As drawn in Fig. 84 the angle of draft G a I is equal to fifteen degrees, but when brought in a position to act as shown at G a' I', Fig. 86, the draw is less even than twelve degrees. The angle C a I remains constant, as shown at C a' I', but the relation to the radial A G changes when the pallet moves through the angle w C w', as it must when locked. A tangential locking in the true sense of the meaning of the phrase is a locking set so that a pallet with its face coinciding with a radial line like A G would be neutral, and the thrust of the tooth would be tangent to the circle described by the locking angle of the tooth. Thus the center C, Fig. 86, is placed on the line w' which is tangent to the circle s; said line w' also being at right angles to the radial line A G.
The facts are, the problems relating to the club-tooth lever escapement are very intricate and require very careful analysis, and without such care the horological student can very readily be misled. Faulty drawings, when studying such problems, lead to no end of errors, and practical men who make imperfect drawings lead to the popular phrase, "Oh, such a matter may be all right in theory, but will not work in practice." We should always bear in mind that theory, if right, must lead practice.
CORRECT DRAWING REQUIRED.
If we delineate our entrance pallet to have a draw of twelve degrees when in actual contact with the tooth, and then construct in exact conformity with such drawings, we will find our lever to "hug the banks" in every instance. It is inattention to such details which produces the errors of makers complained of by Saunier in section 696 of his "Modern Horology," and which he attempts to correct by drawing the locking face at fifteen degrees draw.
We shall show that neither C nor C', Fig. 85, is the theoretically correct position for the pallet center for a tangential locking.
We will now take up the consideration of a club-tooth lever escapement with circular pallets and tangential lockings; but previous to making the drawings we must decide several points, among which are the thickness of the pallet arms, which establishes the angular motion of the escape wheel utilized by such pallet arms, and also the angular motion imparted to the pallets by the impulse faces of the teeth. We will, for the present, accept the thickness of the arms as being equivalent to five degrees of angular extent of the pitch circle of the escape wheel.
In making our drawings we commence, as on former occasions, by establishing the center of our escape wheel at A, Fig. 87, and sweeping the arc a a to represent the pitch circle of such wheel. Through the center A we draw the vertical line A B, which is supposed to also pass through the center of the pallet staff. The intersection of the line A B with the arc a we term the point d, and from this point we lay off on said arc a thirty degrees each side of said intersection, and thus establish the points c b. From A, through the point c, we draw the line A c c'. On the arc a a and two and a half degrees to the left of the point c we establish the point f, which space represents half of the thickness of the entrance pallet. From A we draw through the point f the line A f f'. From f, and at right angles to said line A f, we draw the line f e until it crosses the line A B.
Now this line f e is tangent to the arc a from the point f, and consequently a locking placed at the point f is a true tangential locking; and if the resting or locking face of a pallet was made to coincide with the line A f', such locking face would be strictly "dead" or neutral. The intersection of the line f e with the line A B we call the point C, and locate at this point the center of our pallet staff. According to the method of delineating the lever escapement by Moritz Grossmann the tangent line for locating the center of the pallet staff is drawn from the point c, which would locate the center of the pallet staff at the point h on the line A B.
Grossmann, in delineating his locking face for the draw, shows such face at an angle of twelve degrees to the radial line A f', when he should have drawn it twelve degrees to an imaginary line shown at f i, which is at right angles to the line f h. To the writer's mind this is not just as it should be, and may lead to misunderstanding and bad construction. We should always bear in mind the fact that the basis of a locking face is a neutral plane placed at right angles to the line of thrust, and the "draw" comes from a locking face placed at an angle to such neutral plane. A careful study of the diagram at Fig. 88 will give the reader correct ideas. If a tooth locks at the point c, the tangential thrust would be on the line c h', and a neutral locking face would be on the line A c.