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Unformatted text preview: n F), annular wheel 8 (on B ) and the arm i.e.
casing C. The table of motions is given below :
Table 13.16. Table of motions.
Revolutions of elements
Step No. Conditions of motion Arm Wheel 8 Wheel 7 1. Arm fixed, wheel 8 rotated through
+ 1 revolution 0 +1 + 2. Arm fixed, wheel 8 rotated through
+ x 2 revolutions 0 + x2 + x2 × 3. Add + y 2 r evolutions to all
elements + y2 + y2 + y2 4. Total motion y2 x2 + y2 T8
T7 y2 + x2 × T8
T7 T8
T7 We know that the speed of C in the first train is 0.4 r.p.s., therefore
y 2 = 0.4 ...(v ) Also the speed of wheel 7 is equal to the speed of F or wheel 6 in the second train, therefore y2 + x2 × ∴ T8
= –14
T7 or x2 = ( − 14 − 0.4) 0.4 + x2 × 160
= – 14
66 ...(vi) 66
= − 5.94
160 ∴ Speed of wheel 8 or of the shaft B
x 2 + y 2 = – 5.94 + 0.4 = – 5.54 r.p.s. = 5.54 r.p.s. (clockwise)
We have already assumed that the speed of wheel 1 or the shaft A is 1 r.p.s. anticlockwise
∴ Velocity ratio of the output shaft B to the input shaft A
= – 5.54 Ans.
Note : The – ve sign shows that the two shafts A and B rotate in opposite directions. 13.10. Epicyclic Gear Train with Bevel Gears
The bevel gears are used to make a more compact epicyclic system and they permit a very
high speed reduction with few gears. The useful application of the epicyclic gear train with bevel
gears is found in Humpage’s speed reduction gear and differential gear of an automobile as discussed
below :
1. Humpage’s speed reduction gear. The Humpage’s speed reduction gear was originally
designed as a substitute for back gearing of a lathe, but its use is now considerably extended to all
kinds of workshop machines and also in electrical machinery. In Humpage’s speed reduction gear, as
shown in Fig. 13.20, the driving shaft X and the driven shaft Y are coaxial. The driving shaft carries
a bevel gear A and driven shaft carries a bevel gear E. The bevel gear B meshes with gear A (also
known as pinion) and a fixed gear C. The gear E meshes with gear D which...
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 Fall '08
 CELGHORN

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