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KEY EQUATIONS AND CHARTS FOR DESIGNING MECHANISMS FOUR-BAR LINKAGES AND TYPICAL INDUSTRIAL APPLICATIONS All mechanisms can be broken down into equivalent four-bar linkages. They can be considered to be the basic mechanism and are useful in many mechanical
CHAPTER 4RECIPROCATING ANDGENERAL-PURPOSEMECHANISMSSclater Chapter 4 5/3/01 10:44 AM Page 93 An ingenious intermittent mechanismwith its multiple gears, gear racks, andlevers provides smoothness and flexibil-ity in converting constant rotary motioninto a start-and-stop type of indexing.It works equally well for high-speedoperations, as fast as 2 seconds per cycle,including index and dwell, or for slow-speed assembly functions.The mechanism minimizes shockloads and offers more versatility than theindexing cams and genevas usuallyemployed to convert rotary motion intostart-stop indexing. The number of sta-tions (stops) per revolution of the tablecan easily be changed, as can the periodof dwell during each stop.Advantages. This flexibility broadensthe scope of such automatic machineoperations as feeding, sorting, packag-ing, and weighing that the rotary tablecan perform. But the design offers otheradvantages, too:• Gears instead of cams make themechanism cheaper to manufacture,because gears are simpler tomachine.• The all-mechanical interlocked sys-tem achieves an absolute time rela-tionship between motions.• Gearing is arranged so that themachine automatically goes into adwell when it is overloaded, prevent-ing damage during jam-ups.• Its built-in anti-backlash gear systemaverts rebound effects, play, and lostmotion during stops.How it works. Input from a singlemotor drives an eccentric disk and con-necting rod. In the position shown in thedrawing, the indexing gear and table arelocked by the rack—the planet gear ridesfreely across the index gear withoutimparting any motion to it. Indexing ofthe table to its next position begins whenthe control cam simultaneously releasesthe locking rack from the index gear andcauses the spring control ring gear topivot into mesh with the planet.This is a planetary gear system con-taining a stationary ring gear, a drivingplanet gear, and a “sun” index gear. Asthe crank keeps moving to the right, itbegins to accelerate the index gear withharmonic motion—a desirable type ofmotion because of its low acceleration-deceleration characteristics—while it isimparting high-speed transfer to thetable.94GEARS AND ECCENTRIC DISK COMBINE IN QUICK INDEXINGSclater Chapter 4 5/3/01 10:44 AM Page 94 Outgrowth from chains. Intermittent-motion mechanisms typically haveingenious shapes and configurations.They have been used in watches and inproduction machines for many years.There has been interest in the chain typeof intermittent mechanism (see drawing),which ingeniously routes a chain aroundfour sprockets to produce a dwell-and-index output.The input shaft of such a device has asprocket eccentrically fixed to it. The inputalso drives another shaft through one-to-one gearing. This second shaft mounts asimilar eccentric sprocket that is, however,free to rotate. The chain passes first aroundan idler pulley and then around a secondpulley, which is the output.As the input gear rotates, it also pullsthe chain around with it, producing a95At the end of 180º rotation of thecrank, the control cam pivots the ring-gear segment out of mesh and, simulta-neously, engages the locking rack. As theconnecting rod is drawn back, the planetgear rotates freely over the index gear,which is locked in place.The cam control is so synchronizedthat all toothed elements are in fullengagement briefly when the crank armis in full toggle at both the beginning andend of index. The device can be operatedjust as easily in the other direction.Overload protection. The ring gearsegment includes a spring-load detentmechanism (simplified in the illustra-tion) that will hold the gearing in fullengagement under normal indexingforces. If rotation of the table is blockedat any point in index, the detent springforce is overcome and the ring gear popsout of engagement with the planet gear.A detent roller (not shown) will thensnap into a second detent position, whichwill keep the ring gear free during theremainder of the index portion of thecycle. After that, the detent will automat-ically reset itself.Incomplete indexing is detected by anelectrical system that stops the machineat the end of the index cycle.Easy change of settings. To changeindexes for a new job setup, the eccentricis simply replaced with one heaving adifferent crank radius, which gives theproper drive stroke for 6, 8, 12, 16, 24,32, or 96 positions per