Engineering Mechanics

Chapter 34 : Transmission of Power by Gear Trains „„„„„ 709

First of all, consider the arm C to be fixed. Therefore axes of both the wheels A and B are also
fixed relative to each other. We know what when the wheel A makes one revolution anticlockwise,

the wheel B makes

A

B

T
T revolutions clockwise. Now assuming anticlockwise motion as negative and
clockwise as positive, we may say that when wheels A makes – 1 revolution the wheel B will make

A

B

T

T

+ revolutions and C makes zero revolution. Let us enter this statement of relative motion in

the first row of the Table 34.1.

Similarly, if the wheel A makes – x revolutions, the wheel B will make A

B

xT

T

+ revolutions.

Let (^) us enter this statement of relative motion in the second row of the same Table 34.1.
Now consider each member of the epicyclic gear train to make + y revolutions. Let us enter
this statement of motion in the third row of the Table 34.1. Now add algebraically, the motions of the
arm C, wheel A and wheel B of the second and third rows as shown in the Table 34.1.
Table 34.1
Step No. Conditions of motions
Revolutions of
Arm C Wheel A Wheel B

1. Arm C fixed; wheel A rotates 0 – 1

A

B

T

T

+

through – 1 revolution

2. Arm C fixed; wheel A rotates 0 – x A
   B

xT

T

+

though – x revolutions

3. All parts rotate though + y + y + y + y
   revolutions


4. Total motion (2 + 3) + y – x + y A
   B

xT

y

T

+

The last row of the table gives the final motion of each member in terms of x and y (by adding
rows 2 and 3). Now if the two conditions about the motion of rotation of any two members is known,
then the unknown speed of the third member may be obtained by substituting the given data in the
third column.

2. Algebraic method
   In this method, the motion of each member of the epicyclic gear train is expressed in the form
   of equations. The number of equations depend upon the number of members in the gear train. The
   two conditions (i.e. one member is fixed and the other has a specified motion) are used to solve the
   equations of motion.

Now consider an epicyclic gear train as shown in Fig. 34.12. Let us assume the arm C to be
fixed.

Let TA= No. of teeth on the wheel A,

NA= Speed of the wheel A in r.p.m. and

TB, NB= Corresponding values for the wheel B.