledparts, but without machine losing (argano) sight in of perspective the whole. (Figure For this 3), purpose, and to heits usedright thishe decomposes technique, together it in detail, with also the inidentification a perspective and view, description as if it ofhad the “exploded” parts through but letters so that and although short texts the close mechanisms to the views, are whichalready is separate,why he can they be retain considered their overall the precursor vision. Thus, of the it use does of explosionnot require diagrams any explanation for anatomical for its construction studies and, ortogether to understand with the its Italian operation. engineer Mariano di Jacopo “Il Taccola”, for machines and artefacts. ItAs is ana machine example, for in thelifting Codex weights Atlanticus, composed f. 30 of v ata mechanism the Ambrosian for Libraryalternating of Milan, movement he draws from his a crank,assembled produced machine by (argano)a human in being, perspective which (Figure is conver3), andted to itsa continuous right he decomposes movement it inso detail,that it alsolifts in a weighta perspective steadily. view, The as machine if it had invented “exploded” by butLeonardo so that has although as its themain mechanisms drive a mechanism are already that separate, today wouldthey retain be called their me overallchanical vision. hammers. Thus, it does not require any explanation for its construction or to understand its operation.

(a) (b)

FigureFigure 3. ((aa)) Reciprocating machinemachine for for weight weight lifting lifting (Argano), (Argano), Codex Codex Atlanticus Atlanticus f. 30 f. v,(1478–1480)30 v, (1478–1480) [38]; [38];(b) Model (b) Model at the at Museum the Museum of Science of Science and Technologyand Technology of Milan of Milan [39]. [39].

4.2. DiagramsIt is a machine or Charts for of lifting Route weightsFamilies composed of a mechanism for alternating movement from a crank, produced by a human being, which is converted to a continuous movement so that it lifts a He is also a pioneer in making use of what are now called route family graphics, valid to weight steadily. The machine invented by Leonardo has as its main drive a mechanism that today represent a parameter or a variable that varies only depending on another single variable. would be called mechanical hammers. Leonardo estimated that the increase or decrease in force or natural “potenze” follows a pyramidal law; that is, an arithmetic proportion (he extended his Pyramidal Law of Optics to stresses, which he assimilated to the inclined plane or wedge-shaped triangle, as well as to pressure in his hydraulic studies). He stated that force increases with speed and decreases with distance, while Designs 2020, 4, x FOR PEER REVIEW 8 of 20 weight and percussion increase proportionally with speed. For him, his Pyramidal Law represented a universal constant. In his studies of screw fasteners, to justify their development, he also assimilates them to an inclined plane, and he explains its relationship with helical development in an existing diagram in the Madrid Codex I, f. 86 v at the National Library of Spain (Figure 4). He also studies the phenomenon of pressure in different cases: in open watercourses, as in his design of the irrigation channel to San Cristofano, existing in the Codex Atlanticus f. 1097 r at the AmbrosianaDesigns 2020, 4, 38Library of Milan (1509); in the reach of water jets, as can be seen in the detail of8 ofthe 20 Madrid Codex I, f. 134 v, at the National Library of Spain (Figure 5), where the “pyramidal” consideration4.2. Diagrams orof Chartsthe phenomenon of Route Families is observed again (the distance or reach of the jet decreases by increasing its height); or in closed pressure vessels, in his study of the reach of pressurised water in ManuscriptHe is also C, ac. pioneer7 r, at the in makingFrench Institute use of what in Paris are now (France). called route family graphics, valid to represent a parameterLikewise, or he a variable can be considered that varies a only pioneer depending in the us one of another diagrams single in a variable. circular arrangement, using a simileLeonardo of the estimatedstring diagrams, that the in increase order to or show decrease functional in force orrelationships natural “potenze” between follows different a pyramidal parts of thelaw; drawing, that is, an such arithmetic as force proportion lines. For example, (he extended Leonardo his Pyramidal estimated Law that ofthe Optics force toneeded stresses, to overcome which he theassimilated inclined toplanes the inclined followed plane an arithmetic or wedge-shaped ratio, so triangle, in one of as his well traction as to pressure studies, into hiscalculate hydraulic the necessarystudies). traction He stated force that in forcea bullock increases cart in with relation speed to andthe diameter decreases of withthe car distance, wheels, while he expresses weight theand growth percussion of the increase wheel using proportionally a concentric with circular speed. drawing For him, and hisrelates Pyramidal it to the Law lateral represented pyramid of a theuniversal effort that constant. the oxen must make (Codex Atlanticus f. 561 v, at the Ambrosiana Library of Milan). He alsoIn hisuses studies similar of circular screw diagrams fasteners, for to justifyhis studies their of development, mechanics and he optics also assimilatesin the Arundel them Codex, to an f.inclined 93 r at the plane, British and Library he explains in London, its relationship which records with helical a ratio development between a degree in an existing of momentum diagram and in theits correspondingMadrid Codex degree I, f. 86 vof at percussion the National in Florentine Library of units Spain of (Figure measure.4).

Figure 4. 4. StudyStudy of of screw screw fastener fastener development, development, Madrid Madrid Codex Codex I, f. I,86 f. v 8687 vr. National 87 r. National Library Library of Spain of [4].Spain [4].

He also studies the phenomenon of pressure in different cases: in open watercourses, as in his design of the irrigation channel to San Cristofano, existing in the Codex Atlanticus f. 1097 r at the Ambrosiana Library of Milan (1509); in the reach of water jets, as can be seen in the detail of the Madrid Codex I, f. 134 v, at the National Library of Spain (Figure5), where the “pyramidal” consideration of the phenomenon is observed again (the distance or reach of the jet decreases by increasing its height); or in closed pressure vessels, in his study of the reach of pressurised water in Manuscript C, c. 7 r, at the French Institute in Paris (France). Designs 2020, 4, 38 9 of 20 Designs 2020, 4, x FOR PEER REVIEW 9 of 20

Figure 5. WaterWater reach detail, Codex Madrid I, f. 134 v, National Library of Spain [[4].4].

