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Table 13.5. Table of motions.
Revolutions of elements
Step No. Conditions of motion Arm EF Gear C Gear B 1. Arm fixedgear C rotates through
+ 1 revolution ( i . e . 1 rev.
anticlockwise) 0 +1 – TC
TB 2. Arm fixedgear C rotates through
+ x revolutions 0 +x –x× TC
TB 3. Add + y r evolutions to all
elements +y +y +y 4. Total motion +y x +y y –x× Gear A
– TC TB
T
×
=– C
TB TA
TA
– x× TC
TA +y
TC
TB y –x× TC
TA 444 l Theory of Machines Speed of gear C
We know that the speed of the arm is 18 r.p.m. therefore,
y = 18 r.p.m.
and the gear A is fixed, therefore y –x×
∴ TC
=0
TA 18 – x × or 32
=0
72 x = 18 × 72 / 32 = 40.5 ∴ Speed of gear C = x + y = 40.5 + 18
= + 58.5 r.p.m.
= 58.5 r.p.m. in the direction
of arm. Ans.
Fig. 13.10 Speed of gear B
Let dA, dB and dC be the pitch circle diameters of gears
A , B and C respectively. Therefore, from the geometry of Fig. 13.10,
dB + dC
d
=A
2
2 or 2 dB + dC = dA Since the number of teeth are proportional to their pitch circle diameters, therefore
2 TB + T C = TA
∴ Speed of gear B or 2 T B + 32 = 72 or T B = 20 TC
32
= 18 – 40.5 ×
= – 46.8 r.p.m.
20
TB
= 46.8 r.p.m. in the opposite direction of arm. Ans.
= y –x× Example 13.7. An epicyclic train of gears is arranged as shown in
Fig.13.11. How many revolutions does the arm, to which the pinions B and
C are attached, make :
1. when A makes one revolution clockwise and D makes half a
revolution anticlockwise, and
2. when A makes one revolution clockwise and D is stationary ?
The number of teeth on the gears A and D are 40 and 90
respectively. Fig. 13.11 Solution. Given : T A = 40 ; T D = 90
First of all, let us find the number of teeth on gears B and C (i.e. TB and T C). Let dA, dB, dC
and dD be the pitch circle diameters of gears A , B , C and D respectively. Therefore from the geometry
of the figure,
dA + dB + dC = dD or dA + 2 dB = dD ...(3 dB = dC) Since the number of teeth are proportional to their pitch circle diameters, therefore,
TA + 2 T B = T D
∴ T B = 25, or
and 40 + 2 T B = 90
T C = 2...
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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.
 Fall '08
 CELGHORN

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