how to control a hot-wire foam cutter using arduino 

This circuit was used to control a hot-wire foam cutter. You can see the inductor for a buck power supply near the top of the circuit along with the MOSFET switches near the power relay.

This is a simple circuit that uses the Arduino PWM output to control the buck power supply. The user selects the duty cycle via the knob seen in the lower part of the circuit. It worked reasonably well for the cutter. In hindsight, a foot pedal would have been more effective. The hands free control would improve the effectiveness of the cutter…

What is the most useful Arduino project you have made?

Simple, it’s the project you built yourself because you wanted to explore the world of electronics. The most useful circuit is the one that taught you something.