The connecting rod and crank system is used to transform rotary motion into direct reciprocating motion. A crank fixed to a connecting rod at one end is applied to a wheel. The connecting rod is a system composed of two poles joined by pivots. The last pole of the connecting rod is fixed so that it can turn in only one direction and, when it is pulled and pushed by the attached crank, it moves as a result.

The wedge is a pyramid-shaped object that is placed in groove or between two surfaces to separate them. The energy derived from a blow applied to the head of a wedge is distributed toward the surfaces. It is used to distribute energy in different directions. The basic idea of the wedge is the inclined plane.

Every type of gear depends on the idea of the axle and the wheel. An axle that rests on or passes through a circular hole will stay in place but will still turn. Leonardo also studied the effects of wear and tear on axles when different materials are used.

To apply a brake to a gear mechanism, Leonardo often uses a lever that interlocks with teeth cut out of a wheel so that the wheel is blocked. However, by doing it this way the wheel is still free to rotate in the opposite direction; a small spring can be added to the stop lever (pawl) to return it to its position. This kind of stop is often used for blocking system and for loading leaf springs.

The flywheel accumulates kinetic energy; Leonardo calls it “auxiliary motion”. At first, a large amount of energy is required to start turning the wheel or the weight attached to it, but once it is in motion the weight itself creates its own energy and it is difficult to slow down the system. The flywheel was to prove fundamental to Watt’s steam engine and to feedback systems.

The various kinds of articulated mechanical joints are essential for building robots and automata. Codex Madrid I shows several types. The basis of these joints is the use of the pivot or axle: each pivot has a degree of free rotation. The surprise lies in the innovative notion of using the ball and socket joint, which imitates the joints in the human skeleton and allows for considerable freedom of movement.

A cam is a device created with a wheel which has an irregular rim or with pegs that will make the desired shape. The rim of the irregular wheel pushes or moves a lever and makes it perform a movement that follows its shape. In this case, the wheel rim moves a lever, raising the hammer, which is then made to drop with a bang at each turn of the cam.

Leonardo drew many types of chains. The chain is an assembly of metal elements connected to each other by pins. Compared to a pulley, the chain can be grasped between the teeth of a gear and is in any case much stronger. It is a mistake to think that here we have proof that Leonardo had thought of a bicycle with pedals and a chain because in fact he only drew vertical chain systems for the purpose of lifting weights or containers.

First of all, Leonardo makes a serious study of the use of bearings to reduce wear and tear. If balls or cylindrical objects are placed between two rotating surfaces they greatlyy reduce the effects of wear and tear that would tend to slow the mechanism. Leonardo studied various shapes and materials for different uses.

Leonardo analyses the screw in terms of mathematics and geometry, describing it as an inclined plane coiled around an axis. In these terms, the “nut” slides and moves upwards on the screw’s plane; when the nut’s progress is blocked the “plane” moves. Part of the screw can be used to engage a toothed wheel and it is then known as an “endless screw”.

A spring is a long piece of flexible metal, coiled several times in a spiral around an axle. If the axle is rotated, the metal band behaves like an accumulator for “flexible” energy which, when released, returns the axle to its starting position. The principle characteristic of the spring is that the accumulated flexible energy is greatest at the first moment of release and very weak at the end. Spiral springs release rotary energy; springs of a different shape release energy in the opposite direction from that in which it was accumulated.

The main property of a pendulum is that (in simplified terms) the time of oscillation is proportional to the length of the cord and independent of the weight and amplitude of the swing. Leonardo studied the effects of the pendulum and used it to provide power in a large number of gadgets, not just those for measuring time, but also in mills and mechanisms.

Leonardo called the effect of these two machines “contrary friction”. The first, operated by the handle, makes use of the movement of a large toothed wheel with pegs arranged in groups on the flat surface. These groups of pegs engage alternately with, first, the small cylinder at the top and then with the one at the bottom. The two cylinders then transmit the reciprocating motion to the toothed, 3-sided curved part (lunula), which makes the notched bar slide first one way, then the other.

