Large diagram showing a complete lever escapement.[Larger image.]
[Larger image.]
We will begin by drawing the center lineA′ A B;use the pointBfor the escape center; place the compass on it and strikeG H, the primitive or geometrical circle of the escape wheel; set the center of the protractor atBand mark off an angle of30°on each side of the line of centers; this will give us the anglesA B EandA B Ftogether, forming the angleF B Eof60°, which represents from lock to lock of the pallets. Since the chord of the angle of60°is equal to the radius of the circle, this gives us an easy means of verifying this angle by placing the compass at the points of intersection ofF BandE Bwith the primitive circleG H; this distance must be equal to the radius of the circle. At these points we will construct right angles toE BandF B, thus forming the tangentsC AandD Ato the primitive circleG H. These tangents meet on the line of centers atA, which will be the pallet center. Place the compass atAand draw the locking circleM Nat the points of intersection ofE BandF Bwith the primitive circleG H. The locking edges of the pallets will alwaysstand on this circle no matter in what relation the pallets stand to the wheel. Place the center of the protractor atBand draw the angle of width of pallets of6°;I B Ebeing for the engaging andJ B Ffor the disengaging pallet. In the equidistant palletI Bis drawn on the side towards the center, whileJ Bis drawn further from the center. If we were drawing a circular pallet, one-half the width of pallets would be placed on each side ofE BandF B. At the points of intersection ofI BandJ Bwith the primitive circleG Hwe draw the pathOfor the discharging edge of the engaging andPfor that of the disengaging pallet. The total lock being1¾°, we constructV′ Aat this angle fromC A; the point of intersection ofV′ Awith the locking circleM N, is the position of the locking corner of the engaging pallet. The pallet having12°draw when locked we place the center of the protractor on this corner and draw the angleQ M E.Q Mwill be the locking face of the engaging pallet. If the face of the pallet were on the lineE Bthere would be no draw, and if placed to the opposite side ofE Bthe tooth would repel the pallet, forming what is known as the repellant escapement.
The pallets when unlocked.Fig. 28.
Fig. 28.
Having shown how to delineate the locking face of the engaging pallet when locked, we will now consider how to draft both it and the disengaging pallet in correct positions when unlocked; to do so we direct our attention until further notice toFig. 28. The locking facesQ Mof the engaging andS Nof the disengaging pallets are shown in dotted lineswhen locked. We must now consider the relation which the locking faces will bear toE Bin the engaging, and toF Bin the disengaging pallets when unlocked. This is a question of some importance; it is easy enough to represent the12°from the30°angles when locked; we must be certain that they would occupy exactly that position and yet show them unlocked; we shall take pains to do so. In due time we shall show that there is no appreciable loss of lift on the engaging pallet in theescapement illustrated; the angleT A Vtherefore shows the total lift; we have not shown the corresponding angles on the disengaging side because the angles are somewhat different, but the total lift is still the same.G Hrepresents the primitive circle of the escape wheel, andX Zthat of the real, whileM Nrepresents the circular course which the locking corners of the pallets take in an equidistant escapement. At a convenient position we will construct the circleC C′ Dfrom the pallet centerA. Notice the pointseandc, whereV AandT Aintersect this circle; the space betweeneandcrepresents the extent of the motion of the pallets at this particular distance from the centerA; this being so, then let us apply it to the engaging pallet. At the point of intersectionoof the dotted lineQ M(which is an extended line on which the face of the pallet lies when locked), with the circleC C′ D, we will plant our dividers and transfere ctoo n. By setting our dividers onoMand transferring tonM′, we will obtain the location ofQ′ M′, the locking face when unlocked. Let us now turn our attentionto the disengaging pallet. The dotted lineS Nrepresents the location of the locking face of the disengaging pallet when locked at an angle of12°fromF B. At the intersection ofS Nwith the circleC C′ Dwe obtain the pointj. The motion of the two pallets being equal, we transfer the distancee cwith the dividers fromjand obtain the pointl. By setting the dividers onjNand transferring tolN′we draw the lineS′ N′on which the locking face of the disengaging pallet will be located when unlocked. It will be perfectly clear to anyone that through these means we can correctly represent the pallets in any desired position.