4.3. Bird’s-EyeLikewise, Maps he can be considered a pioneer in the use of diagrams in a circular arrangement, using a simileLeonardo of the string is also diagrams, the author in order of several to show plans functional and maps, relationships especially between of cities di andfferent land parts linked of the to Tuscanydrawing, and, such to as a forcelesser lines. extent, For to example, the Papal Leonardo States of that estimated time. He that developed the force neededthem during to overcome his second the Florentineinclined planes period followed (1500–1506), an arithmetic at the beginning ratio, so in of one which of his he traction served studies,César Borgia to calculate (Rome the 1475–Viana necessary 1507),traction who force appointed in a bullock him cart architect in relation and to general the diameter engineer of theof the car wheels,papal dominions. he expresses “We the order growth and of commandthe wheel usingthat the a concentric bearer of circularthis, our drawing well-loved and and relates very it exalted to the lateral architect pyramid and general of the e ffengineerort that Leonardothe oxen must da Vinci, make who (Codex we have Atlanticus commissioned f. 561 v, atthe the in Ambrosianaspection of the Library squares of Milan).and fortresses He also of uses our states,similar be circular given diagramsthe help required for his studies in each of case mechanics or that in and his optics judgement in the he Arundel deemsCodex, necessary f. 93 ”[32]. r at theAt hisBritish service, Library he incarried London, out which studies records of fortificatio a ratio betweenns and acities degree and of accompanied momentum and him its in corresponding his military campaignsdegree of percussion on Romagna. in Florentine units of measure. During the government (Signorina) of the city of Florence, Leonardo was chosen to write the 4.3. Bird’s-Eye Maps project for the diversion of the Arno river so that Florence would have direct access to the sea, without goingLeonardo through Pisa, is also its theenemy author city. of The several promoter plans of and the maps, idea had especially been Nicolas of cities Machiavelli and land (Florence linked to Tuscany1469–1527) and, in to1503, a lesser as secretary extent, to of the the Papal Florentine States of Chancellery. that time. He It developedwas in this them project during that hisLeonardo second actedFlorentine the longest period as (1500–1506), a cartographer/topographer, at the beginning of producing which he magnificent served César plans Borgia and (Rome maps 1475–Vianawith detail 1507),and precision who appointed like no one him else architect had ever and achieved general be engineerfore. Most of of the them papal are dominions. found in the “We Royal order Library and ofcommand Windsor, that in the the Design bearer and of this, Prints our Cabinet well-loved of the and Uffizi very Gallery exalted in architectFlorence, and and general in the Leonardo engineer Museum,Leonardo in da Vinci. Vinci, who we have commissioned the inspection of the squares and fortresses of our states,He be also given studied the help and requiredimproved in the each perspective case or that tech innique, his judgement so that together he deems with necessary” his mastery [32 of]. Atdrawing his service, and colour, he carried he was out able studies to generate of fortifications views from and the cities sky and of the accompanied areas and highlight him in his whatever military hecampaigns wanted at on any Romagna. time in an exceptional way (Figure 6). Until the “Quattroccento”, and even much later,During slopes were the government represented (Signorina) as simple “molehil of the cityls” of(e.g., Florence, the Map Leonardo of the “Trasimeno” was chosen toLake write or “di the projectPerugia” for from the diversion1600, by the of theItalian Arno cartographer river so that and Florence mathematician would have Giovanni direct access Antonio to the Magini sea, without (1555– 1617),going throughalmost 100 Pisa, years its enemyafter Leonardo’s). city. The promoter of the idea had been Nicolas Machiavelli (Florence 1469–1527)Leonardo in 1503,overcomes as secretary all this of and the Florentineuses contour Chancellery. shading and It was his in “chiaroscuro” this project that technique Leonardo to achieveacted the greater longest objectivity as a cartographer in the representation/topographer, of producing the territory. magnificent In addition, plans he used and maps the distortion with detail of scalesand precision technique like in no the one appropriate else had ever areas achieved to highli before.ght what Most he of considered them are found necessary in the (watercourses, Royal Library cities,of Windsor, mountains in the and Design valleys, and Printsetc.). The Cabinet combination of the U ffiofzi all Gallery these intechniques Florence, shows and in maps the Leonardo with an exceptionalMuseum, in finish Vinci. for those who see them, with an adequate sense of depth, size, or comparative distance in relation to the rest of the drawing, making Leonardo the precursor of “bird’s-eye view” plans and maps, when it was not possible to view places from the air. Designs 2020, 4, 38 10 of 20

He also studied and improved the perspective technique, so that together with his mastery of drawing and colour, he was able to generate views from the sky of the areas and highlight whatever he wanted at any time in an exceptional way (Figure6). Until the “Quattroccento”, and even much later, slopes were represented as simple “molehills” (e.g., the Map of the “Trasimeno” Lake or “di Perugia” from 1600, by the Italian cartographer and mathematician Giovanni Antonio Magini (1555–1617), almost 100 years after Leonardo’s). Designs 2020, 4, x FOR PEER REVIEW 10 of 20

Figure 6. Map of the Val di Chiana, Royal Collection, RLW 12278, (1502–1504). [40]. Figure 6. Map of the Val di Chiana, Royal Collection, RLW 12278, (1502–1504) [40]. 4.4. Contribution of This Techniques to the Practice of Design Leonardo overcomesPlans, along all with this models and usesand prototypes, contour are shading the most andimportant his “chiaroscuro”form of communication technique in to achieve greater objectivitydesign in practice. the representation As seen in the three oftechniques the territory. presented, Leonardo In addition, takes advantage he used of his the creative distortion of scales ingenuity, his mastery of drawing and painting, and his exceptionally advanced knowledge of technique in thegeometry appropriate and perspective areas to to innovate highlight in the whattechniques he consideredof graphic repres necessaryentation with (watercourses, highly cities, mountains andaccurate valleys, diagrams, etc.). graphs, The combination charts and plans, of and all impressive these techniques graphic quality. shows maps with an exceptional finish for those whoIn this see regard, them, the Director with anof the adequate Institute and sense Museum of for depth, the History size, of Science or comparative in Florence, distance in Paolo Galluzi, states: “The objective pursued by Leonardo is to provide a precise and absolutely clear relation to the restrepresentation of the of drawing, the structure making and operation Leonardo of extremely the complex precursor mechanisms, of “bird’s-eye using a series view”of plans and maps, when it wasgraphic not resources possible (plan toand view elevation places views, from transp thearency air. views, component views, simulation of kinematic chains, use of “chiaroscuro” to underline the surfaces in contact, schematization of the lines of force, etc.) that nobody before he had organically conceived and, above all, consciously applied to 4.4. Contributiona communication of This Techniques project related to the to Practicethe horizon of of Designtechnology” [33].

