The Modern Clock / A Study of Time Keeping Mechanism; Its Construction, Regulation and Repair

by Ward L. Goodrich

Fig. 25.

These systems of levers have another advantage, which is that one arm need not be on the opposite side of the fulcrum from the other. It may be on the same side as in the verge or at any other convenient point. This enables us to save space in arranging our trains, as such a collection of wheels and pinions is called, by placing them in any position which, on account of other facts, may seem desirable.

Peculiarities of Angular Motion.—Now our collections of levers must move in certain directions in order to be serviceable and in order to describe these things properly, we must have names for these movements so that we can convey our thoughts to each other. Let us see how they move. They will not move vertically (up or down) or horizontally (sidewise), because we have taken great pains to prevent them from doing so by confining the central bars of our levers in a fixed position by making pivots on their ends and fitting them carefully into pivot holes in the plates, so that they can move only in one plane, and that movement must be in a circular direction in that predetermined plane. Consequently we must designate any movement in terms of the portions of a circle, because that is the only way they can move.

These portions of a circle are called angles, which is a general term meaning always a portion of a circle, measured from its center; this will perhaps be plainer if we consider that whenever we want to be specific in mentioning any particular size of angle we must speak of it in degrees, minutes and seconds, which are the names of the standard parts into which a circle is divided. Now in every circle, large or small, there are 360 degrees, because a degree is ¹⁄₃₆₀th part of a circle, and this measurement is always from its center. Consequently a degree, or any angle composed of a number of degrees, is always the same, because, being measured from its center, such measurements of any two circles will coincide as far as they go. If we draw two circles having their centers over each other at A, [Fig. 26], and take a tenth part of each, we shall have 360° ÷ 10 = 36°, which we shall mark out by drawing radial lines to the circumference of each circle, and we shall find this to be true; the radii of the smaller circle AB and AC will coincide with the radii AD and AE as far as they go. This is because each is the tenth part of its circle, measured from its center. Now that portion of the circumference of the circle BC will be smaller than the same portion DE of the larger circle, but each will be a tenth part of its own circle, although they are not the same size when measured by a rule on the circumference. This is a point which has bothered so many people when taking up the study of angular measurement that we have tried to make it absurdly clear. An angle never means so many feet, inches or millimeters; it always means a portion of a circle, measured from the center.

Fig. 26.

There is one feature about these angular (or circular) measurements that is of great convenience, which is that as no definite size is mentioned, but only proportionate sizes, the description of the machine described need not be changed for any size desired, as it will fit all sizes. It thus becomes a flexible term, like the fraction “one-half,” changing its size to suit the occasion. Thus, one-half of 300,000 bushels of wheat is 150,000 bushels; one-half of 10 bushels is 5 bushels; one-half of one bushel is two pecks; yet each is one-half. It is so with our angles.

There are some other terms which we shall do well to investigate before we leave the subject of angular measurements, which are the relations between the straight and curved lines we shall need to study in our drawings of the various escapements. A radius (plural radii) is a straight line drawn from the center of a circle to its circumference. A tangent is a straight line drawn outside the circumference, touching (but not cutting) it at right angles (90 degrees) to a radius drawn to the point of tangency (point where it touches the circumference). A general misunderstanding of this term (tangent) has done much to hinder a proper comprehension of the writers who have attempted to make clear the mysteries of the escapements. Its importance will be seen when we recollect that about the first thing we do in laying out an escapement is to draw tangents to the pitch circle of the escape wheel and plant our pallet center where these tangents intersect on the line of centers. They should always be drawn at right angles to the radii which mark the angles we choose for the working portion of our escape wheel. If properly drawn we shall find that the pallet arbor will then locate itself at the correct distance from the escape wheel center for any desired angle of escapement. We shall also discover that it will take a different center distance for every different angle and yet each different position will be the correct one for its angle, [Fig. 27].

Because an angle is always the same, no matter how far from the center the radii defining it are carried, we are able to work conveniently with large drawing instruments on small drawings. Thus we can use an eight or ten inch protractor in laying off our angles, so as to get the degrees large enough to measure accurately, mark the degrees with dots on our paper and then draw our lines with a straight edge from the center towards the dots, as far as we wish to go. Thus we can lay off the angles on a one-inch escape wheel with a ten inch protractor more easily and correctly than if we were using a smaller instrument.