We will notice that the faceQ′ M′of the engaging pallet when unlocked stands at a greater angle toE Bthan it did when locked, while the opposite is the case on the disengaging pallet, in which the angleS′ N′ Fis much less thanS N F. This shows that thedeeperthe engaging pallet locks, the lighter will the draw be, while the opposite holds good with the disengaging pallet; also, that the draw increases during the unlocking of the engaging, and decreases during the unlocking of the disengaging pallet. These points show that the draw should be measured with thefork standing against the bank; not when the locking corner of the pallet stands on the primitive circle, as is so often done. The recoil of the wheel (which determines the draw), is illustrated by the difference between the locking circleM Nand the faceQ Mfor the engaging, andS Nfor the disengaging pallet, and along theactingsurface it is alike on each pallet, showing that the draft angle should be the same on each pallet.
A number of years ago we constructed the escapement model which we herewith illustrate. All the parts are adjustable; the pallets can be moved in any direction, the draft angles can be changed at will. Through this model we can practically demonstrate the points of which we have spoken. Such a model can be made by workmen after studying these papers.
The adjustable model escapement.
In both the equidistant and circular pallets the locking faceS Nof the disengaging pallet deviates more from the locking circleM Nthan does the locking faceQ Mof the engaging pallet, as will be seen in the diagram. This is because the draft angle is struck fromE Bwhich deviates from the locking circle in such a manner, that if the face of a pallet were planted on it andlocked deep enoughtoshow it, the wheel would actuallyrepelthe pallet, whereas with the disengaging pallet if it were planted onF B, it would actually produce draw if locked very deep; this is on account of the natural deviation of the30°lines from the locking circle. This difference is more pronounced in the circular than in the equidistant pallet, because in the former we have two locking circles, the larger one being for the engaging pallet, and as an arc of a large circle does not deviate as much from a straight line as does that of a smaller circle, it will be easily understood that the natural difference before spoken of is only enhanced thereby. For this reason in order to produce anactualdraw of12°, the engaging pallet may be set at a slightly greater angle fromE Bin the circular escapement; the amount depends upon the width of the pallets; the requirements are that the recoil of the wheel will be the same on each pallet. We must, however, repeat that one of the most important points is to measure the draw when the fork stands against the bank, therebyincreasingthe draw on the engaging anddecreasingthat of the disengaging palletduringthe unlocking action, thusnaturallybalancing one fault with another.
We will again proceed with the delineation of the escapement here illustrated. After having drawn the locking faceQ M, we draw the angle of width of teeth of4½°, by planting the protractor on the escape centerB. We measure the angleE B K, from the locking face of the pallet; the lineE Bdoes not touch the locking face of the pallet at the present time of contact with the tooth, therefore a line must be drawn from the point of contact to the centerB. We did so in our drawing but do not illustrate it, as in a reduced engraving of this kind it would be too close toE Band would only cause confusion. We will now draw in the lifting angle of3°for the tooth. From the tangentC Awe drawT Aat the required angle; at the point of intersection ofT Awith the30°lineE Bwe havethe real circumference of the escape wheel. It will only be necessary to connect the locking edge of the tooth with the lineK B, where the real or outer circle intersects it. It must be drawn in the same manner in the circular escapement; if the tooth were drawn up to the intersection ofK BwithT A, the lift would be too great, as that point is further from the centerAthan the points of contact are.
