I am asking for confirmation on the subject matter
The jack is a third-class lever (driving force between the fulcrum and the resistant part), just like the hammer which presents the power force in the center relative to the resistance (given by the weight of the stiletto and the hammer). Regarding the upright lever, being interfulcrumed, it is of the first class; however, since the powerful part is the short side of the L, it is also disadvantageous.
If this reasoning is correct, the entire mechanism is built to allow double escapement and fine regulation of movement, not to gain in terms of working efficiency
On page 8 of the indicated handouts, it actually speaks about the pulley principle (a variant of the lever principle), which represents the originality of B. Cristofori's design. By adopting the pulley principle, is the trestle system always a disadvantageous system in terms of working performance?
The work output on the escapement lever contributes very little because the resistance forces are several orders of magnitude lower than the driving force. It would be like choosing to install high-speed bench bearings instead of simple ones on a truck with a 20,000 cc displacement; it is practically useless. In reality, the escapement lever acts as a hammer lifter until it meets the felted button, therefore in this section it is not yet a lever. Only when it meets the button does it begin to function as a lever. At this instant, the extreme upper part of the escapement lever escapes from under the roller and the resistance force is inversely proportional to the driving force (which always derives from the first lever of the key), for an extremely simple reason: a greater push from the hammer in the initial moments by the escapement lever determines a greater inertial moment at the instant when the escapement lever meets the felted button and begins to behave as a lever. In fact, it accompanies the hammer only for part of its stroke towards the strings, and subsequently the hammer hits the string accompanied only by its inertial component, as it is completely devoid of other driving forces acting upon it.
Reasoning in purely physical terms: The escapement lever (if we speak of the moment when it functions as a lever) is certainly disadvantageous in terms of work, but even in this case we cannot express ourselves without including the forces, and we have seen that the driving force (or effort) and resistance forces are not comparable. The length of the short part of the escapement lever is imposed by other distances. If we speak of sensitivity, then it is undoubtedly better to lengthen the levers. In particular, if we were to lengthen the short side of the escapement lever, given the same threading of the felted button, we could count on a greater excursion (more turns) to produce the same effect, and this ensures us greater sensitivity.
The action is formed by a set of levers; however, if we decompose it and speak only of the lever found immediately above the key lever (which represents the point that transmits the driving force), then this represents a third-class lever.
perhaps the explanation regarding the efficiency of the system lies trivially in the fact that the key is a huge first-class lever (relative to the rest) in which the resistance (the stand system) is located closer to the fulcrum: it would therefore be an advantageous first-class lever which, by summing all the components involved, always results in a final mechanical advantage.
That goes without saying. I didn't express myself regarding the key leverage, but that is obviously the case. But what matters most is that on one hand we have kilograms and on the other hand grams...
