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The table of motions is drawn as follows :
Table 13.10. Table of motions.
Revolutions of elements
Step
No. Conditions of motion Arm Wheel A 1. Arm fixed A rotated through
– 1 revolution (i.e. 1 revolution clockwise) 0 2. Arm fixedwheel A rotated
through – x revolutions 0 –x + x× 3. Add – y revolutions to all elements –y –y –y 4. Total motion –y –x–y –1 Compound
wheel BC
+ TA
TB Wheel D + TA TC
×
TB TD Wheel E + TA TB
×
TB TE
=+ x× TA
TB TA
–y
TB + x× TA TC
×
TB TD + x× –y x× TA TC
×
–y
TB TD TA
TE TA
TE –y x× TA
–y
TE Chapter 13 : Gear Trains l 451 Since the wheel A makes 1 r.p.s. clockwise, therefore from the fourth row of the table,
– x – y = – 1 or
x+y=1
...(i)
Also, the wheel D makes 5 r.p.s. counter clockwise, therefore TA TC
12 14
– y=5
×
or
x×
– y=5
×
TB TD
30 56
∴
0.1 x – y = 5
From equations (i) and (ii),
x = 5.45
and
y = – 4.45
∴ Angular velocity of arm OP
= – y = –(– 4.45) = 4.45 r.p.s
= 4.45 × 2 π = 27.964 rad/s (counter clockwise) Ans.
x× ...(ii) 12
TA
– y = 5.45 ×
– (– 4.45) = 5.36 r.p.s.
72
TE
= 5.36 × 2 π = 33.68 rad/s (counter clockwise) Ans.
Example 13.12. An internal wheel B with 80 teeth is keyed to a shaft F. A fixed internal
wheel C with 82 teeth is concentric
with B. A compound wheel DE
gears with the two internal wheels;
D has 28 teeth and gears with C
while E gears with B. The compound
wheels revolve freely on a pin which
projects from a disc keyed to a shaft
A coaxial with F. If the wheels have
the same pitch and the shaft A makes
800 r.p.m., what is the speed of the
Helicopter
shaft F ? Sketch the arrangement. and angular velocity of wheel E = x × Solution. Given : T B = 80 ; T C
= 82 ; T D = 28 ; N A = 500 r.p.m. Note : This picture is given as additional information and is not a
direct example of the current chapter. The arrangement is shown in Fig. 13.16. Fig. 13.16 First of all, let us find out the number of teeth on wheel E (T E). Let dB , dC , dD and dE be the
pitch circle diameter of wheels B , C, D and E respectively. From the geometry of the figure,
dB = dC – (dD – dE ) 452 l Theory of Machines or dE = dB + dD –...
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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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