table rotation.Because indexing occurs during one-half revolution of the eccentric disk, theinput gear must rotate at two or threetimes per cycle to accomplish indexingof 1⁄2, 1⁄4, or 1⁄16of the total cycle time(which is the equivalent to index-to-dwell cycles of 180/180º, 90/270º or60/300º). To change the cycle time, it isonly necessary to mount a difference setof change gears between input gear andcontrol cam gear.A class of intermittent mechanisms basedon timing belts, pulleys, and linkages(see drawing) instead of the usualgenevas or cams is capable of cyclicstart-and-stop motions with smoothacceleration and deceleration.Developed by Eric S. Buhayar andEugene E. Brown of the EngineeringResearch Division, Scott Paper Co.(Philadelphia), the mechanisms areemployed in automatic assembly lines.These mechanisms, moreover, canfunction as phase adjusters in which therotational position of the input shaft canbe shifted as desired in relation to theoutput shaft. Such phase adjusters havebeen used in the textile and printingindustries to change the “register” of oneroll with that of another, when both rollsare driven by the same input.TIMING BELTS, FOUR-BAR LINKAGETEAM UP FOR SMOOTH INDEXINGSclater Chapter 4 5/3/01 10:44 AM Page 95 modulated output rotation. Two spring-loaded shoes, however, must beemployed because the perimeter of thepulleys is not a constant figure, so thedrive has varying slack built into it.Commercial type. A chain also linksthe elements of a commercial phase-adjuster drive. A handle is moved tochange the phase between the input andoutput shafts. The theoretical chainlength is constant.In trying to improve this chain device,Scott engineers decided to keep the inputand output pulleys at fixed positions andMODIFIEDRATCHET DRIVE96maintain the two idlers on a swing frame.The variation in wraparound lengthturned out to be surprisingly little,enabling them to install a timing beltwithout spring-loaded tensioners insteadof a chain.If the swing frame is held in one posi-tion, the intermittent mechanism pro-duces a constant-speed output. Shiftingthe swing frame to a new position auto-matically shifts the phase relationshipbetween the input and output.Computer consulted. To obtain inter-mittent motion, a four-bar linkage issuperimposed on the mechanism byadding a crank to the input shaft and aconnecting rod to the swing frame. Thedevelopers chose an iterative program ona computer to optimize certain variablesof the four-bar version.In the design of one two-stop drive, adwell period of approximately 50º isobtained. The output displacementmoves slowly at first, coming to a“pseudo dwell,” in which it is virtuallystationary. The output then picks upspeed smoothly until almost two-thirdsof the input rotation has elapsed (240º).After the input crank completes a full cir-cle of rotation, it continues at a slowerrate and begins to repeat its slow-down—dwell—speed-up cycle.A ratchet drive was designed to assuremovement, one tooth at a time, in onlyone direction, without overriding. The keyelement is a small stub that moves alongfrom the bottom of one tooth well, acrossthe top of the tooth, and into an adjacenttooth well, while the pawl remains at thebottom of another tooth well.The locking link, which carries thestub along with the spring, comprises asystem that tends to hold the link andpawl against the outside circumferenceof the wheel and to push the stub andpawl point toward each other and intodifferently spaced wells between theteeth. A biasing element, which might beanother linkage or solenoid, is providedto move the anchor arm from one side tothe other, between the stops, as shown bythe double arrow. The pawl will movefrom one tooth well to the next tooth wellonly when the stub is at the bottom of atooth well and is in a position to preventcounter-rotation.Sclater Chapter 4 5/3/01 10:44 AM Page 96 • Relatively little flexibility in thedesign of the geneva mechanism.One factor alone (the number of slotsin the output member) determines thecharacteristics of the motion. As aresult, the ratio of the time of motionto the time of dwell cannot exceedone-half, the output motion cannot beuniform for any finite portion of theindexing cycle, and it is always oppo-site in sense to the sense of inputrotation. The output shaft, moreover,must always be offset from the inputshaft.Many modifications of the standardexternal geneva have been proposed,97ODD SHAPES IN PLANETARY GIVE SMOOTH STOP AND GOThis intermittent-motion mechanism for automatic processing machinery combines gears with lobes; some pitch curves are circular and some are noncircular.This intermittent-motion mechanismcombines circular gears with