If the real or outer circle of the wheel intersects both the locking circleM Nand the pathOof the discharging edge at the points whereT Aintersects them, then there will beno lossof lift on the engaging pallet. This is precisely how it is in the diagram; but if there is any deviation, then the angle of loss must be measured on therealdiameter of the wheel and not on the primitive, as is usually done, as the real diameter of the wheel, or in other words the heel of the tooth, forms the last point of contact. With a wider tooth and a greater lifting angle there will even be againof lift on the engaging pallet; the pallet in such a case would actually require a smaller lifting angle, according to the amount of gain. We gave full directions for measuring the loss when describing its effects inFig. 8. Whatever the loss amounts to, it is added to the lifting plane of the pallet. In the diagram under discussion there is no loss, consequently the lifting angle on the pallet is to be5½°. FromV′ Awe drawV Aat the required angle; the point of intersection ofV Awith the pathOwill be the discharging edgeO. It will now only be necessary to connect the locking cornerMwith it, and we have the lifting plane of the pallet; the discharging side of the pallet is then drawn parallel to the locking face and made a suitable length. We will now draw the locking edges of the tooth by placing the center of the protractor on the locking edgeMand construct the angleB M M′of24°and draw a circle from the scape centerB, to which the lineM M′will be a tangent. We will utilize this circle in drawing in the faces of the other teeth after havingspaced them off24°apart, by simply putting a ruler on the locking edges and on the periphery of the circle.
We now constructW′ Aas a tangent to the outer circle of the wheel, thus forming the lifting angleD A W′of3°for the teeth; this corresponds to the angleT A Con the engaging side.W′ Atouches the outer circle of the wheel at the intersection ofF Bwith it. We will notice that there is considerable deviation ofW′ Afrom the circle at the intersection ofJ Bwith it. At the intersecting of this point we drawU A; the angleU A W′is the loss of lift. This angle must be added to the lifting angle of the pallets; we see that in this action there is no loss on the engaging pallet, but on the disengaging the loss amounts to approximately⅞°in the action illustrated. As we have allowed¼°of run for the pallets, the discharging edgePis removed at this angle fromU A; we do not illustrate it, as the lines would cause confusion being so close together. The lifting angle on the pallet is measured from the pointPand amounts to5½°+ the angle of the loss; the angleW A Uembraces the above angles besides¼°for run. If the locks are equal on each pallet, it proves that the lifts are also equal. This gives us a practical method of proving the correctness of the drawing; to do so, place the dividers on the locking circleM Nat the intersection ofT AandV Awith it, as this is the extent of motion; transfer this measurement toN, if theactuallift is the same on each pallet, the dividers will locate the point which the locking cornerNwill occupywhen locked; this, in the present case, will be at an angle of1¾°below the tangentD A. By this simple method, the correctness of our proposition that the loss of lift should be measured from the outside circle of the wheel, can be proven. We often see the loss measured for the engaging pallet on the primitive circumferenceG H, and on the real circumference for the disengaging; if one is right then the other must be wrong, asthere is a noticeable deviation of the tangentC Afrom the primitive circleG Hat the intersection of the locking circleM N; had we added this amount to the lifting angleV′ A Vof the engaging pallet, the result would have been that the discharging edgeOwould be over1°below its present location, thus showing that by the time the lift on the engaging pallet had been completed, the locking cornerNof the disengaging pallet would be locked at an angle of2¾°instead of only1¾°. Many watches contain precisely this fault. If we wish to make a draft showing the pallets at any desired position, at the center of motion for instance, with the fork standing on the line of centers, we would proceed in the following manner:10¼°being the total motion, one-half would equal5⅛°; as the total lock equals1¾°, we deduct this amount from it which leaves5⅛−1¾=3⅜°, which is the angle at which the locking cornerMshould be shown above the tangentC A. Now let us see where the locking cornerNshould stand;Mhaving moved up5⅛°, thereforeNmoved down by that amount, the lift on the pallet being5½°and on the tooth3°(which is added to the tangentD A), it follows thatNshould stand5½+ 3 −5⅛=3⅜°aboveD A. We can prove it by the lock, namely:3⅜°+1¾=5⅛°, half the remaining motion. This shows how simple it is to draft pallets in various positions, remembering always to use the tangents to the primitive circle as measuring points. We have fully explained how to draw in the draft angle on the pallets when unlocked, and do not require to repeat it, except to say, that most authorities draw a tangentR Nto the locking circleM N, forming in other words, the right angleR N A, then construct an angle of12°fromR N. We have drawn ours in by our own method, which is the correct one. While we here illustrateS N Rat an angle of12°it is in realitylessthan that amount; had we constructedS Nat an angle of12°fromR N, then the draw would be12°fromF B, when the primitive circumference of the wheel isreached, butmorethan12°when the fork is against the bank.
