I was wandering if it would be possible using any method to control a variable transformer using an arduino board?
I have thought the most obvious way would be, since the variable transformer has a manual tuning knob, would be to have a stepper motor calibrated to 0 value and the 100% value and have the motor control the variable of the transformer?
If anyone can come up with an easier or more obvious solution I would be very grateful!
Generally that would be the way to do it. But the variable transformer (Variac ?) needs quite a bit of torque to turn it so you might be better off using a step down gear ratio, say about 4:1 with the stepper motor mounted beside the transformer and using a toothed belt drive arrangement. Hence for 300 degrees (or so) of transformer rotation your stepper will rotate around 1200 degrees ( 3+ revolutions)
A million years ago I worked at a place that used motor-driven Variacs for "theater" light dimming... So, I knew you can buy them with motors. It looks like the motorized Variacs you can buy are "dumb". They have connections for an up-down switch and limit switches, but no positional feedback. (It "looks like" a geared-down AC bi-directional AC motor.)
Assuming you do want feedback (for precise-programmable contol) you have two choices. You can use a stepper motor or a servo. Either way, your motor/controller is likely to be more expensive than the Variac.
A servo or a stepper can be controlled with the Arduino. From a design/construction perspective, a servo is complete. You just provide the power and a control pulse from the Arduino. A stepper motor requires a separate motor driver circuit (MOSFETs, etc).
If you use a stepper, it's standard practice to add a "home" sensor (plus maybe a limit sensor) to get your starting point and to correct for any errors or missed-steps.
Maybe you can "adapt" a small torque wrench to the Variac to see how much torque is required before selecting a motor. It can get tricky, because you have starting-friction and rotational inertia, but a torque measurement is better than nothing.