noncirculargears in a planetary arrangement, asshown in the drawing.The mechanism was developed byFerdinand Freudenstein, a professor ofmechanical engineering at ColumbiaUniversity. Continuous rotation appliedto the input shaft produces a smooth,stop-and-go unidirectional rotation in theoutput shaft, even at high speeds.This jar-free intermittent motion issought in machines designed for packag-ing, production, automatic transfer, andprocessing.Varying differential. The basis forFreudenstein’s invention is the varyingdifferential motion obtained between twosets of gears. One set has lobular pitchcircles whose curves are partly circularand partly noncircular.The circular portions of the pitchcurves cooperate with the remainder ofthe mechanism to provide a dwell time orstationary phase, or phases, for the out-put member. The non-circular portionsact with the remainder of the mechanismto provide a motion phase, or phases, forthe output member.Competing genevas. The main com-petitors to Freudenstein’s “pulsatingplanetary” mechanism are externalgenevas and starwheels. These deviceshave a number of limitations thatinclude:• Need for a means, separate from thedriving pin, for locking the outputmember during the dwell phase ofthe motion. Moreover, accurate man-ufacture and careful design arerequired to make a smooth transitionfrom rest to motion and vice versa.• Kinematic characteristics in thegeneva that are not favorable forhigh-speed operation, except whenthe number of stations (i.e., the num-ber of slots in the output member) islarge. For example, there is a suddenchange of acceleration of the outputmember at the beginning and end ofeach indexing operation.At heart of new planetary (in front view, circular set stacked behind noncircular set), two setsof gears when assembled (side view) resemble conventional unit (schematic).including multiple and unequally spaceddriving pins, double rollers, and separateentrance and exit slots. These proposalshave, however, been only partly success-ful in overcoming these limitations.Differential motion. In deriving theoperating principle of his mechanism,Freudenstein first considered a conven-tional epicyclic (planetary) drive inwhich the input to the cage or armcauses a planet set with gears 2 and 3 torotate the output “sun,” gear 4, whileanother sun, gear 1, is kept fixed (seedrawing).Letting r1, r2, r3, r4, equal the pitchradii of the circular 1, 2, 3, 4, then theoutput ratio, defined as:is equal to: Now, if r1= r4and r2= r3, there is no“differential motion” and the outputremains stationary. Thus if one gear pair,say 3 and 4, is made partly circular andpartly noncircular, then where r2= r3andr1= r4for the circular portion, gear 4dwells. Where r2≠ r3and r1≠ r4for thenoncircular portion, gear 4 has motion.The magnitude of this motion dependsSclater Chapter 4 5/3/01 10:44 AM Page 97 on the difference in radii, in accordancewith the previous equation. In this man-ner, gear 4 undergoes an intermittentmotion (see graph).Advantages. The pulsating planetaryapproach demonstrates some highly use-ful characteristics for intermittent-motion machines:• The gear teeth serve to lock the out-put member during the dwell as wellas to drive that member duringmotion.• Superior high-speed characteristicsare obtainable. The profiles of thepitch curves of the noncircular gearscan be tailored to a wide variety ofdesired kinematic and dynamic char-acteristics. There need be no suddenterminal acceleration change of thedriven member, so the transition fromdwell to motion, and vice versa, willbe smooth, with no jarring ofmachine or payload.• The ratio of motion to dwell time isadjustable within wide limits. It caneven exceed unity, if desired. Thenumber of indexing operations perrevolution of the input member alsocan exceed unity.• The direction of rotation of the out-put member can be in the same oropposite sense relative to that of theinput member, according to whetherthe pitch axis P34for the noncircularportions of gears 3 and 4 lies whollyoutside or wholly inside the pitchsurface of the planetary sun gear 1.• Rotation of the output member iscoaxial with the rotation of the inputmember.• The velocity variation during motionis adjustable within wide limits.Uniform output velocity for part ofthe indexing cycle is obtainable; byvarying the number and shape of thelobes, a variety of other desirablemotion characteristics can beobtained.