Arm fixed wheel e rotated through x revolutions 0 x x

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Unformatted text preview: utions of elements Step No. Conditions of motion Arm or wheel F Wheel E Wheel H 1. Arm fixed-wheel E rotated through – 1 revolution ( i . e . 1 revolution clockwise) 0 –1 2. Arm fixed-wheel E rotated through – x revolutions 0 –x –x + x× 3. Add – y revolutions to all elements –y –y –y –y 4. Total motion –y –x–y –x–y – 1( 3 E and H are on the same shaft) Compound wheel K-L + x× Wheel C TH TK TH TK TH –y TK + TH TL × TK TC + x× TH TL × TK TC –y x× TH TL × –y TK TC Since the speed of wheel E is 400 r.p.m. (clockwise), therefore from the fourth row of the table, or – x – y = – 400 or Also the wheel C is fixed, therefore T T x× H × L – y=0 TK TC 40 30 x× – y=0 × 20 90 2x ∴ – y=0 3 From equations (i) and (ii), x = 240 and x + y = 400 ...(i) ...(ii) y = 160 ∴ Speed of wheel F, N F = y = – 160 r.p.m. Since the wheel F is in mesh with wheel G, therefore speed of wheel G or speed of shaft B = – NF × 50 TF = – – 160 × = 100 r.p.m. 80 TG ...(3 Wheel G will rotate in opposite direction to that of wheel F.) = 100 r.p.m. anticlockwise i.e. in opposite direction of shaft A . Ans. Chapter 13 : Gear Trains 455 l Example 13.15. Fig. 13.19 shows a compound epicyclic gear in which the casing C contains an epicyclic train and this casing is inside the larger casing D. Determine the velocity ratio of the output shaft B to the input shaft A when the casing D is held stationary. The number of teeth on various wheels are as follows : Wheel on A = 80 ; Annular wheel on B = 160 ; Annular wheel on C = 100 ; Annular wheel on D = 120 ; Small pinion on F = 20 ; Large pinion on F = 66. Fig. 13.19 Solution. Given : T 1 = 80 ; T 8 = 160 ; T 4 = 100; T 3 = 120 ; T 6 = 20 ; T 7 = 66 First of all, let us consider the train of wheel 1 (on A ), wheel 2 (on E), annular wheel 3 (on D) and the arm i.e. casing C. Since the pitch circle diameters of wheels are proportional to the number of teeth, therefore from the geometry of Fig. 13.19, T 1 + 2 T2 = T 3 or 80 + 2 T 2 = 120 ∴ T 2 = 20 The tabl...
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