Assuming the anticlockwise rotation as positive and

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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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