Explain how a gear system can be used to obtain: (a) gain in speed

(a) A gear system can be used to obtain gain in speed when the bigger wheel drives the smaller wheel, i.e. when the driving gear has more number of teeth than the driven gear.

To obtain gain in speed, the gear ratio should be more than one. Mathematically, Gain in speed = Number of teeth in driving wheel/Number of teeth in driving wheel

Example: A toy motor car uses the gear principle to obtain gain in speed. It has a key and spring on the axle fitted with a driving gear having more teeth which engages the driven gear having fewer teeth. The wheels of the car are fitted on the axle of the driven gear.

When the key is turned clockwise (or the toy car is pulled back by hand) the spring is wound up. On releasing the key (or the toy car), the spring turns the driving gear anti-clockwise, which in turn rotates the wheels of the toy car clockwise and the car moves forward at a greater speed.

(b) A gear system can be used to obtain gain in torque when the smaller wheel drives the bigger wheel, i.e. when the driving gear has less number of teeth than the driven gear.

To obtain gain in torque, the gear ratio should be less than one. Mathematically,

Gain in torque = Number of teeth in driving wheel/Number of teeth in driving wheel

Example: While ascending a hill, an automobile driver changes gears and puts the driving gear of less number of teeth with a driven gear of more number of teeth. By doing so, he obtains a gain in torque, as more torque is required to go up the hill than to move along a level road.

(c) A gear system can be used to obtain change in direction when both the wheels of the gear system have the same number of teeth. Two gears mesh together in such a way that the driven gear rotates in direction opposite to the driving gear without any gain in speed or torque. So, if the driving gear turns clockwise, the driven gear turns counterclockwise. To obtain change in direction, the gear ratio should be equal to 1.

Example: In a car, the differential (a gearbox in the middle of the rear axle of a rear-wheel drive car) uses a cone-shaped bevel gear to turn the driveshaft's power through 90 degrees and turn the back wheels.