11 table of motions revolutions of elements step no

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Unformatted text preview: dC Since the number of teeth are proportional to their pitch circle diameters for the same pitch, therefore T E = T B + T D – T C = 80 + 28 – 82 = 26 The table of motions is given below : Table 13.11. Table of motions. Revolutions of elements Step No. Conditions of motion Arm (or shaft A) Wheel B (or shaft F) Compound gear D-E 1. Arm fixed - wheel B rotated through + 1 revolution (i.e. 1 revolution anticlockwise) 0 +1 + 2. Arm fixed - wheel B rotated through + x revolutions 0 +x + x× 3. Add + y r evolutions to all elements +y +y +y 4. Total motion +y x +y y + x× TB TE Wheel C + TB TE TB TD × TE TC + x× TB TD × TE TC +y TB TE y + x× TB TD × TE TC Since the wheel C is fixed, therefore from the fourth row of the table, y+ x× ∴ TB TD × =0 TE TC or y+ x× 80 28 × =0 26 82 y + 1.05 x = 0 ...(i) Also, the shaft A (or the arm) makes 800 r.p.m., therefore from the fourth row of the table, y = 800 ...(ii) From equations (i) and (ii), x = – 762 ∴ Speed of shaft F = Speed of wheel B = x + y = – 762 + 800 = + 38 r.p.m. = 38 r.p.m. (anticlockwise) Ans. Example 13.13. Fig. 13.17 shows an epicyclic gear train known as Ferguson’s paradox. Gear A is fixed to the frame and is, therefore, stationary. The arm B and gears C and D are free to rotate on the shaft S. Gears A, C and D have 100, 101 and 99 teeth respectively. The planet gear has 20 teeth. The pitch circle diameters of all are the same so that the planet gear P meshes with all of them. Determine the revolutions of gears C and D for one revolution of the arm B. Solution. Given : T A = 100 ; T C = 101 ; T D = 99 ; T P = 20 Fig. 13.17 l Chapter 13 : Gear Trains 453 The table of motions is given below : Table 13.12. Table of motions. Revolutions of elements Step No. Conditions of motion Arm B Gear A Gear C TA TC 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 0 +x + x× 3. Add + y r evolutions to all elements +y +y Total motion +y x +y y + x× + TA TC T × =+ A TC TD TD +y 4. Gear D TA TC + x× TA TD +y TA TC y + x× TA TD The arm B makes one revolution,...
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