This is the page to accumulate the information for the shuttle design.  There will be links to part models, specification sheets, design sketches, and more.

A sketch of the shuttle design shows the various bits that need to get designed.

A video describing the design requirements (hopefully) makes the details in the sketch clearer.

Since the Vex 393 motor has several internal gearing options, we can use a 1:1 gear ratio to drive the bevel gears.

This will leave the output travel of the shuttle as about: .083 inches per turn * (50/80/120) turns per minute = 4.15/6.64/9.96 inches per minute = .069/.111/.166 inches per second.  This might be a little slow, but it will give a reasonable proof-of-concept.

Parts and CAD files

A1CY20025 Stock Drive Miter Gears (20 pitch, carbon steel, 25 teeth) [CAD-zipped][product-page]

Lead screw from Mcmaster-Carr [CAD-zipped]

Acme nut from Mcmaster-Carr [CAD-zipped]

Small bearings [CAD-zipped] mcmaster: 7487N35 (NOTE: this is a metric bearing.)

Regular bearings [CAD-zipped] mcmaster: 5908K12

Linear bearings [CAD-zipped] mcmaster: 6489K61

48t, 24p Spur gear stock [CAD-zipped]

54t, 24p Spur gear stock [CAD-zipped]

Vex 393 Motor [CAD-zipped] [spec sheet]