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Let the arm c be fixed in an epicyclic gear train as

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Unformatted text preview: e speed of the gear A relative to the arm C = NA – N C and speed of the gear B relative to the arm C, = NB – N C Since the gears A and B are meshing directly, therefore they will revolve in opposite directions. ∴ NB – NC T =– A NA – NC TB Since the arm C is fixed, therefore its speed, N C = 0. ∴ NB T =– A NA TB If the gear A is fixed, then N A = 0. N B – NC T =– A 0 – NC TB or NB T =1+ A NC TB Note : The tabular method is easier and hence mostly used in solving problems on epicyclic gear train. Example 13.4. In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p.m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B ? Solution. Given : T A = 36 ; T B = 45 ; N C = 150 r.p.m. (anticlockwise) The gear train is shown in Fig. 13.7. Fig. 13.7 Chapter 13 : Gear Trains l 439 We shall solve this example, first by tabular method and then by algebraic method. 1. Tabular method First of all prepare the table of motions as given below : Table 13.2. Table of motions. Revolutions of elements Step No. Conditions of motion Arm C Gear A Gear B 1. Arm fixed-gear A r otates through + 1 revolution (i.e. 1 rev. anticlockwise) 0 +1 – TA TB 2. Arm fixed-gear A r otates through + x revolutions 0 +x – x× TA TB 3. Add + y revolutions to all elements +y +y +y 4. Total motion +y x +y y –x× TA TB Speed of gear B when gear A is fixed Since the speed of arm is 150 r.p.m. anticlockwise, therefore from the fourth row of the table, y = + 150 r.p.m. Also the gear A is fixed, therefore x+y=0 or ∴ Speed of gear B , NB = y – x × x = – y = – 150 r.p.m. 36 TA = 150 + 150 × = + 270 r.p.m. 45 TB = 270 r.p.m. (anticlockwise) Ans. Speed of gear B when gear A makes 300 r.p.m. clockwise Since the gear A makes 300 r.p.m.clockwise, therefor...
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