Plans, along5. Contributions with models to Design and prototypes, Tools and Instruments are the most important form of communication in design practice. As seen inProject the threetheorists techniques emphasise the presented, importance of the Leonardo instruments takes and tools advantage applicable to of it, histhus creativethe ingenuity, his mastery of drawingso-called systemic and ones painting, such as Hubka and and his Eder exceptionally in their “Theory advancedof Technical Systems” knowledge [22] specify of geometry and the need to be knowledgeable of the instruments that can be used to design, while the non-systemic perspective to innovateones such as inGómez-Senent the techniques classify the of Operating graphic Instruments representation as a fundamental with dimension highly of accurate the diagrams, graphs, charts andProject/Design plans, and[41]. impressive graphic quality. Leonardo contributed innovations such as the improvement of the adjustable opening compass, In this regard,the creation the Directorof a parabolic of compass the Institute as the first andgeneration Museum of ellipsographs, for the the History improvement of Scienceof the in Florence, Paolo Galluzi, states:prospectograph, “The objectivehis odometer, pursued or his darkroom. by Leonardo is to provide a precise and absolutely clear representation5.1. of The the Compasses structure and operation of extremely complex mechanisms, using a series of graphic resourcesSince (plan ancient and times, elevation the compass views, has transparencybeen an important views, design componentinstrument both views,for the simulation of kinematic chains,generation use of of “chiaroscuro” circumferences, as to well underline as for obtaining the surfaces the bisectors in contact,of angles, the schematization drawing of of the lines of force, etc.) thatperpendicular nobody and before parallel he lines, had the organically comparison between conceived measurements, and, aboveand evenall, has been consciously used in applied to a proportional calculation. communication projectThe Greeks related already to considered the horizon it as the of most technology” elegant and extremely [33]. simple construction tool, not only due to its application area is design, but also for mathematics, astronomy, navigation, 5. Contributionstopography, to Design military Tools use, etc. and It has Instruments also been widely used as an indicative representation element of science and art. Project theoristsA large emphasise number of special the importance compasses were of created the instruments in the Renaissance, and with tools specific applicable functions to it, thus the such as the generation of ellipses, parables, etc. Leonardo is no stranger to it; he designed various so-called systemiccompass ones models such both as for Hubka conventional and use Eder with an in adjustable their “Theory opening, as well of Technical as other more Systems”complex [22] specify the need to be knowledgeable of the instruments that can be used to design, while the non-systemic ones such as Gómez-Senent classify the Operating Instruments as a fundamental dimension of the Project/Design [41]. Leonardo contributed innovations such as the improvement of the adjustable opening compass, the creation of a parabolic compass as the first generation of ellipsographs, the improvement of the prospectograph, his odometer, or his darkroom. Designs 2020, 4, 38 11 of 20

5.1. The Compasses Since ancient times, the compass has been an important design instrument both for the generation of circumferences, as well as for obtaining the bisectors of angles, the drawing of perpendicular and parallel lines, the comparison between measurements, and even has been used in proportional calculation. The Greeks already considered it as the most elegant and extremely simple construction tool, not only due to its application area is design, but also for mathematics, astronomy, navigation, topography, military use, etc. It has also been widely used as an indicative representation element of science and art. A large number of special compasses were created in the Renaissance, with specific functions such as the generation of ellipses, parables, etc. Leonardo is no stranger to it; he designed various compass models both for conventional use with an adjustable opening, as well as other more complex ones suitable for drawing conical curves such as ellipses (the so-called ellipsograph), or parables (parabolic Designs 2020, 4, x FOR PEER REVIEW 11 of 20 compass). He also designed moving centre reduction compasses and even created a compass for epicycloidones curves. suitable for drawing conical curves such as ellipses (the so-called ellipsograph), or parables As a(parabolic true example compass). of theHe also Renaissance designed moving and as centre a humanist, reduction hecompasses assimilated and even man created as the a centre of compass for epicycloid curves. the universe,As and a true as aexample great of lover the Renaissance of nature, and he as studied a humanist, its he proportions assimilated man and as the established centre of the their ideal, generatinguniverse, around and 1492 as hisa great famous lover “Vitruvian of nature, he Man” studied (in its honor proportions of the brilliantand established Roman their architect) ideal, or of the “divine proportions”generating around (existing 1492 his in famous the Accademia “Vitruvian Gallery,Man” (in honor Venice). of the In brilliant his attached Roman architect) text he writes:or of “ ... if a man liesthe on “divine his back, proportions” with his (existing hands andin the feet Accademia extended, Gallery, and Venice). places In the his endattached of a text compass he writes: on his navel, “… if a man lies on his back, with his hands and feet extended, and places the end of a compass on the fingershis and navel, toes the will fingers touch and toes the will circumference touch the circumference of the circle of the that circle we that thus we thus draw” draw [42 ”[42].]. His compassHis compass models models (Figure (Figure7) are 7) are reflected reflected in in severalseveral of of his his codices codices and manuscripts, and manuscripts, some with some with exceptionalexceptional detail that detail would that would allow allow their their construction construction and and use. use.

