Question

In a simple gear train, if the number of idler gears is odd, then the direction of motion of the driven gear will be:

• A. Be same as that of the driving gear
• B. Be opposite to that of the driving gear
• C. Depend upon the number of teeth on the driving gear
• D. Depends on type of gears

Hint:

Remember that each idler gear in a simple gear train reverses the direction of rotation. An even number of idler gears results in the driven gear rotating in the opposite direction to the driver, while an odd number results in the same direction.

Answer 1

The Correct Option is A

Step 1: Understand the function of an idler gear.
An idler gear is an intermediate gear placed between the driving gear and the driven gear. Its primary purpose is to change the direction of rotation of the driven gear without affecting the speed ratio. Step 2: Analyze the effect of one idler gear on the direction of rotation.
When the driving gear rotates, it causes the idler gear to rotate in the opposite direction. This idler gear, in turn, causes the driven gear to rotate in the opposite direction to the idler gear, which means the driven gear rotates in the same direction as the driving gear. Thus, one idler gear reverses the direction of rotation twice, resulting in the same direction for the driver and driven gears. Step 3: Analyze the effect of an odd number of idler gears on the direction of rotation.
Let \( n \) be the number of idler gears. Each idler gear introduces a reversal in the direction of rotation.
If \( n = 1 \) (odd), the direction is reversed once by the driver to the first idler, and then reversed again by the first idler to the driven gear. The final direction of the driven gear is the same as the driving gear.
If \( n = 3 \) (odd), there will be three reversals, resulting in the driven gear rotating in the same direction as the driving gear.
In general, for an odd number of idler gears, the total number of direction reversals will be odd. However, let's consider the interaction sequentially. The driver reverses the direction of the first idler. The first idler reverses the direction of the second idler, and so on. The last idler reverses the direction of the driven gear. For an odd number of idler gears, there will be an even number of reversals between the driver and the driven gear (each pair of idlers cancels out the reversal effect), leaving the final driven gear rotating in the same direction as the driver. Step 4: Consider the given condition of an odd number of idler gears.
As established in Step 3, if the number of idler gears is odd, the driven gear will rotate in the same direction as the driving gear. Step 5: Evaluate the other options.
Option 2 is incorrect because an odd number of idler gears results in the same direction of rotation.
Option 3 is incorrect because the direction of rotation is determined by the number of idler gears, not the number of teeth on the driving gear (the number of teeth affects the speed ratio).
Option 4 is incorrect because for simple external gear trains (which is implied here), the direction depends on the number of idler gears, not the type of gears (spur, helical, etc., would still follow the same principle for direction reversal).
Step 6: Select the correct answer.
The direction of motion of the driven gear will be the same as that of the driving gear when the number of idler gears is odd. This corresponds to option 1.