The male connector is wired to a Propeller Proto Board. There's a right angle 2x8 male header on a small piece of proto board just to the left of the black female connector. You should be able to see the 2x8 black connector in the upper center of this photo.
I cut an old parallel cable and soldered some normal 0.1" headers onto the wires I needed. I think there were at least six (I'm remembering nine) ground lines used by the CNC controller I have. Often devices which use Parallel ports have many shared pins.
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Since the parallel port is sending one way, I wonder if it needs a common ground, plus I am assuming that I would be dealing with just eight wires plus ground if necessary. I know of a web store that sells parallel port break out boards, then I would need some wires going to a breadboard, which would connect to the Propeller pins. If you don't have that, I found this project online where they did the hard work of disassembling the robot's Z80 firmware to figure out the commands for you: Some applications kludged the printer port for bi-directional communications using the handshake lines, so you need to be sure you know how the port on the robot is set up. You'll also need to level shift, since the parallel port expects TTL levels. You'll have to look at the robot docs to see if it uses any of the other pins. The first reference I picked up with the Centronics connector pinout shows the strobe as pin 1, then eight data bits on pins 2-9 (LSB on 2) and ground on pins 18-25. The robot docs should give you a timing spec, or failing that generic port info should be easy to find online.
You have to set the data up on the data lines, let them settle, then pulse the strobe line. The other thing you'll need is the strobe line to latch the parallel data. It's been forever since I've used a parallel printer port for I/O, but I can say that yes, you will need a common ground between the Prop and the robot.