(b)

(a) (c)

Figure 7. Figure(a) Reproduction 7. (a) Reproduction of a of compass a compass designed designed by by Leonardo, Leonardo, [43];[ (43b)]; proportional (b) proportional or reduction or reduction compass. Forster Codex I f. 45 (1485), [44]; (c) Parabolic Compass. Codex Atlanticus f. 1093 r, [45]. compass. Forster Codex I f. 45 (1485), [44]; (c) Parabolic Compass. Codex Atlanticus f. 1093 r, [45]. 5.2. The Prospectograph The Italian architect León Battista Alberti (1404–1472) already mentioned the use of this instrument in some of his works [46], but Leonardo is the first to draw it in detail in his Codex Atlanticus in f. 5 r (1480–1482) and describe its use. Even Leonardo himself is drawn using his veil prospectograph, drawing an armillary sphere (Figure 8). Leonardo distinguishes and uses two kinds of prospectographs: the veiled and the glass one. For the one with a veil, already named by Alberti, the observed image is drawn directly with some staining element (e.g., bitumen) and is later transferred to paper. The other, the glass one, is based on the representation on glass of the external reality maintaining a fixed point of view; it is the one that Designs 2020, 4, 38 12 of 20 Designs 2020, 4, x FOR PEER REVIEW 12 of 20 uses5.2. Thea window Prospectograph full of grids (also known as Leonardo’s Window), where the designer observes the object through the scope of the prospectograph and transfers them to his paper, where there are also gridsThe similar Italian to architect those of Le theón Battistawindow Alberti (this (1404–1472)model is the already one that mentioned Albert theDürer use (1471–1528) of this instrument later popularisedin some of his in Germany). works [46], but Leonardo is the first to draw it in detail in his Codex Atlanticus in f. 5 rFrom (1480–1482) the study and describe and analysis its use. of Even the Leonardo drawings himself thus ismade, drawn the using principles his veil prospectograph,governing the representationdrawing an armillary in a conical sphere perspect (Figureive8). were subsequently established.

Figure 8. Enlarged detail of the prospectograph being used byby Leonardo.Leonardo. Codex AtlanticusAtlanticus f.f. 5 r [47]. [47]. Leonardo distinguishes and uses two kinds of prospectographs: the veiled and the glass one. 5.3.For Odometer the one with and aPedometer veil, already named by Alberti, the observed image is drawn directly with some stainingAn odometer element (e.g., is a device bitumen) that andindicates is later the transferred distance travelled to paper. by The the other,person, the or glassby the one, vehicle is based that hason theit incorporated representation (from on glassthe Greek of the “hodo” external = road reality and maintaining “metron” = ameasurement). fixed point of view;It is the it precursor is the one ofthat the uses distance a window indicators full of and grids tachographs (also known of astoda Leonardo’sy’s vehicles. Window), Initially where of mechanical the designer constitution, observes todaythe object they through are electronic. the scope of the prospectograph and transfers them to his paper, where there are also gridsThe Greek similar mathematician, to those of the engineer, window and (this astronom model iser the Archimedes one that Albert of Syracuse Dürer (1471–1528)(287 BC–212 laterBC) popularisedis credited with in Germany). the possible invention of this instrument. Later, the Roman architect and engineer VitruvioFrom (80 the≈70 study BC–15 and BC) analysis mentions of the it drawings again in thushis treatise made, the “De principles Architectura”. governing It seems the representation that its first usein a conicalwas made perspective by the wereengineer subsequently and mathematicia established.n Herón de Alejandría (1st–75th century), by incorporating5.3. Odometer andgears Pedometer into the carriage wheels in order to know the distance travelled by them. However, it was not until the Renaissance that Leonardo described its construction and characteristics,An odometer being isa the device first thatto draw indicates it to detail. the distance travelled by the person, or by the vehicle that has itLeonardo, incorporated in (from1502 (first the Greek Roman “hodo” stage),= road was and commissioned “metron” = measurement).by César Borgia It is (son the precursorof Pope Alexanderof the distance VI) when indicators he was and named tachographs “architect of today’s and general vehicles. engineer Initially of of the mechanical Papal dominions”, constitution, to establishtoday they defences are electronic. and improvements in the fortifications of the Pope “Borgia” dominions. To do this, he neededThe Greek to carry mathematician, out large longitudinal engineer, and measurements, astronomer Archimedesfor which he of devised Syracuse several (287 BC–212automated BC) lengthis credited measurement with the possible machines. invention On folio of1b this r (aroun instrument.d 1504) of Later, the Codex the Roman Atlanticus architect at the and Ambrosian engineer Vitruvio (80 70 BC–15 BC) mentions it again in his treatise “De Architectura”. It seems that its first use Library in Milan≈ (Figure 9), two odometers and a pedometer are drawn in detail. was madeThe trolley-shaped by the engineer andodometer mathematician measured Her ólengthn de Alejandrs with íthea (1st–75th units century),established by incorporatingat the time (“braccias”),gears into the while carriage the pedometer wheels in order measured to know it with the distancethe equivalence travelled to by“steps” them. of However, the person it wasdriving not it.until the Renaissance that Leonardo described its construction and characteristics, being the first to drawIn it Leonardo’s to detail. Odometer, the cogwheel was “designed to advance one tooth every 10 bracces travelledLeonardo, (about in 6 1502m), until, (first Romanwhen reaching stage), was sixteen commissioned hundred meters by César (one Borgia mile), (son a pebble of Pope fell Alexander audibly VI)into when a metal he container” was named [10]. “architect For each and turn general of the engineer large central of the wheel, Papal dominions”,one tooth of tothe establish lateral cogwheel defences wasand improvementsadvanced vertically; in the fortifications once the total of the turn Pope of “Borgia” the latter dominions. had been To exhausted, do this, he neededanother to upper carry horizontalout large longitudinal wheel was already measurements, activated, for which which had he devised incorporated several small automated balls or length round measurement stones in its uppermachines. part, Onand folio one 1bof rthem (around was 1504)dropped of theinto Codex a box Atlanticuslocated in the at the lower Ambrosian part of the Library trolley. in It Milan was (Figureenough9 to), twocount odometers the number and of a balls pedometer that had are fallen drawn to inknow detail. the length travelled. Designs 2020,, 4,, 38x FOR PEER REVIEW 13 of 20

(a) (b)

Figure 9. ((a)) Study ot two odometers.odometers. Codex Codex Atlanticus, Atlanticus, f. f. 1b 1b r, r, [48] [48];; ( (bb)) Odometer model at the National Museum of Science and Technology ofof MilanMilan [[49].49].

