4 total motion gear b tc ta tc ta tc t a tc tb tb

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Unformatted text preview: on Arm Gear A Gear C * TA 1. Arm B fixed, gear A rotated through + 1 revolution (i.e. 1 revolution anticlockwise) 0 +1 ± 2. Arm B fixed, gear A rotated through + x revolutions Add + y r evolutions to all elements 0 +x ± x× +y +y +y +y x +y y ± x× 3. 4. * Total motion Gear B – TC TA TC TA TC T × =– A TC TB TB – x× TA TB +y TA TC y – x× TA TB The ± sign is given to the motion of the wheel C because it is in a different plane. So we cannot indicate the direction of its motion specifically, i.e. either clockwise or anticlockwise. 460 l Theory of Machines Since the speed of the arm is 100 r.p.m. anticlockwise, therefore from the fourth row of the table, y = + 100 Also, the speed of the driving shaft X or gear A is 100 r.p.m. clockwise. ∴ x + y = – 100 or x = – y – 100 = – 100 – 100 = – 200 ∴ Speed of the driven shaft i.e. shaft Y , N Y = Speed of gear B = y – x × 40 TA = 100 – – 200 × 30 TB = + 366.7 r.p.m. = 366.7 r.p.m. (anticlockwise) Ans. Example 13.17. In a gear train, as shown in Fig. 13.23, gear B is connected to the input shaft and gear F is connected to the output shaft. The arm A carrying the compound wheels D and E, turns freely on the output shaft. If the input speed is 1000 r.p.m. counter- clockwise when seen from the right, determine the speed of the output shaft under the following conditions : 1. When gear C is fixed, and 2. when gear C is rotated at 10 r.p.m . counter clockwise. Solution. Given : T B = 20 ; T C = 80 ; T D = 60 ; T E = 30 ; T F = 32 ; N B = 1000 r.p.m. (counter-clockwise) Fig. 13.23 The table of motions is given below : Table 13.19. Table of motions. Revolutions of elements Step No. Conditions of motion Arm A Gear B (or input shaft) 1. Arm fixed, gear B rotated through + 1 revolution (i.e. 1 revolution anticlockwise) 0 +1 2. Arm fixed, gear B rotated through + x revolutions 0 +x 3. Add + y revolutions to all elements +y +y 4. Total motion +y x +y Compound wheel D-E + TB TD Gear C – TB TD × TD TC =– + x× TB TD +y y + x× Gear F (or output shaft) – TB TE × TD TF TB TC – x...
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