First of all you should be trained and have experience working around high voltages. You must be able to operate a voltmeter and practice extreme caution while performing tests on a Twister Speed Lathe that has the housing removed as deadly voltages are present even when the machine is not running.
Make sure the speed control on the front panel is set to maximum. Also verify that the power switch is on and that the forward / reverse switch is NOT in the center position.
Step on the foot switch or flip the run / brake switch to run. The motor should run. If it does not, note if the relay pulls in. If the relay does not pull in the problem is possibly the power cord, power switch, forward / reverse switch, relay, or relay socket. If the relay pulls in, place a AC voltmeter (minimum 250 volt range) across L1 and L2 on the circuit Board. You should see 110 to 220 volts AC depending on what voltage your lathe is plugged in to. If you see less than line voltage the problem is possibly the relay, relay socket, or wiring. If you see line voltage remove the test leads and switch to a 250 volt DC range. Measure the voltage between A1 and A2 on the circuit board, it should be between 80 and 100 volts. if voltage is present, the problem is most likely the motor or the wiring going to the motor. If no voltage is present the problem is most likely the circuit board.