DRAWING AN ESCAPEMENT TO SHOW ANGULAR MOTION.
To delineate our locking face we draw a line at right angles to the line B b'' from the point t, said point being located at the intersection of the arc o with the line B b''. To draw a line perpendicular to B b'' from the point t, we take a convenient space in our dividers and establish on the line B b'' the points x x' at equal distances from the point t. We open the dividers a little (no special distance) and sweep the short arcs x'' x''', as shown at Fig. 91. Through the intersection of the short arcs x'' x''' and to the point t we draw the line t y. The reader will see from our former explanations that the line t y represents the neutral plane of the locking face, and that to have the proper draw we must delineate the locking face of our pallet at twelve degrees. To do this we draw the line t x' at twelve degrees to the line t y, and proceed to outline our pallet faces as shown. We can now understand, after a moment's thought, that we can delineate the impulse face of a tooth at any point or place we choose by laying off six degrees on the arc m, and drawing radial lines from A to embrace such arc. To illustrate, suppose we draw the radial lines w' w'' to embrace six degrees on the arc a. We make these lines contiguous to the entrance pallet C for convenience only. To delineate the impulse face of the tooth, we draw a line extending from the intersection of the radial line A' w' with the arc m to the intersection of the arc a with the radial line A w''.
We next desire to know where contact will take place between the wheel-tooth D and pallet C. To determine this we sweep, with our dividers set so one leg rests at the escape-wheel center A and the other at the outer angle t of the entrance pallet, the short arc t' w. Where this arc intersects the line w (which represents the impulse face of the tooth) is where the outer angle t of the entrance pallet C will touch the impulse face of the tooth. To prove this we draw the radial line A v through the point where the short arc t t' passes through the impulse face w of the tooth D. Then we continue the line w to n, to represent the impulse face of the tooth, and then measure the angle A w n between the lines w n and v A, and find it to be approximately sixty-four degrees. We then, by a similar process, measure the angle A t s' and find it to be approximately sixty-six degrees. When contact ensues between the tooth D and pallet C the tooth D will attack the pallet at the point where the radial line A v crosses the tooth face. We have now explained how we can delineate a tooth or pallet at any point of its angular motion, and will next explain how to apply this knowledge in actual practice.
PRACTICAL PROBLEMS IN THE LEVER ESCAPEMENT.
To delineate our entrance pallet after one-half of the engaged tooth has passed the inner angle of the entrance pallet, we proceed, as in former illustrations, to establish the escape-wheel center at A, and from it sweep the arc b, to represent the pitch circle. We next sweep the short arcs p s, to represent the arcs through which the inner and outer angles of the entrance pallet move. Now, to comply with our statement as above, we must draw the tooth as if half of it has passed the arc s.
To do this we draw from A as a center the radial line A j, passing through the point s, said point s being located at the intersection of the arcs s and b. The tooth D is to be shown as if one half of it has passed the point s; and, consequently, if we lay off three degrees on each side of the point s and establish the points d m, we have located on the arc b the angular extent of the tooth to be drawn. To aid in our delineations we draw from the center A the radial lines A d' and A m', passing through the points d m. The arc a is next drawn as in former instructions and establishes the length of the addendum of the escape-wheel teeth, the outer angle of our escape-wheel tooth being located at the intersection of the arc a with the radial line A d'.
As shown in Fig. 92, the impulse planes of the tooth D and pallet C are in contact and, consequently, in parallel planes, as mentioned on page 91. It is not an easy matter to determine at exactly what degree of angular motion of the escape wheel such condition takes place; because to determine such relation mathematically requires a knowledge of higher mathematics, which would require more study than most practical men would care to bestow, especially as they would have but very little use for such knowledge except for this problem and a few others in dealing with epicycloidal curves for the teeth of wheels.
For all practical purposes it will make no difference whether such parallelism takes place after eight or nine degrees of angular motion of the escape wheel subsequent to the locking action. The great point, as far as practical results go, is to determine if it takes place at or near the time the escape wheel meets the greatest resistance from the hairspring. We find by analysis of our drawing that parallelism takes place about the time when the tooth has three degrees of angular motion to make, and the pallet lacks about two degrees of angular movement for the tooth to escape. It is thus evident that the relations, as shown in our drawing, are in favor of the train or mainspring power over hairspring resistance as three is to two, while the average is only as eleven to ten; that is, the escape wheel in its entire effort passes through eleven degrees of angular motion, while the pallets and fork move through ten degrees. The student will thus see we have arranged to give the train-power an advantage where it is most needed to overcome the opposing influence of the hairspring.