• The mechanism is compact and hasrelatively few moving parts, whichcan be readily dynamically balanced.Design hints. The design techniqueswork out surprisingly simply, saidFreudenstein. First the designer mustselect the number of lobes L3and L4onthe gears 3 and 4. In the drawings, L3= 2and L4= 3. Any two lobes on the twogears (i.e., any two lobes of which one ison one gear and the other on the othergear) that are to mesh together must havethe same arc length. Thus, every lobe ongear 3 must mesh with every lobe on gear4, and T3/T4= L3/L4= 2/3, where T3andT4are the numbers of teeth on gears 3and 4. T1and T2will denote the numbersof teeth on gears 1 and 2.Next, select the ratio S of the time ofmotion of gear 4 to its dwell time, assum-ing a uniform rotation of the arm 5. For thegears shown, S = 1. From the geometry,(θ30+ ∆θ30)L3= 360ºandS = ∆θ3/θ30Henceθ30(1 + S)L3= 360ºFor S = 1 and L3+ 2,θ30= 90ºand∆θ3= 90ºNow select a convenient profile forthe noncircular portion of gear 3. Oneprofile (see the profile drawing) thatFreudenstein found to have favorablehigh-speed characteristics for stop-and-go mechanisms isr3= R3The profile defined by this equationhas, among other properties, the charac-teristic that, at transition from rest tomotion and vice versa, gear 4 will havezero acceleration for the uniform rotationof arm 5.In the above equation, λ is the quan-tity which, when multiplied by R3, givesthe maximum or peak value of r3– R3,differing by an amount h′ from the radiusR3of the circular portions of the gear.The noncircular portions of each lobeare, moreover, symmetrical about theirmidpoints, the midpoints of these por-tions being indicated by m.12123303+−−λπθθθcos()∆98Output motion (upper curve) has long dwell periods; velocity curve (center) has smooth tran-sition from zero to peak; acceleration at transition is zero (bottom).Sclater Chapter 4 5/3/01 10:44 AM Page 98 To evaluate the quantity λ,Freudenstein worked out the equation:where R3λ = height of lobeTo evaluate the equation, select a suit-able value for µ that is a reasonably sim-ple rational fraction, i.e., a fraction suchas 3⁄8whose numerator and denominatorare reasonably small integral numbers.Thus, without a computer or lengthytrial-and-error procedures, the designercan select the configuration that willachieve his objective of smooth intermit-tent motion.µα== +=++RARR RSSLL333 4341()()λµµααµα αµααµ=−×+−+ −−+−+11112[ ( )][ ( )][( )]SSA metering pump for liquid or gas has anadjustable ring gear that meshes with aspecial-size planet gear to provide aninfinitely variable stroke in the pump.The stroke can be set manually or auto-matically when driven by a servomotor.Flow control from 180 to 1200 liter/hr.(48 to 317 gal./hr.) is possible while thepump is at a standstill or running.Straight-line motion is key. Themechanism makes use of a planet gearwhose diameter is half that of the ringgear. As the planet is rotated to roll on theinside of the ring, a point on the pitchdiameter of the planet will describe astraight line (instead of the usual hypocy-cloid curve). This line is a diameter of thering gear. The left end of the connectingrod is pinned to the planet at this point.The ring gear can be shifted if a sec-ond set of gear teeth is machined in itsouter surface. This set can then bemeshed with a worm gear for control.Shifting the ring gear alters the slope ofthe straight-line path. The two extremepositions are shown in the diagram. Inthe position of the mechanism shown, thepin will reciprocate vertically to producethe minimum stroke for the piston.Rotating the ring gear 90º will cause thepin to reciprocate horizontally to producethe maximum piston stroke.The second diagram illustratesanother version that has a yoke instead ofa connecting rod. This permits the lengthof the stroke to be reduced to zero. Also,the length of the pump can be substan-tially reduced.99Profiles for noncircular gears are circulararcs blended to special cam curves.CYCLOID GEAR MECHANISMCONTROLS STROKE OF PUMP An adjustable ring gear meshes with a planet gear having half of its diameter to provide aninfinitely variable stroke in a pump. The adjustment in the ring gear is made by engaging otherteeth. In the design below, a yoke replaces the connecting rod.Sclater Chapter 4 5/3/01 10:44 AM Page 99 CONVERTING ROTARY-TO-LINEAR MOTIONA compact gear system that provides lin-ear motion from a rotating shaft wasdesigned by Allen G. Ford of The JetPropulsion Laboratory in California. Ithas a planetary gear system so that theend of an arm attached to the planet gearalways moves in a linear path (drawing).The gear system is set in motion by amotor attached to the base plate. Gear A,attached to the motor shaft, turns the caseassembly, causing Gear C to rotate alongGear B, which is fixed. The arm is thesame length as the center distancebetween Gears B and C. Lines betweenthe centers of Gear C, the end of the arm,and the case axle form an