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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 gearcutting 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.
 Fall '08
 CELGHORN

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