5.4. ContributionThe trolley-shaped of this Tool odometers to the measuredPractice of lengthsDesign. with the units established at the time (“braccias”), while the pedometer measured it with the equivalence to “steps” of the person driving it. Designers need tools that allow them to trace their plans and drawings with precision; they need In Leonardo’s Odometer, the cogwheel was “designed to advance one tooth every 10 bracces tools to transfer to said plans the existing reality on which the designed object is going to be inserted; travelled (about 6 m), until, when reaching sixteen hundred meters (one mile), a pebble fell audibly they need tools so that the designed object, the artifact, is brought to life, and built to the correct into a metal container” [10]. For each turn of the large central wheel, one tooth of the lateral cogwheel dimensions. Leonardo was not just satisfied with proposing innovative designs and leaving them at was advanced vertically; once the total turn of the latter had been exhausted, another upper horizontal a conceptual level; he wanted to put them into practice, materialize them, and build them. wheel was already activated, which had incorporated small balls or round stones in its upper part, The tools that Leonardo refined contributed to improving the detailed design of the designed and one of them was dropped into a box located in the lower part of the trolley. It was enough to count objects, as well as being the perfect complement to take advantage of the advances in graphic the number of balls that had fallen to know the length travelled. representation techniques shown in the previous section. 5.4. Contribution of this Tools to the Practice of Design 6. Discussion on the Functional Feasibility of His Designs Designers need tools that allow them to trace their plans and drawings with precision; they need toolsA to large transfer number to said of plansthe devices, the existing machines, reality and on mechanisms which the designed designed object by Leonardo is going toDa be Vinci, inserted; and theyrepresented need tools in his so thatnearly the 7000 designed preserved object, manuscript the artifact, folios, is brought only reached to life, andthe level built of to conceptual the correct dimensions.design. For Leonardothis reason, was Leonardo’s not just satisfied activities with as proposing an engineer innovative have designsbecome andparticularly leaving them famous at a conceptualthrough a series level; heof wantedmodels towhose put them construction into practice, began materialize in Milan them, in the and 1930s build [33]. them. Although the accuracyThe toolsof some that of Leonardo the recons refinedtructions contributed has since to been improving questioned, the detailed and his designfamous of war the machines designed objects,were perhaps as well the as area being where the he perfect was least complement innovative to, his take contribution advantage lay of not the so advances much in the in gadgets graphic representationas in his new ways techniques of drawing shown them in theand previous his methodical section. approach to their underlying principles. It is also important to note that Leonardo’s designs of mechanisms and devices were based on 6.in-depth Discussion study on and the experimentation Functional Feasibility on the statics of His of Designs the rigid solid. He studied the deflection of bent beams subjected to different loads applied at different positions, trying to correlate stress and A large number of the devices, machines, and mechanisms designed by Leonardo Da Vinci, and deformation, also dealing with compound stresses, in terms of normal stress or bending. In order to represented in his nearly 7000 preserved manuscript folios, only reached the level of conceptual design. carry out these theoretical studies and characterise the strength of the materials, he designed For this reason, Leonardo’s activities as an engineer have become particularly famous through a series machines to perform tensile tests (Codex Atlanticus f. 82 r) and also for repeated impact tests (Codex of models whose construction began in Milan in the 1930s [33]. Although the accuracy of some of the Atlanticus f. 21 r) [50]. reconstructions has since been questioned, and his famous war machines were perhaps the area where On the other hand, most of Leonardo’s scientific-technical projects, due to the technological he was least innovative, his contribution lay not so much in the gadgets as in his new ways of drawing limitations of his time, never materialised, and none of them last to this day. For this reason, there is them and his methodical approach to their underlying principles. controversy over whether they could be put into practice with current instruments and materials, It is also important to note that Leonardo’s designs of mechanisms and devices were based on and, during the last decades, different researchers have tried to demonstrate the feasibility and in-depth study and experimentation on the statics of the rigid solid. He studied the deflection of benefits of his designs, some of which are analysed in this section. bent beams subjected to different loads applied at different positions, trying to correlate stress and Leonardo da Vinci carried out an enormous number of designs and projects, but to maintain deformation, also dealing with compound stresses, in terms of normal stress or bending. In order to coherence with the previous sections, when analysing examples of the functional feasibility of carry out these theoretical studies and characterise the strength of the materials, he designed machines Leonardo’s designs, artifacts linked to the material execution of construction projects have been to perform tensile tests (Codex Atlanticus f. 82 r) and also for repeated impact tests (Codex Atlanticus chosen; that is, tools that can be used in the works that Leonardo designed and/or carried out, such f. 21 r) [50]. as the crank lift, the hammer for piling, and the mechanical jacks. The self-propelled vehicle has also been included due to the absolute originality of this design. Designs 2020, 4, 38 14 of 20

On the other hand, most of Leonardo’s scientific-technical projects, due to the technological limitations of his time, never materialised, and none of them last to this day. For this reason, there is controversy over whether they could be put into practice with current instruments and materials, and, during the last decades, different researchers have tried to demonstrate the feasibility and benefits of his designs, some of which are analysed in this section. Leonardo da Vinci carried out an enormous number of designs and projects, but to maintain coherence with the previous sections, when analysing examples of the functional feasibility of Leonardo’s designs, artifacts linked to the material execution of construction projects have been chosen; that is, tools that can be used in the works that Leonardo designed and/or carried out, such as the crank lift, the hammer for piling, and the mechanical jacks. The self-propelled vehicle has also been included due to the absolute originality of this design.

