A parallel to USB adapter will not work. You will need to use a USB interface like the ones below:
Mach3 USB interface:
To answer the question in more detail, the parallel port is actually an extension straight from the CPU and is also called the GPIO (General Purpose I/O) pins. These pins carry signals independently, hence the description as being a parallel port.
The stepper motor driver receives a pulse train (series of pulses). A single pin on the parallel port sends a pulse train to one stepper motor driver and stepper motor for a single axis. Another pin on the parallel port sends a pulse train to another stepper motor driver on another axis. This happens simultaneously as with the direction signals for each axis.
If a parallel port is adapted through a USB (using an adapter), the parallel port cannot have these signals happen in a simultaneous fashion and will cause the stepper motors of a CNC router or machine to be very clunky, if it works at all. To elaborate, the computer sends an instruction to the USB to send a high signal to pin 1, so it does, then another signal to pin 2, so it does. This is happening one after another. The speed at which this happens is reduced dramatically, and the position of one axis may now be out of sync to another axis.
The reason the USB interfaces (linked above) work is that the USB delivers broad instructions to the interface (to a microcontroller) and the interface parses the instructions and outputs simultaneous signals to the stepper motor drivers.
Hope this helps.
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My computer doesn't have a parallel port connection. Can I use a usb to parallel port cable to communicate with my breakout board?