Most writers on horological matters term this act the "lift," which name was no doubt acquired when escapements were chiefly confined to pendulum clocks. Very little thought on the matter will show any person who inspects Fig. 126 that if the tooth C is released or escapes from the inside of the half shell of the cylinder A, said cylinder must turn or revolve a little in the direction of the arrow j, and also that the next succeeding tooth of the escape wheel will engage the cylinder on the outside of the half shell, falling on the dead or neutral portion of said cylinder, to rest until the hairspring causes the cylinder to turn in the opposite direction and permitting the tooth now resting on the outside of the cylinder to assume the position shown on the drawing.
The first problem in our consideration of the theoretical action of the cylinder escapement, is to arrange the parts we have described so as to have these two movements of the escape wheel of like angular values. To explain what we mean by this, we must premise by saying, that as our escape wheel has fifteen teeth and we make each tooth give two impulses in alternate directions we must arrange to have these half-tooth movements exactly alike, or, as stated above, of equal angular values; and also each impulse must convey the same power or force to the balance. All escape wheels of fifteen teeth acting by half impulses must impel the balance during twelve degrees (minus the drop) of escape-wheel action; or, in other words, when a tooth passes out of the cylinder from the position shown at Fig. 126, the form of the impulse face of the tooth and the shape of the exit lip of the cylinder must be such during twelve degrees (less the drop) of the angular motion of the escape wheel. The entire power of such an escape wheel is devoted to giving impulse to the balance.
The extent of angular motion of the balance during such impulse is, as previously stated, termed the "lifting angle." This "lifting angle" is by horological writers again divided into real and apparent lifts. This last division is only an imaginary one, as the real lift is the one to be studied and expresses the arc through which the impulse face of the tooth impels the balance during the act of escaping, and so, as we shall subsequently show, should no more be counted than in the detached lever escapement, where a precisely similar condition exists, but is never considered or discussed.
We shall for the present take no note of this lifting angle, but confine ourselves to the problem just named, of so arranging and designing our escape-wheel teeth and cylinder that each half of the tooth space shall give equal impulses to the balance with the minimum of drop. To do this we will make a careful drawing of an escape-wheel tooth and cylinder on an enlarged scale; our method of making such drawings will be on a new and original system, which is very simple yet complete.
DRAWING THE CYLINDER ESCAPEMENT.
All horological—and for that matter all mechanical—drawings are based on two systems of measurements: (1) Linear extent; (2) angular movement. For the first measurement we adopt the inch and its decimals; for the second we adopt degrees, minutes and seconds. For measuring the latter the usual plan is to employ a protractor, which serves the double purpose of enabling us to lay off and delineate any angle and also to measure any angle obtained by the graphic method, and it is thus by this graphic method we propose to solve very simply some of the most abstruce problems in horological delineations. As an instance, we propose to draw our cylinder escapement with no other instruments than a steel straight-edge, showing one-hundredths of an inch, and a pair of dividers; the degree measurement being obtained from arcs of sixty degrees of radii, as will be explained further on.
In describing the method for drawing the cylinder escapement we shall make a radical departure from the systems usually laid down in text-books, and seek to simplify the formulas which have heretofore been given for such delineations. In considering the cylinder escapement we shall pursue an analytical course and strive to build up from the underlying principles. In the drawings for this purpose we shall commence with one having an escape wheel of 10" radius, and our first effort will be the primary drawing shown at Fig. 129. Here we establish the point A for the center of our escape wheel, and from this center sweep the short arc a a with a 10" radius, to represent the circumference of our escape wheel. From A we draw the vertical line A B, and from the intersection of said line with the arc a a we lay off twelve degree spaces on each side of the line A B on said arc a and establish the points b c. From A as a center we draw through the points b c the radial lines b' c'.
To define the face of the incline to the teeth we set our dividers to the radius of any of the convenient arcs of sixty degrees which we have provided, and sweep the arc t t. From the intersection of said arc with the line A b' we lay off on said arc sixty-four degrees and establish the point g and draw the line b g. Why we take sixty-four degrees for the angle A b g will be explained later on, when we are discussing the angular motion of the cylinder. By dividing the eleventh degree from the point b on the arc a a into thirds and taking two of them, we establish the point y and draw the radial line A y'. Where this line A y' intersects the line b g we name the point n, and in it is located the point of the escape-wheel tooth. That portion of the line b g which lies between the points b and n represents the measure of the inner diameter of the cylinder, and also the length of the chord of the arc which rounds the impulse face of the tooth. We divide the space b n into two equal portions and establish the point e, which locates the position of the center of the cylinder. From A as a center and through the point e we sweep the arc e' e', and it is on this line that the points establishing the center of the cylinder will in every instance be located. From A as a center, through the point n we sweep the arc k, and on this line we locate the points of the escape-wheel teeth. For delineating the curved impulse faces of the escape-wheel teeth we draw from the point e and at right angles to the line b g the line e o. We next take in our dividers the radius of the arc k, and setting one leg at either of the points b or n, establish with the other leg the point p' on the line e o, and from the point p' as a center we sweep the arc b v n, which defines the curve of the impulse faces of the teeth. From A as a center through the point p' we sweep the arc p, and in all instances where we desire to delineate the curved face of a tooth we locate either the position of the point or the heel of such tooth, and setting one leg of our dividers at such point, the other leg resting on the arc p, we establish the center from which to sweep the arc defining the face of said tooth.