One way to distinguish the center tap (common wire) from a coil-end wire is by measuring the resistance. Resistance between common wire and coil-end wire is always half of the resistance between coil-end wires. This is because there is twice the length of coil between the ends and only half from center (common wire) to the end. A quick way to determine if the stepper motor is working is to short circuit every two pairs and try turning the shaft. Whenever a higher than normal resistance is felt, it indicates that the circuit to the particular winding is closed and that the phase is working.
The motor can be directly pulsed by the arduino. The arduino can also supply power to the motor, but normally this is only a good idea for demonstration purposes. The arduino has a very weak power supply, and attempting to power a motor through it can destroy the arduino. Furthermore, the arduino may not be able to supply the exact correct maximum voltage. For this reason, an ESC is placed between the arduino and the motor.
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