From the fourth row of the table the revolutions of

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Unformatted text preview: therefore y=1 Since the gear A is fixed, therefore from the fourth row of the table, x+y=0 or x =–y =–1 Let N C and N D = Revolutions of gears C and D respectively. From the fourth row of the table, the revolutions of gear C, T 100 1 =+ NC = y + x × A = 1 – 1 × Ans. 101 101 TC and the revolutions of gear D, T 100 1 =– ND = y + x × A = 1 – Ans. 99 99 TD From above we see that for one revolution of the arm B , the gear C rotates through 1/101 revolutions in the same direction and the gear D rotates through 1/99 revolutions in the opposite direction. Example 13.14. In the gear drive as shown in Fig. 13.18, the driving shaft A rotates at 300 r.p.m. in the clockwise direction, when seen from left hand. The shaft B is the driven shaft. The casing C is held stationary. The wheels E and H are keyed to the central vertical spindle and wheel F can rotate freely on this spindle. The wheels K and L are rigidly fixed to each other and rotate together freely on a pin fitted on the underside of F. The wheel L meshes with internal teeth on the casing C. The numbers of teeth on the different wheels are indicated within brackets in Fig. 13.18. Find the number of teeth on wheel C and the speed and direction of rotation of shaft B. Solution. Given : N A = 300 r.p.m. (clockwise) ; T D = 40 ; T B = 30 ; T F = 50 ; T G = 80 ; T H = 40 ; T K = 20 ; T L = 30 Fig. 13.18 In the arrangement shown in Fig. 13.18, the wheels D and G are auxillary gears and do not form a part of the epicyclic gear train. 454 l Theory of Machines Speed of wheel E, N E = N A × 40 TD = 300 × = 400 r.p.m. (clockwise) 30 TE Number of teeth on wheel C Let T C = Number of teeth on wheel C. Assuming the same module for all teeth and since the pitch circle diameter is proportional to the number of teeth ; therefore from the geometry of Fig.13.18, T C = T H + T K + T L = 40 + 20 + 30 = 90 Ans. Speed and direction of rotation of shaft B The table of motions is given below. The wheel F acts as an arm. Table 13.13. Table of motions. Revol...
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