6.1. The Manual or Crank Lift Designs 2020, 4, x FOR PEER REVIEW 14 of 20 Leonardo designed important works that required large land movements and lifting loads, so he designed6.1. The severalManual or machines Crank Lift and tools to facilitate these tasks. The Madrid Codex I, f. 9 r, at the National LibraryLeonardo of Spaindesigned contains important the works design that of required a device large suitable land tomovements act as a lift and or lifting manual loads, elevator so for loads (Figurehe designed 10). several It works machines by means and oftools a crank, to facilitate which these moves tasks. a wormThe Madrid screw Codex that makes I, f. 9 r, the at the gear rims and innerNational nuts Library turn, through of Spain contains which the the “pull”design ropeof a device or cable suitable slides. to act As as the a lift lifting or manual screw elevator prevents the mechanismfor loads from (Figure turning 10). It in works both by directions, means of a it crank, allows which for safemoves load a worm raising screw or that lowering. makes the Furthermore, gear rims and inner nuts turn, through which the “pull” rope or cable slides. As the lifting screw prevents with proper multiplication, it allows movement with very little effort. the mechanism from turning in both directions, it allows for safe load raising or lowering. AsFurthermore, proof of his with mastery proper multiplication, in weightlifting, it allows the movement Milanese with painter very little and effort. historian Giovanni Paolo Lomazzo (MilanAs proof 1538–1600) of his mastery stated in inweightlifting, 1590: “And the he Milanese showed painter the art and of lifting historian weights Giovanni with Paolo ease [with his books],Lomazzo of which(Milan 1538–1600) all of Europe stated is in full 1590: and “And are he held showed in high the art esteem of lifting among weights experts, with ease because [with they considerhis thatbooks], no of more which can all be of doneEurope than is full what and heare has held already in high done”esteem [among51]. In experts, fact, practically because they the same designconsider continues that tono bemore used can today be done in than construction what he has sites already for done” lifting [51]. loads In fact, or even practically for people-carrying the same design continues to be used today in construction sites for lifting loads or even for people-carrying scaffolding in façade work. scaffolding in façade work.

FigureFigure 10. Study 10. Study for thefor the mechanism mechanism of of a a manual manual lift (1495–1497), (1495–1497), Madrid Madrid Codex Codex I, f. 9 I, r, f. National 9 r, National Library of Spain [4,52]. Library of Spain [4,52]. 6.2. The Hammer for Piling Piling machines serve to insert precast wooden, concrete, or metal elements into the ground, in the form of a post or column. Its function is to prepare foundations in terrains that are unsuitable for building. Said elements, called “piles”, are usually “driven” into the ground by “hammer” blows, so that the element descends penetrating the ground until reaching the designed depth. In the Codex Atlanticus, f. 785 (around 1500) (Figure 11), Leonardo draws his machine for driving logs into the terrain that he intended to use in his project to divert the Arno river in Florence. It consists of a device that lifted a weight in a guided way using pulleys and cranks so that it hit the log with the highest possible force. The crank pulley ratio enabled the repetition of the operation. The essence of this way of working has not changed to this day compared to Leonardo’s design, except for the power source used for weightlifting. Designs 2020, 4, 38 15 of 20

6.2. The Hammer for Piling Piling machines serve to insert precast wooden, concrete, or metal elements into the ground, in the form of a post or column. Its function is to prepare foundations in terrains that are unsuitable for building. Said elements, called “piles”, are usually “driven” into the ground by “hammer” blows, so that the element descends penetrating the ground until reaching the designed depth. In the Codex Atlanticus, f. 785 (around 1500) (Figure 11), Leonardo draws his machine for driving logs into the terrain that he intended to use in his project to divert the Arno river in Florence. It consists of a device that lifted a weight in a guided way using pulleys and cranks so that it hit the log with the highest possible force. The crank pulley ratio enabled the repetition of the operation. The essence of this way of working has not changed to this day compared to Leonardo’s design, except for the power Designssource 2020 used, 4, x for FOR weightlifting. PEER REVIEW 15 of 20

(a) (b)

FigureFigure 11. 11. (a(a) )Study Study of of a apiling piling machine, machine, Codex Codex Atlanticus Atlanticus,, f 785, f 785, Ambrosian Ambrosian Library Library of Milan of Milan [53]; [ (53b)]; Model(b) Model of Leonardo’s of Leonardo’s pile pile machine, machine, at the at the National National Museum Museum of ofScience Science and and Technology Technology of of Milan Milan [54]. [54].

6.3.6.3. The The Mechanical Mechanical Jacks Jacks LeonardoLeonardo states states in in his his Notebooks: Notebooks: “Mechanics “Mechanics is is the the paradise paradise for for mathematical mathematical sciences, sciences, because because withwith it mathematics bear fruit”. A A great great connoisse connoisseurur of of physics, physics, mechanics, mechanics, metallurgy metallurgy and and the the operatingoperating principles principles of of machine machine elements, elements, he he uses uses this this knowledge knowledge to to develop develop several several machine machine tools. tools. AmongAmong them, them, he he designs at least three different different mechanical jacks. TheThe ratchet ratchet jack jack consists consists of of holding holding a a vertical vertical fixed fixed rack rack and and makes makes the the gear gear system system rise rise or or fall fall withwith the the weight by turning a crank. The The adequate adequate reduction reduction ratio ratio between between wheel wheel and and pinion pinion will will reducereduce the eeffortffort requiredrequired toto lift lift weights. weights. Leonardo Leonardo includes includes it it in in his his Codex Codex Atlanticus, Atlanticus, f. 0998f. 0998 r, at r, theat theAmbrosiana Ambrosiana Library Library of Milan of Milan (Figure (Figure 12a). 12a). Both Both in electromechanical in electromechanical workshops workshops and in and jacks in to jacks change to changewheels wheels in vehicles, in vehicles, this mechanism this mechanism is still used is still today. used today. The spindle jack uses a screw-nut mechanism that allows the displacement of the former by making a rotating movement over it while keeping the nut fixed. In this way, a circular movement is transformed into a rectilinear one. It is simple and safe, but slow to operate, since with one turn of the screw it only moves forward the length of the thread pitch. In the Codex Atlanticus f. 0138 r, at the Ambrosiana Library of Milan , he describes the design of a mechanical jack for lifting or dragging cannons, as well as another similar device for fixed dragging of loads, both using the spindle system. This type of jack is still common in both the metal mechanic and construction sectors. The screw jack with anti-friction bearing incorporates a kind of rotating toothed ball bearing, between the fixed support platform and the rotating upper toothed disc. In addition, it incorporates a lateral crank to facilitate rotation. Due to the presence of the ball bearing and a tooth sprocket on its upper part, the device works more easily and with less effort. It is included in the Madrid Codex I f. 34 r (Figure 12b) and f26 r (Figure 12c) at the National Library of Spain. This solution from Leonardo continues to be used today by tool manufacturing companies for mechanical workshops. Designs 2020, 4, 38x FOR PEER REVIEW 16 of 20

