Design

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412 Theoryof Machines

GearTrains 413

turns loosely on the hub ofgear C. Shafts 51 and 52 form the rear axle to which are fixed the rear wheels of the automobile. Gears C and D are keyed to the,shafts Sr and 52 respectively. C and D rgear'with equalbevel pinions E and Fwhich are free to rotate on their respective axes."The wheel B carries tvi'obrackets that supporb the bearings for gearsE and F. When the automobile moves,in a straight path, the bevel pinion A drives the wheel B. The whole differential acts as one unit and rotates with the bevel wheel B so that the wheels C and D rotate with the same speed and in the same direction asB. There is no relative motion betrveen gears C and D, and E and F. Fig.11.19 Gears E and F also do not rotate about just like keys to their own axesl They act transmit motion from B to C'-andD. Thus C and D, which are keyed to the shafts that carry the wheels rotate at the same speedas B. When a turn is taken, E and F'rotate about tliriir own axesand the system works as an epicyclicgear giving two outputs at C and D with one input at B. Prepare a table as below: Action

C/Sr

B f ix ed .C + 1 re v .

D/Sz

E/F

-1

T" TE

ii

t

TE\

li.

ri :i il

Tc

Bfixed,C+rrev.

Addy

y+x

y-x

kr*" TE

With reference to the above table, it is seen that the speed of B is the arithrneticalmean of the speedsof C andD, becausey= {(/ + i + Q - x)) 12. This shows that while taking a turn, if the speedof C decreasesthan that of B, there will be a correspondingincreasein the speedof D.

PROBLEMS ,&uu wplcyclicgear consistsrofa pinion, a whcel of 40 teeth and an annulus with llfilsrmternalteeth concentric with the wheel. The pinion gears with,the wheel rwuil" nheaanulus. The arm that cariieg theaiis of the pinion rotates at 100rpm. M"'meannulus is fxeil, find the speed,ofthe wheel; if wheer is flxed, find the rwreedof the annulus,

flm,um gear shown inFig.11.?, rhepirch ryicyclic

iri"';i##rl

"rr"",ui*fl'"?##i ,*"ir$t' be approximat,aty:szl mm,and thermodule 6 mm. when the annulus is jffiLiEaar]', the thrc.e-armedspider makes one revolution for weryfive revolu:,uss cf the wheel s. Find the number of teeth for aII the wheels arid exact pitch 'unce djameter of the annulus. If a torque of B0 N.m .is applied to the shaft mnu:yi.ng S, determine the fuing torque of the.annulus. (ts = 74, Tp = 27, Trt = 56; 120 N.m) iffim,ernnine a suitable train of wheels to satisfy the requirements of a clock, the luuumrutehand of which,isfxedto a spindleandthehourhandto a slewe rotating ffih**d.* on the same spindle. The pitch is the same for an the wheels and each witM has at least 11 teeth. The total number of teeth should be as small as grumm{hle. 'grtrine pinionS (Fig.t t;8)has15teeth,andis

fxed to !i;!f"::#f:i{l

'gtdly rmLsoreel P bas 20 teeth and gears with s and also with a fixed annulus wheel A. l$he,piaionC has l5,tcteth,andis fxed to the wheel P C,gearswith the annular D, which is kqyed to a machine shafl P and c can rotate togcther on a 'nrftnee'l puun carried by an arm which rotates about the shaft on which s is fixed. Find =e of thc machine shaft,if the motor rotates at 1000 rpm. "peed (3,7.5.rpmin the same direction as S) 0m.,en epicyclicgear (Fig. 11.7),thewheelA has also external teeth and is driven @ a piaion B. Number ,of teeth on,.S = number of teeth on B -- one fourth of mmlmberof teeth ctnA. The wheel A has same number of teeth internally and ec.ernally, f,erermine the specdof the driven shaft fxed to the arm a, when B makes 600 += in the same dirc'ction ass whose speedis 400 rpm. AIso find the speedand ailmestioa of rotation ofB if the driven shaft rotates at the samespeedas above lmnm in the oppositc direction. (40 rpm in a direction oppositeto S;200 rpm in directionof S) 11.20 shows an cpicyclic -€lrre traln known as Ferguson's ,trarador The gears have number ,.ldtcreth as indicatcd. Gear 1 is acu"tito the frame and is stationaa-.The arm a and the gears2 and ;H,a-refree to rotate on the shafts. T:e pitch circle diamcters of all ;unethe same so that the planet guerP mesheswith them all. Find llile aumber of rcvolutions ofgcars

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