The space between the discharging edgePand the heel of the tooth forms the angle of dropJ B Iof1½°; the definition for drop is that it is the freedom for wheel and pallet. This is not, strictly speaking, perfectly correct, as, during the unlocking action there will be a recoil of the wheel to the extent of the draft angle; the heel of the tooth will therefore approach the edgeP, and the discharging side of the pallet approaches the tooth, as only the discharging edge moves on the pathP.
A good length for the teeth is1⁄10the diameter of the wheel, measured from the primitive diameter and from the locking edge of the tooth.
The backs of the teeth are hollowed out so as not to interfere with the pallets, and are given a nice form; likewise the rim and arms are drawn in as light and as neat as possible, consistent with strength.
Having explained the delineation of the wheel and pallet action we will now turn our attention to that of the fork and roller. We tried to explain these actions in such a manner that by the time we came to delineate them no difficulty would be found, as in our analysis we discussed the subject sufficiently to enable any one of ordinary intelligence to obtain a correct knowledge of them. The fork and roller action in straight line, right, or any other angle is delineated after the methods we are about to give.
We specified that the acting length of fork was to be equal to the center distance of wheel and pallets; this gives a fork of a fair length.
Having drawn the line of centersA′ Awe will construct an angle equal to half the angular motion of the pallets; the latter in the case under consideration being10¼°, therefore5⅛°is spaced off on each side of the line of centers, forming the anglesmAkof10¼°. Placing our dividers onA Bthe center distance of ’scape wheel andpallets, we plant them onAand constructc c; thus we will have the acting length of fork and its path. We saw in our analysis that the impulse angle should be as small as possible. We will use one of28°in our draft of the double roller; we might however remark that this angle should vary with the construction of the escapements in different watches; if too small, the balance may be stopped when the escapement is locked, while if too great it can be stopped during the lift; both these defects are to be avoided. The angles being respectively10¼°and28°it follows they are of the following proportions:28°÷ 10.25 = 2.7316. The impulse radius therefore bears this relation (but in the inverse ratio to the angles), to the acting length of fork.
We will put it in the following proportion; let Acequal acting length of fork, andxthe unknown quantity; 28∶10.25∷Ac∶x; the answer will be the theoretical impulse radius. Having found the required radius we plant one jaw of our measuring instrument on the point of intersection ofc cwithkAormAand locate the other jaw on the line of centers; we thus obtainA′the balance center. Through the points of intersection before designated we will draftX A′andY A′forming the impulse angleX A′ Yof28°. At the intersection of this angle with the fork anglekA′m, we drawi ifrom the centerA; this gives us the theoretical impulse circle. The total lock being1¾°it follows that the angle described by the balance in unlocking =1¾× 2.7316 = 4.788°. According to the specifications the width of slot is to be5⅛°; placing the center of the protractor onAwe construct half of this angle on each side ofkA, which passes through the center of the fork when it rests against the bank; this gives us the anglesAnof5⅛°. If the disengaging pallet were shown locked thenmAwould represent the center of the fork. The slot is to be made of sufficient depth so there will be no possibility of the ruby pin touching the bottom of it. The ruby pin is to have1¼°freedom in passing the acting edge of the fork; from thecenterAwe construct the angletAnof1¼°; at the point of intersection oftAwithc cthe acting radius of the fork, we locate the real impulse radius and draw the arcri riwhich describes the path made by the face of the ruby pin. The ruby pin is to have¼°of shake in the slot; it will therefore have a width of4⅞°; this width is drawn in with the ruby pin imagined as standing over the line of centers and is then transferred to the position which the ruby pin is to occupy in the drawing.
The radius of the safety roller was given as4⁄7of the theoretical impulse radius. They may be made of various proportions; thus⅔is often used. Remember that the smaller we make it, the less the friction during accidental contact with the guard pin, the greater must the passing hollow be and the horn of fork and guard point must be longer, which increases the weight of the fork.
