- Difficulty
- Intermediate
- Build time
- 60-90 min
- Estimated cost
- $0-$15
- Age range
- 11-17
- Workspace
- A clear table about 90 cm wide
The finish line
What you will build
The final output turns smoothly in the same direction as the input and completes about one turn for every nine input turns in the 3:1 by 3:1 setup.
Learning goals
- Identify how clockwise hand-crank rotation produces slow clockwise shaft rotation.
- Construct and explain a rotary-to-rotary through two stages system.
- Measure how the second-stage driven gear size changes performance.
- Diagnose losses caused by four gear meshes and axle friction.
Before you build
Materials, tools, and safety
Reuse-material cost: Usually under $5 with an existing kit. Supervision: Adult help recommended for sharp or heated tools.
Tools
- Ruler
- Removable tape for motion marks
Low-cost swaps
- Use equivalent brick-compatible parts from any kit.
- Use cardboard beams and straw bearings for a larger demonstration model.
- Use any two known gear pairs and multiply their measured ratios.
Project-specific safety
- Keep fingers, hair, and loose sleeves clear of moving parts.
- Turn the mechanism by hand; do not attach a high-speed motor.
- Brace the middle shaft before applying resistance so a flexing axle cannot throw a loose gear.
Orient the build
Place the build so clockwise hand-crank rotation is on your left and slow clockwise shaft rotation is on your right. Call the side facing you the front, the far side the back, the tabletop the bottom, and the opposite face the top.
Build it
Step-by-step instructions
Step 1
Build the ladder frame
Connect two long side rails with four cross braces so the frame stays square.
Leave a clear center channel for three parallel axles.
Step 2
Install the input shaft
Mount the first small gear near the left side and add a crank outside the frame.
Use collars with a thin running gap on both rails.
Step 3
Place the middle shaft
Mesh the first large gear with the input gear and support its axle on both rails.
Spin the pair before adding any second-stage parts.
Builder checkpoint: After place the middle shaft, the first subassembly should stay aligned when handled gently.
Step 4
Lock the second driver
Add the second small gear to the middle axle so both middle gears rotate together.
Keep enough spacing that the two gears cannot rub each other.
Watch for: If this stage binds or drifts, inspect backlash before adding more parts.
Step 5
Locate the output shaft
Mesh the second large gear with the middle small gear and mark equal-height supports.
Check that neither gear pair forces its axle sideways.
Step 6
Brace every bearing
Add cross pieces beside the three axle locations without touching rotating collars.
Press the frame lightly and watch for center-distance changes.
Builder checkpoint: After brace every bearing, operate the build slowly and confirm that slow clockwise shaft rotation begins without binding.
Step 7
Mark and count rotations
Point all paper flags upward and turn the crank exactly nine times at a slow pace.
Record middle and output rotations instead of estimating from speed.
Step 8
Load the output gently
Pinch the output flag lightly while turning the input to feel the torque tradeoff.
Stop before teeth skip and reinforce the weakest support.
Builder checkpoint: At the final checkpoint, The final output turns smoothly in the same direction as the input and completes about one turn for every nine input turns in the 3:1 by 3:1 setup.
See the engineering
Why it works
- Input
- clockwise hand-crank rotation
- Output
- slow clockwise shaft rotation
- Motion
- rotary-to-rotary through two stages
- Energy losses
- four gear meshes, axle friction, middle-shaft flex, backlash
Why this works
Compound gear ratio
When separate reductions act in sequence, the total ideal ratio is the product of the stage ratios rather than their sum. The shared middle axle carries one driven gear and one driver gear together.
Look for: Mark all three shafts and count how the middle shaft slows first, then the output slows again.
Where the energy goes
Efficiency and losses
The ideal model leaves out four gear meshes, axle friction, middle-shaft flex, backlash. These effects turn some input energy into heat, sound, vibration, or unwanted motion, so measured performance will be lower than an ideal calculation.
Look for: Run the build slowly and locate the first place where four gear meshes becomes visible or audible.
Math bite
Multiply the two stages
Formula: total ratio = stage 1 ratio × stage 2 ratio
- Stage 1 = 36/12 = 3
- Stage 2 = 36/12 = 3
Substitute: total ratio = 3 × 3 = 9
Result: Nine input turns produce one ideal output turn.
Ideal output torque is nine times input torque before losses.
Four tooth contacts and three axle bearings add friction, so real torque is lower.
Make it behave
Test, troubleshoot, and tune
Controlled test
Start here: Turn the unloaded crank nine times at one turn per second.
Success looks like: The middle shaft turns three times and the output turns once without skipping.
Measure: Input, middle, and output rotations plus time for nine input turns.
Change: the second-stage driven gear size
Keep constant: the first stage, frame, crank rate, and shaft markers
- 12:36 followed by 12:36
- 12:36 followed by equal gears
- equal gears followed by 12:36
| Symptom | Likely cause | Confirm it | Fix |
|---|---|---|---|
| The middle gears rotate separately | They are not locked to the same axle | Hold one gear and test whether the other moves | Add axle-compatible hubs or collars that couple both gears |
| The second pair skips | Output supports spread under load | Hold the output and watch the axle centers | Add a brace directly beside the second mesh |
| The train binds once per revolution | A gear is off-center or an axle is bent | Mark the tight angle and repeat slowly | Reseat the gear and replace the bent axle |
| The measured ratio is wrong | A middle gear tooth count or partial rotation was miscounted | Reset all three flags and repeat eighteen turns | Count teeth and full flag passes from one shared start mark |
Choose your tradeoff
Shorter unsupported axle spans improve alignment, while looser side collars reduce rubbing. Tune the frame before changing ratios because added friction can hide the expected speed and torque tradeoff.
Keep experimenting
Try another version
One active stage
Remove the second pair and verify the first 3:1 reduction alone.
Three-stage gearbox
Add a third supported reduction and predict the multiplied ratio before turning it.
Backlash study
Reverse the crank under each ratio and measure the angle lost before the output responds.
Build together
Classroom and access options
Classroom version
Teams can compare the second-stage driven gear size while keeping the first stage, frame, crank rate, and shaft markers. Assign builder, tester, recorder, and explainer roles; have each team predict the result before collecting three trials.
Access adaptations
- Use high-contrast tape to distinguish input and output parts.
- Replace a small crank with a wider handle for an easier grip.
- Use three different tactile markers on the input, middle, and output shafts.
Reflect on the design
- How did the second-stage driven gear size change the measured result?
- Where did four gear meshes affect the build most strongly?
- What evidence shows that compound gear ratio explains the motion?
- Which change would improve slow clockwise shaft rotation without creating a new problem?
Glossary
- Compound gear ratio
- When separate reductions act in sequence, the total ideal ratio is the product of the stage ratios rather than their sum.
- Input
- The action or energy supplied to a system; here it is clockwise hand-crank rotation.
- Output
- The useful response produced by a system; here it is slow clockwise shaft rotation.
- Efficiency
- The fraction of input energy that becomes useful output instead of friction, sound, heat, or unwanted motion.
Build your dreams
One build can start the next.
Share what you learned, change one variable, and help another builder understand what worked.
Explore more guidesSources and build notes
An original BrickLabClips interpretation of a standard mechanical mechanism.
- Mechanism verification: Standard kinematics were checked for motion direction, constraint, clearance, and likely friction points.
Written and edited by BrickLabClips. Published 2026-07-22; updated 2026-07-22.
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