isosceles trian-gle, the base of which is always along theplane through the center of rotation. Sothe output motion of the arm attached toGear C will be in a straight line.When the end of travel is reached, aswitch causes the motor to reverse,returning the arm to its original position.100The end of arm moves in a straight line because of the triangle effect (right).NEW STAR WHEELS CHALLENGEGENEVA DRIVES FOR INDEXINGStar wheels with circular-arc slots can be analyzedmathematically and manufactured easily.Star Wheels vary in shape, depending on the degree of indexing that must be done during one input revolution.Sclater Chapter 4 5/3/01 10:44 AM Page 100 A family of star wheels with circularinstead of the usual epicyclic slots (seedrawings) can produce fast start-and-stopindexing with relatively low accelerationforces.This rapid, jar-free cycling is impor-tant in a wide variety of productionmachines and automatic assembly linesthat move parts from one station toanother for drilling, cutting, milling, andother processes.The circular-slot star wheels wereinvented by Martin Zugel of Cleveland,Ohio.The motion of older star wheels withepicyclic slots is difficult to analyze andpredict, and the wheels are hard to make.The star wheels with their circular-arcslots are easy to fabricate, and becausethe slots are true circular arcs, they canbe visualized for mathematical analysisas four-bar linkages during the entireperiod of pin-slot engagement.Strong points. With this approach,changes in the radius of the slot can beanalyzed and the acceleration curve var-ied to provide inertia loads below thoseof the genevas for any practical designrequirement.Another advantage of the star wheelsis that they can index a full 360º in a rel-atively short period (180º). Such one-stop operation is not possible withgenevas. In fact, genevas cannot do two-stop operations, and they have difficultyproducing three stops per index. Mosttwo-stop indexing devices available arecam-operated, which means they requiregreater input angles for indexing.101The one-stop index motion of the unit can be designed to take longer to complete itsindexing, thus reducing its index velocity.Geared star sector indexes smoothly a full 360º during a 180º rotation of thewheel, then it pauses during the other 180º to allow the wheel to catch up.An accelerating pin brings the output wheel up to speed. Gear sectors mesh to keep the output rotating beyond 180º.Sclater Chapter 4 5/3/01 10:44 AM Page 101 Operating sequence. In operation, theinput wheel rotates continuously. Asequence starts (see drawing) when theaccelerating pin engages the curved slotto start indexing the output wheel clock-wise. Simultaneously, the locking sur-face clears the right side of the outputwheel to permit the indexing.Pin C in the drawings continues toaccelerate the output wheel past the mid-point, where a geneva wheel would startdeceleration. Not until the pins are sym-metrical (see drawing) does the accelera-tion end and the deceleration begin. PinD then takes the brunt of the decelerationforce.Adaptable. The angular velocity of theoutput wheel, at this stage of exit of theacceleration roller from Slot 1, can bevaried to suit design requirements. Atthis point, for example, it is possibleeither to engage the deceleration roller asdescribed or to start the engagement of aconstant-velocity portion of the cycle.Many more degrees of output index canbe obtained by interposing gear-elementsegments between the acceleration anddeceleration rollers.The star wheel at left will stop andstart four times in making one revolution,while the input turns four times in thesame period. In the starting position, theoutput link has zero angular velocity,which is a prerequisite condition for anystar wheel intended to work at speedsabove a near standstill.In the disengaged position, the angu-lar velocity ratio between the output andinput shafts (the “gear” ratio) is entirelydependent upon the design angles αandβ and independent of the slot radius, r.Design comparisons. The slot radius,however, plays an important role in themode of the acceleration forces. A four-stop geneva provides a good basis forcomparison with a four-stage “Cyclo-Index” system.Assume, for example, that α = β =22.5º. Application of trigonometryyields:which yields R = 0.541A. The onlyrestriction on r is that it be large enoughto allow the wheel to pass through itsmid-position. This is satisfied if:There is no upper limit onr, so thatslot can be straight.rRAARAA>−−−≈( cos )cos.1201ααRA=+sinsin( )βαβ102The accelerating force of star wheels (curves A, B, C) varies with input rota-tion. With an optimum slot (curve C), it is lower than for a four-stop geneva.This internal star wheel has a radius difference to cushion the indexing shock.Star-wheel action is improved with curved slots over the radius r, centered on the initial-contact line OP. The units then act as four-bar linkages, 001PQ.Sclater Chapter 4 5/3/01 10:44 AM Page 102 [...]