The second idea is simpler: the handle turns two toothed semi-circles and these engage alternately with the pegs on the two adjacent bars. The two bars are linked by a cord passed around the cylinder, which returns them to their original position, at the same time receiving reciprocating motion from them.

On page 7r, Leonardo sets out the rule on the number of teeth in a gear. He also portrays two machines to create reciprocating motion. The first, moved by the handle, turns a wheel with 5 pegs or teeth that move alternately above and below two blades connected to a vertical rod. The rod with the blades moves alternately, moving the horizontal rod by reciprocating motion. The second machine shows two large wheels moved by a handle. Each wheel has 9 long pegs staggered against those on the opposite wheel so that they engage and push the split lever alternately, making it move from side to side. Finally, the mechanism pushes the upper rod with reciprocating direct motion.

These two systems include a remarkable innovation: a wavy line is carved into a large wheel, making a track that can be “programmed” as desired. One or more pointed rods fixed to a pivot are inserted into the groove so that the pivot has to follow the track when the wheel is turned. In this way, oscillating motion is produced which can also be programmed by altering how the wheel turns. In the first example, the symmetrical twin tracks could be used to operate a pair of shears held in position by a block above the wheel. In the second, the mechanism is a blade like the ones used in clocks, but Leonardo says it is quieter.

This system of rings enables the inner hemisphere to keep its original position independently of its rotation. Two ring pivots fix the three outer rings to each other as they rotate, with a 90° displacement between each pair of rings. In this way, the inner system can move freely on three axes (X, Y, Z). The weight beneath the rotational axis keeps the inner hemisphere horizontal. The same system had always been used on ships to hold oil lamps steady in spite of the pitching caused by waves.

Inside the cylinder there is a spring that moves the toothed wheel below. On top, there is a metal arch with a castor that runs and rests on the upper surface of the cylinder, which has a step in it. The metal arch keeps the castor under pressure. In this way, the mechanism can only turn in one direction, because if it turned the other way it would be blocked by the castor bumping into the step.

This complex gear system makes maximum use of the energy produced by a spring. The tightened spring is hidden inside the container. When the stop lever is released, the spring begins to turn the helical (spiral) gear, which makes use of the initial strong energy from the spring to rotate briefly. As the gear rotates, it automatically moves down the screw, increasing its pace as it descends. In this way, full use is made of even the spring’s slight residual energy. The helical gear turns the cylinder and thus the upper wheel. At the same time, the lower mechanism enables the spring-blocking device to move slowly and gradually to the right. The handle is used to rewind the spring by hand.

The tightened spring is hidden inside the container; its center of rotation is the axle. Winding is therefore decentralized and will cause the drum to move in an odd, but useful, way. In fact, a toothed spiral is placed on the drum which rises as it becomes further away from the axle. As it rotates, this spiral gear engages the upper conical cylinder which is fixed between points n and h. The cylinder is a conical cage-wheel gear. The narrow radius makes use of the initial energy from the spring, while the wide radius at the end exploits the residual energy. The cylinder is connected directly to the final wheel.

Leonardo tried to improve the system of reciprocating motion because it had gear problems. Here he suggests making the main mechanism by using a quarter-circle (45° segment). The handle turns the wheel which has 32 teeth arranged on only half its circumference. The teeth engage alternately first segment, which makes disc rotate, completing four turns. At the next stage, wheel, which continues turning in the same direction, engages segment which, in the same way as above, makes disc rotate four times. Interestingly, Leonardo uses a bell which is shaken when segment reaches the end of its course and rings while segment is turning.

In this system, transmission of the manually driven reciprocating motion to a bell that rings is made by means of cloth or leather belts. Leonardo suggests using belt transmission to avoid the noise of the gears. In the second mechanism the reciprocating motion is supplied by the double-headed toothed “axe” which engages alternately with the cylinders. The “axe” is operated manually by the rod.

