Add y revolutions to all elements y y y 4 total

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Unformatted text preview: evolution 0 +1 – 2. Arm fixed - gear C rotates through + x revolutions 0 +x – x× 3. Add + y revolutions to all elements +y +y +y 4. Total motion +y x+y y – x× Gear G – TC TD TC TE × TD TG – x× TC TE × TD TG +y TC TD y – x× TC TE × TD TG Since the gear G is fixed, therefore from the fourth row of the table, y – x× ∴ TC TE × =0 TD TG y– 5 x=0 6 or y – x× 50 35 × =0 20 105 ...(i) 450 l Theory of Machines Since the gear C is rigidly mounted on shaft A , therefore speed of gear C and shaft A is same. We know that speed of shaft A is 110 r.p.m., therefore from the fourth row of the table, x + y = 100 ...(ii) From equations (i) and (ii), x = 60, and y = 50 ∴ Speed of shaft B = Speed of arm = + y = 50 r.p.m. anticlockwise Ans. Example 13.11. Fig. 13.15 shows diagrammatically a compound epicyclic gear train. Wheels A , D and E are free to rotate independently on spindle O, while B and C are compound and rotate together on spindle P, on the end of arm OP. All the teeth on different wheels have the same module. A has 12 teeth, B has 30 teeth and C has 14 teeth cut externally. Find the number of teeth on wheels D and E which are cut internally. If the wheel A is driven clockwise at 1 r.p.s. while D is driven counter clockwise at 5 r.p.s., determine the magnitude and direction of the angular velocities of arm OP and wheel E. Fig. 13.15 Solution. Given : T A = 12 ; T B = 30 ; T C = 14 ; NA = 1 r.p.s. ; N D = 5 r.p.s. Number of teeth on wheels D and E Let T D and T E be the number of teeth on wheels D and E respectively. Let dA , dB , dC , dD and dE be the pitch circle diameters of wheels A , B , C, D and E respectively. From the geometry of the figure, dE = dA + 2dB and dD = dE – (dB – dC) Since the number of teeth are proportional to their pitch circle diameters for the same module, therefore T E = T A + 2T B = 12 + 2 × 30 = 72 Ans. and T D = T E – (T B – T C) = 72 – (30 – 14) = 56 Ans. Magnitude and direction of angular velocities of arm OP and...
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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- Toronto.

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