🎯 Two-Stage Rack Positioner: step-by-step build

Combine a two-stage reduction, shared shafts and a captured rack to position a slider in small increments.

The red input turns a blue intermediate shaft, then a yellow pinion shaft, which feeds a guided rack. Two 8-to-24 tooth reductions multiply to nine input turns per pinion turn. A quarter input turn commands about 0.70 mm of ideal rack movement. Investigate an actual target and direction reversal: small commanded motion does not guarantee accuracy, remove backlash or make a lifting brake.

• Level 4 of 5 (tricky)
• About 50 minutes
• 28 steps, 76 parts
• Powered by: Hand-crank
• Series: Mechanical Wonders

What you will learn

• Compound Gears: Two gear stages in a row multiply their ratios.
• Gear Ratio: Fast or Slow: A big gear turning a small gear makes it spin faster.
• Rack & Pinion Steering: A gear rolling on a straight rack slides it sideways.
• Axles: An axle is a cross-shaped rod — anything on it turns together.
• Bushes & Spacers: Bushes stop things sliding off an axle.
• Frames: A frame is a ready-made strong rectangle.
• Friction: Friction is the rubbing force that slows things down.

Build these first

• ⚙️ Gear Friends: Three gears holding hands — spin one and they all dance. (level 1 of 5, about 8 minutes, 6 steps)
• 📏 Rack Travel Bench: Turn a small gear and measure the straight travel of a captured rack. (level 3 of 5, about 25 minutes, 13 steps)

Parts you need

• 1 × Open frame 5×11
• 5 × Axle 10
• 19 × Bush
• 3 × Tiny gear (8 teeth)
• 5 × Beam 5
• 4 × Axle 5
• 20 × Half bush
• 10 × Black pin (grippy)
• 2 × Beam 7
• 1 × Axle 4
• 1 × Steering rack
• 2 × Beam 3
• 2 × Medium gear (24 teeth)
• 1 × Beam 9

Steps

1. Lay the 5×11 frame flat on a smooth tabletop. Use the middle hole on a short edge for the pinion axle.
2. Fit the long 10-module output axle through the middle short-edge hole, its lower end level with the bottom of the full lower bush. Seat the lower bush, 8-tooth rack pinion and red upper bush as shown. The longer shaft will also carry a reduction gear and an upper bearing.
3. Fit a 5-hole lower crosspiece beneath the left side of the frame, extending two holes outward. Retain its guide axle underneath, and pin its next inner hole to the frame so it cannot swing.
4. Fit the same retained and pinned lower crosspiece beneath the right side. Both crosspieces support the rack channel.
5. Lay a 7-hole outer rail two modules outside the frame edge. Fit its left guide axle, lower half-bush foot and upper full-bush spacer.
6. Fit the right outer guide axle with its lower foot and upper spacer. Two fixed axle lines now prevent the outer rail swinging.
7. Add full-bush spacers to the two inner guide axles. All four spacers will support the top retainers.
8. Support the far end of the long frame: fit a 4-module axle through its middle rear hole. Stack a full bush and half bush underneath as a foot, then retain it above with another half bush.
9. Make the carrier: lay a red 7-hole beam flat, with its holes facing up. Its long edge will follow the outside of the frame.
10. Fit two friction pins through the beam ends and press the rack onto them, teeth toward the frame. The pins retain the rack without hardware projecting below the carrier.
11. Bring the carrier in from the left, outside the frame, until its middle is beside the pinion. Turn the whole shaft slightly so teeth fit gaps. The carrier sits on the lower crosspieces between the frame edge and outer rail; the next steps close the top. Limit travel to one module each side of this centre position.
12. Close the guide with two 3-hole crosspieces across the channel. The carrier must still slide; the crosspieces keep it from lifting off.
13. Retain each top crosspiece with two half bushes. Check the carrier cannot lift, yaw or move sideways, then slide it gently through the short stroke.
14. Pin a 5-hole crossbeam across the frame at the hole line 3. Two black pins, one at each end, prevent it hinging. Its centre hole will support a reduction shaft.
15. Pin a 5-hole crossbeam across the frame at the hole line 5. Two black pins, one at each end, prevent it hinging. Its centre hole will support a reduction shaft.
16. Pin a 5-hole crossbeam across the frame at the hole line 7. Two black pins, one at each end, prevent it hinging. Its centre hole will support the rear upper-bearing post.
17. At the middle crossbeam, fit a 10-module shaft. Seat half bushes directly below and above the crossbeam, then a full spacer above. Rotate the whole keyed stack slightly to align the later meshes.
18. At the input crossbeam, fit another 10-module shaft with half bushes directly below and above the beam. Add the first full spacer above it.
19. Add the second full spacer to the input now, before the upper mesh closes its insertion path.
20. On the output shaft add a half-bush spacer above the red bush, then a 24-tooth gear and a half bush touching its upper face. The 24T and lower 8T rack pinion share one axle and cannot turn independently.
21. Fit an 8-tooth gear to the middle shaft at the same height as that output 24T gear. Fit a 24T gear directly above it and a half bush above. Both middle gears share the same cross axle. Align teeth with gaps without forcing the output shaft or rack.
22. Fit an 8-tooth gear above the preloaded input spacers level with the upper middle 24T, and a half bush above. The drive path is input8→middle24, same-shaft middle8→output24, same-shaft output8→rack. The two reduction meshes live on separate height layers.
23. Fit a stationary 10-module pole through the centre of the outer guide rail. Seat a full bush directly below and another directly above that bearing. These poles support the upper bearing bridge; they do not drive the gears.
24. Fit a stationary 10-module pole through the centre of the rear crossbeam. Seat a full bush directly below and another directly above that bearing. These poles support the upper bearing bridge; they do not drive the gears.
25. Slide a full bush onto each stationary pole and position it as the upper shelf stop shown. They will carry the bridge at both ends.
26. Lower a 9-hole bridge along the stationary poles and all three moving shafts. It rests on both shelf stops. Cap the two stationary poles above it. Its three interior round bearings keep the long drive shafts aligned.
27. Cap the input and middle shafts directly above the upper bridge with full bushes: red for input and blue for middle. The yellow output cap follows next. These caps also provide removable-mark handles. Keep each cap seated; wait for the final cap before operating.
28. Fit the yellow output cap and handle. Check both gear meshes, both main bearings on every moving shaft and the full rack channel. No fingers should be needed to hold the rack in mesh.

Play time

Hold the stationary frame level. Mark the rack centre and place a scale clear of its sweep. Turn the red input slowly by quarter turns, predicting about 0.698 mm travel per quarter turn. Stay within ±8 mm from centre (about ±2.86 input turns). Try a 2.79 mm target, return to centre and repeat three times from the same direction; then reverse and record any take-up before movement. Smaller commanded steps do not prove accuracy. No physical end stops, motor, added load, self-locking or physical test rating is provided. Stop for lifting, shaft movement, rubbing or teeth reaching the rack tabs.

Credited demonstrations and component sources

• Compound gear train 125:1 model with Lego Technic — Tools & Machines Lab: Independent shared-shaft compound-gearing demonstration inspires the serial-stage principle. Our original two-stage 9:1 linear positioner has different gears, supports, dimensions and instructions; it is not the creator’s 125:1 model.
• LEGO Education — Gear: Primary teaching reference for compound gearing and conversion between rotary and linear motion. Our target/reversal experiment and geometry calculations are original.