(a) (b) (c)

Figure 12. ((aa)) Detail Detail of of the the Codex Codex Atlanticus, Atlanticus, f. f.0998 0998 r, r,Ambrosian Ambrosian Library Library of ofMilan, Milan, [55]; [55 (];b) ( bdetail) detail of theof the Madrid Madrid Codex Codex I, f. I, 34 f. 34r, r,National National Library Library ofof Spain Spain [4]; [4 ];(c ()c )detail detail of of the the Madrid Madrid Codex Codex I, I, f. f. 26 26 r, r, National Library of Spain [[4].4].

6.4. TheThe First spindle Self-Propelled jack uses Vehicle a screw-nut mechanism that allows the displacement of the former by making a rotating movement over it while keeping the nut fixed. In this way, a circular movement Thoroughly knowledgeable about the elements of machines (his Madrid Codex I, entitled is transformed into a rectilinear one. It is simple and safe, but slow to operate, since with one turn “Treatise on Static and Mechanics”, from 1493, can be considered the most complete treatise on of the screw it only moves forward the length of the thread pitch. In the Codex Atlanticus f. 0138 r, Mechanics of the Renaissance), Leonardo designed the first self-propelled vehicle known in history. at the Ambrosiana Library of Milan, he describes the design of a mechanical jack for lifting or dragging He takes advantage of the force on two previously loaded spiral winding springs, enclosed in drum- cannons, as well as another similar device for fixed dragging of loads, both using the spindle system. shaped compartments, which transfer their power to two wheels. In the Codex Atlanticus, f. 812 r This type of jack is still common in both the metal mechanic and construction sectors. (1478–1480) at the Ambrosiana Library of Milan (Figure 13), he establishes his project with two views: The screw jack with anti-friction bearing incorporates a kind of rotating toothed ball bearing, one plan view, representing springs, gears, crossbows, etc., and another in perspective, where he between the fixed support platform and the rotating upper toothed disc. In addition, it incorporates a adds the idea of a possible steering system. Consisting of a small supplementary wheel coupled to its lateral crank to facilitate rotation. Due to the presence of the ball bearing and a tooth sprocket on its rear part and a stem accessible from above the vehicle, it would act as a steering wheel to be oriented upper part, the device works more easily and with less effort. It is included in the Madrid Codex I at convenience, or through previous programming. For the latter, he used “eccentrics” in different f. 34 r (Figure 12b) and f26 r (Figure 12c) at the National Library of Spain. This solution from Leonardo ways, incorporated into the rotary axes. Depending on the shape of the “eccentrics” initially continues to be used today by tool manufacturing companies for mechanical workshops. introduced, the direction of the vehicle will change. It also incorporates two adjustable front leaf springs6.4. The that First can Self-Propelled act as a control Vehicle for the gears that interconnect the power springs with the wheels to control the speed of the vehicle. Finally, it incorporates a wooden stem that acts as a general brake by Thoroughly knowledgeable about the elements of machines (his Madrid Codex I, entitled “Treatise remote control, acting on the teeth of the gears or horizontal wheels, preventing movement towards on Static and Mechanics”, from 1493, can be considered the most complete treatise on Mechanics the rear vertical wheels, ensuring that power is not transmitted to the wheels even in the event that of the Renaissance), Leonardo designed the first self-propelled vehicle known in history. He takes the springs are loaded. A ring acting on the stem and through a rope removed it from a distance, advantage of the force on two previously loaded spiral winding springs, enclosed in drum-shaped allowing the vehicle to move. In the lower part of the manuscript, the supplementary part that acted compartments, which transfer their power to two wheels. In the Codex Atlanticus, f. 812 r (1478–1480) as an initial brake operated from a distance by means of a rope is represented. at the Ambrosiana Library of Milan (Figure 13), he establishes his project with two views: one plan Used as a theatrical machine that moved by itself, in both straight and curved directions, he view, representing springs, gears, crossbows, etc., and another in perspective, where he adds the idea made an impression at the court parties of the Duke of Milan Ludovico Sforza (Vigevano 1452–Loches of a possible steering system. Consisting of a small supplementary wheel coupled to its rear part and a 1508), and later at the French court of King Francis I (Cognac, 1494–Rambouillet, 1547). stem accessible from above the vehicle, it would act as a steering wheel to be oriented at convenience, In 2004, after several studies carried out in the Science History Museum in Florence, directed by or through previous programming. For the latter, he used “eccentrics” in different ways, incorporated Italian historians and researchers Paolo Galluzzi (Florencia 1942–) and Carlo Pedretti (Bolonia 1928– into the rotary axes. Depending on the shape of the “eccentrics” initially introduced, the direction of Lamporecchio 2018), with the clarifying contributions from the American robotics professor Mark Designs 2020, 4, 38 17 of 20 the vehicle will change. It also incorporates two adjustable front leaf springs that can act as a control for the gears that interconnect the power springs with the wheels to control the speed of the vehicle. Finally, it incorporates a wooden stem that acts as a general brake by remote control, acting on the teeth of the gears or horizontal wheels, preventing movement towards the rear vertical wheels, ensuring that Designs 2020, 4, x FOR PEER REVIEW 17 of 20 power is not transmitted to the wheels even in the event that the springs are loaded. A ring acting on Ellingthe stem Rosheim, and through who digitalised a rope removed all the it fromnecessary a distance, parts, allowingit was possible the vehicle to put to move.into operation In the lower the automobile,part of the manuscript, giving actual the feasibility supplementary to the solution part that that acted Leonardo as an initial projected brake more operated than from 500 years a distance ago. by means of a rope is represented.

