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Unformatted text preview: ame direction,
then the input and output torques will be in opposite directions. Similarly, when the input and output shafts
rotate in opposite directions, then the input and output torques will be in the same direction. Example 13.19. Fig. 13.26 shows an epicyclic gear train. Pinion
A has 15 teeth and is rigidly fixed to the motor shaft. The wheel B has 20
teeth and gears with A and also with the annular fixed wheel E. Pinion
C has 15 teeth and is integral with B (B, C being a compound gear
wheel). Gear C meshes with annular wheel D, which is keyed to the
machine shaft. The arm rotates about the same shaft on which A is fixed
and carries the compound wheel B, C. If the motor runs at 1000 r.p.m.,
find the speed of the machine shaft. Find the torque exerted on the
machine shaft, if the motor develops a torque of 100 Nm. Fig. 13.26 Solution. Given : TA = 15 ; TB = 20 ; TC = 15 ; NA = 1000 r.p.m.; Torque developed by motor (or
pinion A ) = 100 Nm
First of all, let us find the 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 + 2 dB and dD = dE – (dB – dC) Since the number of teeth are proportional to their pitch circle diameters, therefore,
T E = T A + 2 T B = 15 + 2 × 20 = 55
and T D = T E – (T B – T C) = 55 – (20 – 15) = 50 Speed of the machine shaft
The table of motions is given below : 464 l Theory of Machines
Table 13.21. Table of motions.
Revolutions of elements Step
No. Conditions of motion Arm Pinion
A Compound
wheel BC Wheel D 1. Arm fixedpinion A
rotated through + 1
revolution
(anticlockwise) 0 +1 – TA
TB – 2. Arm fixedpinion A
rotated through + x
revolutions 0 +x – x× TA
TB –x × 3. Add + y revolutions to
all elements +y +y 4. Total motion +y x +y +y y – x× TA TC
×
TB TD TA TC
×
TB TD
+y TA
TB y –x× TA TC
×
TB TD Wheel E − TA TB
T
×
=− A
TB TE
TE − x× TA
TE +y y − x× TA
TE We know...
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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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