... diameter and having gear 2 serve as an idler, any member fixed to gear 3 will remain parallel to its previous positions throughout the rotation of the input ring crank The high-volume 2500-ton press is designed to shape such parts as connecting rods, tractor track links, and wheel hubs A simple automatic-feed mechanism makes it possible to produce 240 0 forgings per hour 105 Sclater Chapter 4 5/3/01 10 :44 ... axial control rod of this adjustable-pitch propeller linearly twists the propeller blades around on the common axis by moving the rack and gear arrangement A double rack, one above and on either side of the other, gives the opposing twisting motion required for propeller blades 115 Sclater Chapter 4 5/3/01 10 :45 AM Page 116 ROTARY-TO-RECIPROCATING MOTION AND DWELL MECHANISMS With proper dimensions,... member to reciprocate linearly 117 Sclater Chapter 4 5/3/01 10 :45 AM Page 118 LONG-DWELL MECHANISMS The chain link drives a lever that oscillates A slowdown-dwell occurs when the chain pin passes around the left sprocket The planet gear is driven with a stopand-go motion The driving roller is shown entering the circular-arc slot on the planet link The link and the planet remain stationary while the... double notched-cam arrangement shown is designed to operate the lever once in 100 cycles, imparting a rapid movement to it One of the two identical cams and the 150-tooth gear are keyed to the bushing which turns freely around the cam shaft The cam shaft carries the second cam and the 80-tooth gear The 3 0- and 100-tooth gears are integral, while the 20-tooth gear is attached to the one-cycle drive shaft... at the dead-center positions, so that the motion of the gear is continuously and positively governed By varying the radius R and the diameter of the gear, the number of revolutions made by the output shaft during the operating half of the cycle can be varied to suit many differing requirements 108 Sclater Chapter 4 5/3/01 10 :45 AM Page 109 A cam-driven ratchet A six-sided Maltese cross and double driver... known intermittent mechanisms: the external and internal genevas, the three-gear drive, and the cardioid drive Either three-gear or cardioid can provide a dwell period—but only for a comparatively short period of the cycle With the camplanetary, one can obtain over 180º of dwell during a 360º cycle by employing a 4- to-1 gear ratio between planet and sun And what about a cam doing the job by itself?... shaft and the guide for the output slider As the output slider reaches the end of its stroke (to the right), it remains at a virtual standstill while one crank rotates through angle PP′ 119 Sclater Chapter 4 5/3/01 10 :45 AM Page 120 Dwell Mechanisms (continued ) Fast Cam-Follower Motion Fast cam action every n cycles (where n is a relatively large number) can be obtained with this manifold cam and gear... geneva wheel with a two-crank linkage Input crank a drives crank b through link c The variable angular velocity of driving roller d, mounted on b, depends on the center distance L, and on the radii M and N of the crank arms This velocity is about equivalent to what would be produced if the input shaft were driven by elliptical gears 106 Sclater Chapter 4 5/3/01 10 :44 AM Page 107 Fig 4 The duration of the... expands Fig 3 A V-belt sheave is pushed around when pawl wedges in the groove For a snug fit, the bottom of the pawl is tapered like a V-belt Fig 4 Eccentric rollers squeeze a disk on its forward stroke On the return stroke, rollers rotate backwards and release their grip Springs keep the rollers in contact with the disk 1 24 Fig 5 A rack is wedge-shaped so that it jams between the rolling gear and. .. escapement on an electric meter A solenoid-operated ratchet with a solenoid-resetting mechanism A sliding washer engages the teeth A plate oscillating across the plane of a ratchet-gear escapement carries stationary and spring-held pawls A worm drive, compensated by a cam on a work shaft, produces intermittent motion of the gear 109 Sclater Chapter 4 5/3/01 10 :45 AM Page 110 An intermittent counter mechanism . lobe on gear4, and T3/T4= L3/L4= 2/3, where T3andT4are the numbers of teeth on gears 3and 4. T 1and T2will denote the numbersof teeth on gears 1 and 2.Next,. CHAPTER 4RECIPROCATING ANDGENERAL-PURPOSEMECHANISMSSclater Chapter 4 5/3/01 10 :44 AM Page 93 An ingenious intermittent