Having drawn in the safety roller, and having specified that the freedom between the dart and safety roller was to be1¼°, the dart being in the center of the fork, consequentlykAis the center of it; therefore we construct the anglekA Xof1¼°. At the point of intersection ofX Awith the safety roller we draw the arcg g; this locates the point of the dart which we will now draw in. We will next drawdA′from the balance center and touching the point of the dart; we now constructbA′at an angle of5°to it. This is to allow the necessary freedom for the dart when entering the crescent; fromA′we draw a line through the center of the ruby pin. We do not show it in the drawing, as it would be indiscernible, coming very close toA′ X. This line will also pass through the center of the crescent. At the point of intersection ofA′bwith the safety roller we have one of the edges of the crescent. By placing our compass at the center of the crescent on the periphery of the roller and on the edge which we have just found, it follows that our compass will span the radius of the crescent. We now sweep the arc for the latter, thus also drawing in the remaininghalf of the crescent on the other side ofA′ Xand bringing the crescent of sufficient depth that no possibility exists of the dart touching in or on the edges of it. We will now draw in the impulse roller and make it as light as possible consistent with strength. A hole is shown through the impulse roller to counterbalance the reduced weight at the crescent. When describingFig. 24, we gave instructions for finding the dimensions of crescent and position of guard pin for the single roller. We will find the length of horn; to do so we must closely follow directions given forFig. 25. In locating the end of the horn, we must find the location of the center of the crescent and ruby pinafterthe edge of the crescent has passed the dart. From the point of intersection ofA′bwith the safety roller we transfer the radius of the crescent on the periphery of the safety roller towards the side against the bank, then draw a line fromA′through the point so found. At point of intersection of this line with the real impulse circler i r iwe draw an arc radiating from the pallet center; the end of the horn will be located on this arc. In our drawing the arc spoken of coincides with the dart radiusg g. As before pointed out, we gave particulars when treating onFig. 25, therefore considered it unnecessary to further complicate the draft by the addition of all the constructional lines. We specified that the freedom between ruby pin and end of horn was to be1½°; these lines (which we do not show) are drawn from the pallet center. Having located the end of the horn on the side standing against the bank, we place the dividers on it and on the point of intersection ofkAwithg g—which in this case is on the point of the dart,—and transfer this measurement alongg gwhich will locate the end of the horn on the opposite side.
We have the acting edges of the fork onccand have also found the position of the ends of the horns; their curvature is drawn in the following manner: We place our compasses onAandr i, spanning therefore the real impulseradius; the compass is now set on the acting edge of the fork and an arc swept with it which is then to be intersected by another arc swept from the end of the horn, on the same side of the fork. At the point of intersection of the arcs the compass is planted and the curvature of the horn drawn in, the same operation is to be repeated with the other horn. We will now draw in the sides of the horn of such a form that should the watch rebank, the side of the ruby pin will squarely strike the fork. If the back of the ruby pin strikes the fork there will be a greater tendency of breaking it and injuring the pivots on account of acting like a wedge. The fork and pallets are now drawn in as lightly as possible and of such form as to admit of their being readily poised. The banks are to be drawn at equal distances from the line of centers. In delineating the fork and roller action in any desired position, it must be remembered that the points of location of the real impulse radius, the end of horn, the dart or guard pin and crescent, mustallbe obtainedwhen standing against the bank, and the arcs drawn which they describe; the parts are then located according to the angle at which they are removed from the banks.
We think the instructions given are ample to enable any one to master the subject. We may add that when one becomes well acquainted with the escapement, many of the angles radiating from a common center, may be drawn in at once. We had intended describing the mechanical construction of the escapement, which does unmistakably present some difficulties on account of the small dimensions of the parts, but nevertheless it can be mechanically executed true to the principles enumerated. We have evolved a method of so producing them that young men in a comparatively short period have made them from their drafts (without automatic machinery) that their watches start off when run down the moment the crown is touched. Perhaps later on we will write up the subject. It is our intention of doing so, as we make use of such explanations in our regular work.