Magical Torque......

In the post At the Right Angle, I talked about the definition of force and its application in Robotic Arm and Base. In today's post, I will talk about how Torque can create magic!!

We need to apply a bit of mathematics here to understand the magic.

Torque is calculated by the formula:
T = F*d

T is the torque
F is the force applied perpendicular (at 90 deg.) to the axis
d is the distance

By using the above formula, we can calculate torque for Geared systems. Lets, take the example of the gear system below:

Here, we have attached a gear system with a pulley. Let us assume the load on the pulley is 1 kg and the diameter of the pulley is 1 inch. Then the torque would be:

T= F* d = 1 kg * 1 inch = 1 kg-inch

Now, what would be the torque on the Big Gear? The torque transferred on the Big Gear would also be 1kg-inch. This is because the torque remains constant on the shaft, and is transferred to the big gear.

The next step is to calculate the force on contact point B. We know the Torque is 1 kg-inch and the diameter of the Big Gear 1 inch. So,

F = T/d = 1 kg-inch * 1 inch = 1 kg

So now lets calculate the torque on the motor. The force on the Small Gear is 1 kg and its diameter is 1/4 inch. The resultant torque on the motor shaft is:

T= F * d = 1 kg * 1/4 inch = 1/4 kg-inch

Did you see the magic happen?
Torque at motor = 1/4 kg - inch
Torque at Pulley = 1 kg- inch!!

Torque increases magically, but only if we put the gear systems right!