By turning wheel, the cogwheel moves the little disc, which can only move along the straight groove. If it is fixed or the assembly is stood on end, gravity will make it follow the same pre-programmed path back and forth. On wheel there is a groove in the shape of a double spiral. In this case, a spool is inserted in the groove. When the wheel turns, the spool is fixed so that it can only move in one direction, thus it has to follow the pre-programmed course; because it is lens-shaped it can even negotiate the points where the tracks cross. By altering the shape of the groove, it is possible to program the movement in the desired direction.

The system is operated by the handle which transmits motion to the wheel via an endless screw. The wheel always turns counterclockwise. Wheel R1 has 12 teeth arranged only at the front, with the result that the sequence is divided into two movements. First the wheel engages the bottom cylinder, which pushes the belt and makes it move clockwise. Then, alternately at each turn of wheel R1, the top cylinder is also engaged and this makes the belt move counterclockwise. So the belt moves forward and backward alternately, carrying along the iron rod attached to it. Leonardo suggests that the handle should not be turned too quickly, otherwise the gears jump out of place.

This spring-powered motor is a development of two motors on pages 4r and 16r. The spring, which this time Leonardo states must be of tempered steel, supplies rotary movement to the whole of the central block. In this way, the cylinder, which is fixed to run only vertically between the central axle and the lateral axle, is pushed and made to rotate over the toothed “spiral staircase”. The teeth of the cage gear support and engage the teeth on the outside of the spiral, whereas point C rests on the smooth inner part of the spiral. In two and a half turns this system makes (the others only allowed one turn), the cylinder which is connected to a large wheel with a ring gear not only to rotate, but move upwards, engaging the top disc. The gear turns and slides on the grooved cylinder. To illustrate the mechanism clearly, Leonardo has also shown a section through the central motor.

Very often Leonardo examines the mechanisms and suggests various experiments with minor modifications in order to find better solutions. In this case, for example, he analyzes the efficiency of the rod-and-handle system, suggesting two types of connecting rods (which he calls “la mezana”), one short and one long. He then suggests using an extremely long rod, which has a smoother movement, instead of a short one that may even hamper it.

To operate a flywheel, an inverse rod-and-handle system is used, and this later became the principal mechanism of the steam engine. In this case, to increase speed, Leonardo suggests doubling, tripling and quadrupling the handle assemblies. In the system with four handles set around the flywheel, he adds two rotating discs that indicate a use for the extra energy obtained. The system with four rods is mechanically similar to modern engines with 4-pistons connected to four rods that turn the axle.

A pulley can also be used to move gears, not just to lift weights. In addition, there are countless possible ways of combining different types of motion and the length of the rope allows the movement to be transmitted over a very long distance. The friction and noise produced by gears are also eliminated. It is possible to obtain rotation in any direction, depending on the way the rope is arranged and the inclination of the pulley. What is essential is that the rope must be turned around at least half of the pulley wheel so that the friction will engage it. These systems are the basis for the robot soldier.

In experimenting with the use of pulleys, Leonardo also suggests methods to test his theories. In this case, there are five pairs of weights, each pair connected by a rope and pulleys. The rope for each pair (A, B, C, D and E) passes by way of the central, rotating pillar and, in descending order, each rope is given one more half-turn around the pillar than the previous one. The aim is to understand how far the friction from the pulleys can move the weights as the rope is pulled. In fact, the Codex Madrid is also full of ideas on statics and geometry explained by means of mechanical experiments.

Leonardo also studied tools for making his machines. In this case, he suggests a drill with a diamond-tipped bit, which could be used to make holes in any kind of material. The power comes from a large, handle-operated flywheel whose inertia keeps the system turning. The flywheel makes the drill cylinder rotate. A large ball of lead sits on top of the drill to exert pressure on the piece being drilled. The diamond tip must be cooled with water - exactly the same process used in today’s industry.

This is one of the many mechanisms which can be considered a machine in itself, because we can see its use. In fact, other than the simple machines and composite mechanisms, Madrid I includes suggestions for several machines that are almost complete and ready to work. In this case, Leonardo studies a mechanism for polishing stone or mirrors. In the first system, the handle engages the axle underneath, rotating the plate which holds the mirror to be polished. At the same time, the handle moves a system of connecting rods which supplies rectilinear reciprocating motion to the polishing stone. The stone rests directly on the mirror and runs between four vertical rollers. In the second system, the handle engages the wheel directly and at the same time makes the system of three rods joined at point X move backwards and forwards.

