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Unformatted text preview: tive, we
may say that when gear A makes + 1
revolution, then the gear B will make
(– T A / T B) revolutions. This statement
of relative motion is entered in the first
row of the table (see Table 13.1).
Secondly, if the gear A makes
+ x revolutions, then the gear B will
Inside view of a car engine.
make – x × T A / T B revolutions. This
statement is entered in the second row
Note : This picture is given as additional information and is not
a direct example of the current chapter.
of the table. In other words, multiply
the each motion (entered in the first row) by x .
Thirdly, each element of an epicyclic train is given + y revolutions and entered in the third
row. Finally, the motion of each element of the gear train is added up and entered in the fourth row.
* We know that N B / N A = TA / TB. Since N A = 1 revolution, therefore N B = T A / T B. 438 l Theory of Machines
Table 13.1. Table of motions
Revolutions of elements Step No. Conditions of motion Arm C Gear A Gear B 1. Arm fixed-gear A rotates through + 1
revolution i.e. 1 rev. anticlockwise 0 +1 – TA
TB 2. Arm fixed-gear A rotates through + x
revolutions 0 +x – x× TA
TB 3. Add + y revolutions to all elements +y +y +y 4. Total motion +y x +y y – x× TA
TB A little consideration will show that when two conditions about the motion of rotation of any
two elements are known, then the unknown speed of the third element may be obtained by substituting the given data in the third column of the fourth row.
2. Algebraic method. In this method, the motion of each element of the epicyclic train relative
to the arm is set down in the form of equations. The number of equations depends upon the number of
elements in the gear train. But the two conditions are, usually, supplied in any epicyclic train v iz. some
element is fixed and the other has specified motion. These two conditions are sufficient to solve all the
equations ; and hence to determine the motion of any element in the epicyclic gear train.
Let the arm C be fixed in an epicyclic gear train as shown in Fig. 13.6. Therefor...
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- Fall '08