(a) (b)

Figure 13. ((aa)) Manuscript Manuscript of of the self-propelled vehicle, Codex Atlanticus,Atlanticus, f.f. 812 812 r r (1478–1480), (1478–1480), Ambrosiana Library of Milan, [56] [56];; ( b) Model at the National Museum of of Science Science and and Technology Technology of Milan, based on the Canestrini Model [[57].57].

7. ConclusionsUsed as a theatrical machine that moved by itself, in both straight and curved directions, he made an impression at the court parties of the Duke of Milan Ludovico Sforza (Vigevano 1452–Loches 1508), The figure of Leonardo da Vinci grows as we look deeper into his work. He was a master of and later at the French court of King Francis I (Cognac, 1494–Rambouillet, 1547). painting, delved into physics and anatomy, designed military and industrial machines, designed In 2004, after several studies carried out in the Science History Museum in Florence, directed by buildings and planned cities, and left a huge written work. However, the way in which he protected Italian historians and researchers Paolo Galluzzi (Florencia 1942–) and Carlo Pedretti (Bolonia or concealed his findings and the fragmentation, and even loss of his written work caused by his 1928–Lamporecchio 2018), with the clarifying contributions from the American robotics professor heirs, along with many of his innovations being too advanced for his time, led to the opinion that Mark Elling Rosheim, who digitalised all the necessary parts, it was possible to put into operation the much of Leonardo’s scientific-technical work was speculative. automobile, giving actual feasibility to the solution that Leonardo projected more than 500 years ago. In this paper, some of the main contributions of Leonardo da Vinci in the field of object and artifact7. Conclusions design have been analysed. After reviewing Leonardo’s main codices and manuscripts regarding the design of instruments and machines, and mentioning some of the main scholars of his The figure of Leonardo da Vinci grows as we look deeper into his work. He was a master of work, it focuses on analysing the foundations on which he supported his work as a designer. painting, delved into physics and anatomy, designed military and industrial machines, designed In the third section, from a conceptual approach, the principles of generating solutions most buildings and planned cities, and left a huge written work. However, the way in which he protected or used by Leonardo have been studied; inspiration by nature, the organic vision of mechanisms, concealed his findings and the fragmentation, and even loss of his written work caused by his heirs, analysis to decompose problems and synthesis for the integration of the designed object, the along with many of his innovations being too advanced for his time, led to the opinion that much of analogies with pre-existing designs, and the economy in the design by suppressing the superfluous. Leonardo’s scientific-technical work was speculative. After that, these design approaches have been correlated with some of the existing theories that In this paper, some of the main contributions of Leonardo da Vinci in the field of object and artifact propose the design of technical systems as a scientific discipline. Afterwards, it has been analysed design have been analysed. After reviewing Leonardo’s main codices and manuscripts regarding the how Leonardo applied the principles of observation and experimentation to obtain the physical laws design of instruments and machines, and mentioning some of the main scholars of his work, it focuses necessary to determine the mechanical and structural resistance of the designs developed by him. on analysing the foundations on which he supported his work as a designer. In the following sections, a more applied approach has been adopted, and we have studied how In the third section, from a conceptual approach, the principles of generating solutions most used Leonardo made contributions in the techniques of graphic representation (new exploded diagrams, by Leonardo have been studied; inspiration by nature, the organic vision of mechanisms, analysis to family charts and bird’s-eye maps) and the instruments that he created or improved to increase the precision in the plot (compasses), in the visualization and representation of objects in perspective (prospectograph) and the measurement tools (odometer and pedometer). Finally, we have presented the development of equipment and technical devices (the crank lift, hammer for piling, mechanical jacks, and even the first self-propelled vehicle), many of them designed to improve the effectiveness and efficiency of the projects in which Leonardo was involved. Designs 2020, 4, 38 18 of 20 decompose problems and synthesis for the integration of the designed object, the analogies with pre-existing designs, and the economy in the design by suppressing the superfluous. After that, these design approaches have been correlated with some of the existing theories that propose the design of technical systems as a scientific discipline. Afterwards, it has been analysed how Leonardo applied the principles of observation and experimentation to obtain the physical laws necessary to determine the mechanical and structural resistance of the designs developed by him. In the following sections, a more applied approach has been adopted, and we have studied how Leonardo made contributions in the techniques of graphic representation (new exploded diagrams, family charts and bird’s-eye maps) and the instruments that he created or improved to increase the precision in the plot (compasses), in the visualization and representation of objects in perspective (prospectograph) and the measurement tools (odometer and pedometer). Finally, we have presented the development of equipment and technical devices (the crank lift, hammer for piling, mechanical jacks, and even the first self-propelled vehicle), many of them designed to improve the effectiveness and efficiency of the projects in which Leonardo was involved. All these advances that he made in techniques, instruments, and tools allowed his designs to be better than those of his contemporaries, and many of them could not be materialized at the time for lack of technology and adequate materials. There is no doubt that technological development (materials, their processing, construction and manufacturing technologies, etc.) makes it possible to make reality what was considered impossible in the 15th century, and therefore many of the designs generated by the prodigious mind of Leonardo were unviable in his time. However, section six has shown how some of his proposals for machines, mechanisms, and instruments were put into practice and continue to be used today, while other designs have only been executed more recently as proof of his vision and resourcefulness. Thus, the opinion of the university professor, art critic and director of the “Museo Ideale Leonardo da Vinci”, Alessandro Vezzosi (Italy, 1950), is reinforced. He states: “Da Vinci’s work is unmatched in the history of scientific and technological illustration, not only for his way of exposing procedures without endless and boring demonstrations, but also as a work of art, the creation of the designer” [28].

Author Contributions: Investigation, E.C.-M.; Conceptualization, E.C.-M., P.F.-G., S.F.C.-R.; Project administration, S.F.C.-R.; Supervision, S.F.C.-R.; Validation, P.F.-G.; Visualization, P.F.-G.; Writing—original draft, E.C.-M. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

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