# DC Motor Basics

The physics behind VEX motors

Direct Current (DC) Motors like the ones used on VEX robots move in accordance with a few physics equations. An understanding of these equations will help clarify the relationship between the values commanded to the motor from software and the physical movement of the motor.

## Prerequisites

A basic understanding of electronics (really just Ohm's Law)

## Velocity

The velocity of the motor roughly correlates to the voltage that is commanded to it.

The full equation is:

The "back-EMF" (

**E**lectro**M**otive**F**orce). This is the voltage drop accross the motor corresponding to the velocity of the motor. The faster the motor is spinning, the more back-EMF is produced.

We can rewrite the equation above to show the commanded voltage as the sum of these two voltages:

This back-EMF component, interestingly, is also the explanation for how electric generators work. Traditionally a voltage is provided to a motor to make it spin. This relation works in the opposite direction too though - so manually turning a motor will produce a voltage on the motor. The faster you spin the motor, the larger the voltage produced. On the VEX Cortex you could observe this by spinning a 393 motor fast enough to turn on the Cortex LEDS while there wasn't a battery plugged in.

## Torque

The second kind of output from a DC motor is **torque**. Torque is the rotational force provided by the motor. A motor on the drivetrain for a heavy robot will need to produce a lot of torque to get the robot moving, while a motor on a flywheel should produce relatively little.

The torque that a motor produces is directly related to its current draw:

## Combining the Two

If we substitute our torque equation into the voltage/velocity equation, we get:

The voltage provided to the motor will become a mix of torque and velocity. If the motor is stuck by some external force and cannot move at any velocity, then all of the provided voltage will go toward providing as much torque to try to get the motor moving.

## Determining the Constants

### Torque Constant (K_t)

The torque constant of a motor is equal to the torque provided by the motor divided by the current draw of the motor **while stuck and under stall**.

### Resistance (R)

The R value for a 600RPM V5 Motor is roughly **3.84** Ohms.

### Velocity Constant (K_v)

The velocity constant of a motor can be calculated after finding the resistance. Command a voltage to the motor (while it is not connected to anything or under stall) and measure the velocity and current draw of the motor. Plug those values into the combined equation and solve for K_v.

A 600RPM V5 Motor has a K_v value of roughly **6.68**.

### Converting Constants for Other Gearsets

## Contributing Teams to this Article

BLRS (Purdue SIGBots)

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