I have designed my z axis so that the center housing that contains the lead screw nut and bushings for the rods is actually mounted to the y axis, and the screw and rods will actually move together up and down (rather than mounting the rods and screw on both ends and letting the nut move up and down the screw, pulling everything with it). However, I am having difficulty figuring out exactly where the forces will lie on this and if this will cause any deflection in the screw. Most of the pieces are 3D printed so they are very lightweight. Side note, this is not a typical CNC application, it will actually be mounted on a vertical wall so that the z-axis will actually be moving horizontally rather than vertically. Hopefully this makes sense. Below is my model of my design(it will be completely horizontal, I just rotated it a bit for a more detailed view).
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