Pm clockwise since the gear a makes 300 rpmclockwise

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Unformatted text preview: e from the fourth row of the table, x + y = – 300 or x = – 300 – y = – 300 – 150 = – 450 r.p.m. ∴ Speed of gear B , NB = y – x × 36 TA = 150 + 450 × = + 510 r.p.m. 45 TB = 510 r.p.m. (anticlockwise) Ans. 2. Algebraic method Let N A = Speed of gear A . N B = Speed of gear B , and N C = Speed of arm C. Assuming the arm C to be fixed, speed of gear A relative to arm C = NA – NC and speed of gear B relative to arm C = N B – N C 440 l Theory of Machines Since the gears A and B revolve in opposite directions, therefore NB – NC T =– A NA – NC TB ...(i) Speed of gear B when gear A is fixed When gear A is fixed, the arm rotates at 150 r.p.m. in the anticlockwise direction, i.e. N A = 0, ∴ or and N C = + 150 r.p.m. 36 NB – 150 =– = – 0.8 0 – 150 45 ...[From equation (i)] N B = – 150 × – 0.8 + 150 = 120 + 150 = 270 r.p.m. Ans. Speed of gear B when gear A makes 300 r.p.m. clockwise Since the gear A makes 300 r.p.m. clockwise, therefore N A = – 300 r.p.m. 36 N B – 150 =– = – 0.8 –300 – 150 45 ∴ or N B = – 450 × – 0.8 + 150 = 360 + 150 = 510 r.p.m. Ans. Example 13.5. In a reverted epicyclic gear train, the arm A carries two gears B and C and a compound gear D - E. The gear B meshes with gear E and the gear C meshes with gear D. The number of teeth on gears B, C and D are 75, 30 and 90 respectively. Find the speed and direction of gear C when gear B is fixed and the arm A makes 100 r.p.m. clockwise. Solution. Given : T B = 75 ; T C = 30 ; T D = 90 ; N A = 100 r.p.m. (clockwise) Fig. 13.8 The reverted epicyclic gear train is shown in Fig. 13.8. First of all, let us find the number of teeth on gear E (T E). Let dB , dC , dD and dE be the pitch circle diameters of gears B , C, D and E respectively. From the geometry of the figure, dB + dE = dC + dD Since the number of teeth on each gear, for the same module, are proportional to their pitch circle diameters, therefore TB + T E = T C + T D ∴ TE = T C + T D – T B = 30 + 90 – 75 = 45 The table of motions is drawn as follows : A gear-cutting machine is used to cu...
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This note was uploaded on 02/13/2014 for the course MIE 301 taught by Professor Celghorn during the Fall '08 term at University of Toronto.

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