After many attempts to screw pieces together, I found that 1 inch drywall screws worked best. I first marked my spot by piercing a tiny hole with the screw and then I used a drill with a 5/64 inch bit to cut a pilot hole before using the screw. Next I took a 3/8 inch bit to create a bigger hole about the depth of the screw head. This allows the screw to be nice and flush against the MDF rather than sticking off.

I screwed together the body (as seen below), but left off the back as I will use a hinge to allow for electronic manipulations. I need to cut holes in the bottom in order to allow for the wires to reach the motors at the base.

Body screwed together, still missing back

Meanwhile, I also began putting together the throwing arm. With all of the pieces printed, I was able to use super glue to stick them together. Once dry, I took the 3D pen to fill in any gaps and create an even better adhesive between the pieces. I need to reprint the arm/bottom of the cup because I left off a hole to allow for an eyelet screw, which will hold the springs.