Una delle versioni di macchina volante progettata da Leonardo.
La posizione del pilota era supina e i meccanismi venivano azionati con due pedali.

Una delle diverse versioni di macchina volante progettata da Leonardo.
Questo aliante poteva muovere le ali in su ed in giù tramite il movimento alternato di due pedali.

Il progetto dell'aliante è tra i più originali tra quelli sul volo. Il suo funzionamento è molto simile a quello di un moderno aquilone: la struttura planante in tela è manovrabile tramite due coppie di corde che permettono di spostarla a destra/sinistra e su/giù in modo da direzionare il mezzo.

In the folio 70r we find a project for a flying machine. The designs at the top represent a side view of the wing curve. In the center, a very faint drawing shows the overall front view with a person outlined in the middle. Below, there is a detailed design of the left wing and to its side are specific details for its attachment to the central structure.

Leonardo has designed a special instrument for measuring the center of gravity and the position of equilibrium of a model bird.

Does the design on folio 1051v of the Codex Atlanticus hide the first aeronautical engine in history? Leonardo drew a structure5 containing a device with a spring. This is not a preliminary design but a very concrete idea that he studied purposefully to use in flight, evidenced by the writing bird and cause of movement flanking the drawings. The mechanism was researched thoroughly, since the four wings placed in the upper part would modify their angle as they flap up and down.

The machine’s reconstruction is to be considered faithful to Leonardo’s idea. Despite the absence of the machine drawn in its entirety, there is little space for free interpretation and the textual indications supply excellent guidelines; likewise for fundamental constructive matters, such as the dimensions, the materials and the positioning of the center of gravity. The existence of this design could never be put into question, though it was obviously subject to modification. Indeed, in the course of future studies, some mechanisms may be perfected or their functioning reconsidered.

Leonardo introdusse quello che oggigiorno si chiama il cuscinetto di spinta. Nel Codice di Madrid si introduce l'impiego di cuscinetti a sfere e a rulli, e vi è uno schizzo ove viene presentato un cuscinetto paragonabile ai moderni cuscinetti di spinta a sfere.
Il perno conico impaccato in un gruppo compatto di tre cuscinetti a sfere è il meccanismo reinventato negli Anni '20 per la strumentazione degli aerei per il volo cieco.

Nel Codice di Madrid, il testo estremamente interessante di Leonardo dimostra la sua conoscenza dei problemi di attrito nei cuscinetti a rulli.
Leonardo realizza uno studio dei cuscinetti a rullo ed è favorevole alla soluzione che incorpora tre rulli conici che sostengono un perno munito di testa conica della stessa misura e forma dei rulli.

Al tempo di Leonardo venivano largamente impiegate per il sollevamento di carichi pesanti le binde, azionate girando una vite. La loro utilità era però limitata perchè, sotto una forte pressione, si sviluppava un grande attrito fra il dado girante e il disco su cui esso pesava.
Tra gli studi di Leonardo per ridurre l'attrito fra il dado girante e la placca della binda, vi è anche la tipologia del cuscinetto cilindrico verticale .

This famous drawing of the self-propelling cart is, in fact, a complex model for an automaton, a mechanism to provide theatrical effects. The drawing at the top is an unfinished first draft. In the center is the view from above. The vehicle can be programmed and is wound up by the mainsprings; the “crossbows” are auxiliary systems and the small lower wheels represent the escapement mechanism. The details surrounding the central drawing are studies of braking systems and fixtures for the auxiliary systems.

On-line self-propelling cart

http://brunelleschi.imss.fi.it/automobile/index.htm

Virtual exibit

Leonardo designed many theatrical devices. In this project ingenious stage sets appeared during the theatrical scenes. This particular set was used in staging Orpheus.