In order to realize any power from our escape-wheel tooth, we must provide an impulse face to the pallets faced at _f e_; and the problem before us is to delineate these pallets so that the lever will be propelled through an arc of eight and one-half degrees, while the escape wheel is moving through an arc of ten and one-half degrees. We make the arc of fork action eight and one-half degrees for two reasons--(1) because most text-books have selected ten degrees of fork-and-pallet action; (2) because most of the finer lever escapements of recent construction have a lever action of less than ten degrees.
To "lay out" or delineate our escape-wheel teeth, we continue our drawing shown at Fig. 6, and reproduce this cut very nearly at Fig. 8. With our dividers set at five inches, we sweep the short arc _a a'_ from _f_ as a center. It is to be borne in mind that at the point _f_ is located the extreme point of an escape-wheel tooth. On the arc _a a_ we lay off from _p_ twenty-four degrees, and establish the point _b_; at twelve degrees beyond _b_ we establish the point _c_. From _f_ we draw the lines _f b_ and _f c_; these lines establishing the form and thickness of the tooth _D_. To get the length of the tooth, we take in our dividers one-half a tooth space, and on the radial line _p f_ establish the point _d_ and draw circle _d' d'_.
To facilitate the drawing of the other teeth, we draw the circles _d' c'_, to which the lines _f b_ and _f c_ are tangent, as shown. We divide the circle _n n_, representing the periphery of our escape wheel, into fifteen spaces, to represent teeth, commencing at _f_ and continued as shown at _o o_ until the entire wheel is divided. We only show four teeth complete, but the same methods as produced these will produce them all. To briefly recapitulate the instructions for drawing the teeth for the ratchet-tooth lever escapement: We draw the face of the teeth at an angle of twenty-four degrees to a radial line; the back of the tooth at an angle of thirty-six degrees to the same radial line; and make teeth half a tooth-space deep or long.
We now come to the consideration of the pallets and how to delineate them. To this we shall add a careful analysis of their action. Let us, before proceeding further, "think a little" over some of the factors involved. To aid in this thinking or reasoning on the matter, let us draw the heavy arc _l_ extending from a little inside of the circle _n_ at _f_ to the circle _n_ at _e_. If now we imagine our escape wheel to be pressed forward in the direction of the arrow _j_, the tooth _D_ would press on the arc _l_ and be held. If, however, we should revolve the arc _l_ on the center _k_ in the direction of the arrow _i_, the tooth _D_ would _escape_ from the edge of _l_ and the tooth _D''_ would pass through an arc (reckoning from the center _p_) of twelve degrees, and be arrested by the inside of the arc _l_ at _e_. If we now should reverse the motion and turn the arc _l_ backward, the tooth at _e_ would, in turn, be released and the tooth following after _D_ (but not shown) would engage _l_ at _f_. By supplying motive to revolve the escape wheel (_E_) represented by the circle _n_, and causing the arc _l_ to oscillate back and forth in exact intervals of time, we should have, in effect, a perfect escapement. To accomplish automatically such oscillations is the problem we have now on hand.