*3.3. Three-Dimensional Modeling of the Parts and Final Assembly of the Three-Dimensional CAD Model*

The modeling process of the optical telegraph is long and should be performed in great detail, paying close attention to the detailed information offered by the drawings.

First, the mast frame is modeled (Figure 7). This wooden structure is the skeleton of the invention, and it is important to respect the distances of the holes where the different axes will be housed. The mast is 7.45 m high and rests on a support that is 1.32 m long. This structure is not enough to give stability to the mast, therefore, from the central body of the mast, there is a support that allows the base to be extended to 2.27 m. In a similar manner, Betancourt, aware of the wind resistance that the structure presents, proposed a system of supports to guarantee the stability of the structure, and on the other hand the proposed dimensions of the mast and its structure will always depend on the topographic conditions of the environment. Its function is structural, but it must also be able to place the indicator arrow at a sufficient height, and if the conditions require it to be extended.

**Figure 7.** Mast frame (posterior and anterior view).

The next structure to model is the upper wheel (Figure 8). This is a wooden pulley of 75 cm in diameter in whose perimeter there are two grooves where the main transmission chain will be housed. This wheel is fixed to the mast thanks to a metal axle, and this in turn is supported externally by a metal structure that is screwed to the mast. The structure allows the axle to be perfectly horizontal and the wheel to rotate freely.

**Figure 8.** Detail of the upper wheel.

On the other hand, there is the wooden winch, which is one of the most important elements of the mechanism (Figure 9). This is a wooden wheel of 75 cm in diameter in which there are also two grooves in the perimeter zone, as in the upper wheel, but not in the middle area of the wheel rather towards one side. The other part of the wheel is drilled every 10º so that the sectors in which the wheel is divided can be perfectly distinguished. These divisions will be used to position the indicator arrow in a certain direction. The winch in addition has 12 arms of 1 m in length that facilitate its maneuverability, and in turn is crossed by a metal shaft that has a double function, positioning the winch in the mast support and allowing it to rotate freely.

**Figure 9.** Detail of the winch.

Figure 10 shows the position of the winch on the mast frame, giving a very clarifying overall view.

**Figure 10.** Detail of the position of the winch on the mast frame.

The main transmission, the one that connects the upper wheel and the winch (Figures 11–13), is the most complex modeling element of the mechanism. If the drawings and Betancourt's memory are taken carefully, it is discovered that the transmission that communicates the movement from one to the other is not achieved by a simple hemp rope, since the use of a rope presents the inconvenience of its sliding inside the slit due to the inertia of the movement of the indicator arrow. In order to avoid this slippage, Betancourt proposes a mixed rope-chain transmission system. The belt-like transmission has a central part of the rope and a part of the metal chain that comes into contact with the pulleys. Between them, there is a metal tensor whose mission is to provide greater tension to the transmission or to facilitate its repair tasks.

The modeling of the hemp rope is simple, although from the structural point of view it is very problematic. Most CAD software represent ropes as static elements when their behavior is dynamic. Also, the section and the length of the rope change as a tension is applied to it and no conventional design software is able to simulate this. Therefore, from an aesthetic point of view, the design of the rope does not offer much complication, but if it is intended to use the CAD model for a subsequent CAE analysis, then the model is insufficient.

The modeling of the chain of flat links is very laborious since it is necessary to model each link with its own bolt, defining a relationship between them that allows it to rotate with respect to each other. As can be seen in Figure 14, this chain of links in its description is very similar to that of a current flat link chain transmission, although evidently Betancourt did not know this type of transmission and defines links much larger than those of a current chain.

**Figure 11.** Detail of the upper wheel transmission.

**Figure 12.** Detail of the transmission on the winch.

**Figure 13.** Detail of the transmission between the upper wheel and the winch.

It is known that at the time there were no standardized elements and that each metallic element had to be handmade, so a chain of these characteristics was very complex and required a great manufacturing effort. Therefore, in practice, and for a large number of telegraph stations, it is not surprising that rope transmissions were used instead of mixed transmissions. Finally, it should be noted that the transmission was double in order to ensure the correct synchronization between the indicator arrow and winch.

**Figure 14.** Detail of the chain of links and tensors of the transmission.

Next the telescope frame is modeled (Figure 15). This frame is a simple wooden structure 1.53 m high, 1.45 m wide and 1 m long, which has the function of housing the telescope through which the nearest telegraph station is observed. For this the wooden clamp must at all times allow the telescope to rotate freely while preventing its longitudinal movement, although the telescopes frames do not have to be aligned with respect to the mast frame. In this article, they are presented as aligned, but their position depends on the direction in which the nearest station is located.

**Figure 15.** Telescope frame.

Once the telescope has been modeled, a 22 cm diameter metal pulley is attached to the rear of the telescope where the eyepiece is located (Figure 16). When the pulley rotates, the telescope rotates in unison.

**Figure 16.** Detail of the placement of the telescope pulley on its frame.

The next step in the modeling, also technically complex, is that of the pulley attached to the gimbal joint (Figure 17). The first element to model in this case is the end of the winch axle where a U-shaped metal piece with holes drilled in its two tips is to be placed. The next element is a circular piece that has two main axes, each axle being a metal rod of circular section topped by a square section that prevents it from passing through the hole. In addition, one of the axes goes through the two holes of the U-shaped metal tip mentioned above. It is important to define the relationship of these two elements correctly so as to allow the circular piece to rotate freely.

**Figure 17.** Detail of the gimbal joint with its pulley.

Next a metal pulley of dimensions and characteristics similar to that used in the telescope is modeled, but with a difference: located on one of its faces it has a U-shaped metal piece similar to that of the axle but placed perpendicularly and facing its ends. The tips of this piece are also drilled and its purpose is to house the free shaft that the round metal part possessed.

This articulation, made with these two U-shaped metal parts and the two-axle circular piece, is what is commonly called gimbal joint or universal articulation, and it allows the rotational movement of one axle to be converted into the rotational movement of another axis arranged in an unaligned direction. The use of this joint is what allows the telescope frame to not necessarily have to be aligned with the mast frame.

The transmission that is used between the metal pulleys (the one attached to the gimbal joint and the telescope pulley), has similar characteristics to the transmission between the upper wheel and the winch, but with a lower number of links (Figure 18).

**Figure 18.** Detail of the transmission between metal pulleys.

After modeling the transmission, we can see how moving the winch makes both telescopes rotate simultaneously at the same angle (Figure 19).

Figure 20 shows the modeled indicator arrow. As can be seen, it is a simple T-shaped structure of 6.60 m in length, with its interior emptied so that it offers less wind resistance. The indicator end is signaled by an oil lamp, which could be lit if necessary, and the transverse part of the arrow (opposite end) is in turn signaled by two oil lamps. In this way, one end was also distinguishable from the other in the dark.

**Figure 19.** Turning ratio between the winch and the telescope pulley.

**Figure 20.** Indicator arrow.

Once the indicator arrow has been modeled, it must be placed in its screwed position by means of four screws to the upper wheel (Figure 21) so that when the operator manipulates the winch the arrow rotates in unison with the upper wheel.

**Figure 21.** Detail of the placement of the indicator arrow on the mast.

Figure 22 shows an axonometric view of the optical telegraph assembled with all its elements.
