- Difficulty
- Intermediate
- Build time
- 60-90 min
- Estimated cost
- $0-$18
- Age range
- 11-17
- Workspace
- A clear table about 90 cm wide
The finish line
What you will build
The joint transmits ten slow input turns at shaft angles from 0 to about 30 degrees without yoke collision or joint separation.
Learning goals
- Identify how rotation of one angled shaft produces rotation of a second intersecting shaft.
- Construct and explain a rotary-to-rotary across an angle system.
- Measure how the shaft angle changes performance.
- Diagnose losses caused by cross-pin friction and yoke flex.
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 craft-stick yokes and a four-arm cardboard cross for a large hand-operated model.
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.
- Keep angles below the point of yoke collision and turn only at hand speed.
Orient the build
Place the build so rotation of one angled shaft is on your left and rotation of a second intersecting shaft 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 two shaft towers
Mount input and output bearings so their axes intersect at one central point.
Make one tower adjustable in angle.
Step 2
Assemble the cross
Create two rigid perpendicular pivot axes with equal arm lengths.
Check that opposite pins are collinear.
Step 3
Build matching yokes
Make two forks wide enough to straddle opposite cross pins.
Reinforce each fork root.
Builder checkpoint: After build matching yokes, the first subassembly should stay aligned when handled gently.
Step 4
Join the first yoke
Connect input yoke arms to one cross axis with free pivots.
Limit side motion without squeezing.
Watch for: If this stage binds or drifts, inspect velocity fluctuation before adding more parts.
Step 5
Join the second yoke
Rotate 90 degrees and connect output yoke to the other axis.
Confirm all four pivots move independently.
Step 6
Align at zero degrees
Set shafts collinear and turn through one cycle.
Correct any yoke asymmetry before angling.
Builder checkpoint: After align at zero degrees, operate the build slowly and confirm that rotation of a second intersecting shaft begins without binding.
Step 7
Set measured angles
Move the output tower to 15 and then 30 degrees using the guide.
Check full-rotation clearance each time.
Step 8
Compare phase motion
Turn ten input rotations steadily and watch both flags.
Record output speed changes within each turn.
Builder checkpoint: At the final checkpoint, The joint transmits ten slow input turns at shaft angles from 0 to about 30 degrees without yoke collision or joint separation.
See the engineering
Why it works
- Input
- rotation of one angled shaft
- Output
- rotation of a second intersecting shaft
- Motion
- rotary-to-rotary across an angle
- Energy losses
- cross-pin friction, yoke flex, shaft misalignment, velocity fluctuation
Why this works
Cross-axis coupling
Two perpendicular pivots in a central cross allow the yokes to change angle while remaining rotationally linked. A single joint at a nonzero angle creates cyclic output-speed variation.
Look for: Turn the input steadily and compare output flag speed near quarter-turn positions.
Where the energy goes
Efficiency and losses
The ideal model leaves out cross-pin friction, yoke flex, shaft misalignment, velocity fluctuation. 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 cross-pin friction becomes visible or audible.
Math bite
Compare average turns
Formula: average output turns = input turns for a 1:1 joint
- Input turns = 10
- No reduction gears are present
Substitute: average output turns = 10
Result: The joint preserves average rotation count.
At an angle, instantaneous output speed rises and falls during each turn.
Joint clearance and hand-speed variation affect observation.
Make it behave
Test, troubleshoot, and tune
Controlled test
Start here: Run five turns with shafts aligned at zero degrees.
Success looks like: The joint completes full rotation at each angle with no pin or yoke contact.
Measure: Output turns and visible within-cycle speed variation.
Change: the shaft angle
Keep constant: joint parts, input rate, flags, shaft intersection, and turn count
- 0 degrees
- 15 degrees
- 30 degrees
| Symptom | Likely cause | Confirm it | Fix |
|---|---|---|---|
| A yoke collides with the cross | Shaft angle is too large or fork clearance is small | Rotate slowly to the collision angle | Reduce angle or widen yoke clearance |
| The joint separates | Pins lack collars or yokes flex outward | Pull shafts lightly while stopped | Add retention and reinforce forks |
| Rotation binds at one phase | Shaft axes miss the same intersection point | View both centerlines from above | Move tower so axes meet at cross center |
| Output fluctuation seems random | Input speed or flags are inconsistent | Use a metronome-like count and larger flags | Repeat at slower steady hand speed |
Choose your tradeoff
Smaller shaft angles reduce velocity fluctuation and joint stress. Preserve a common intersection point before changing clearance, because offset axes create binding that wider pivots cannot solve.
Keep experimenting
Try another version
Zero-angle coupler
Assemble and test with shafts collinear.
Double Cardan pair
Use two joints with aligned yokes to reduce speed fluctuation.
Phase timing
Video the flags at slow speed and compare quarter-turn timing.
Build together
Classroom and access options
Classroom version
Teams can compare the shaft angle while keeping joint parts, input rate, flags, shaft intersection, and turn count. 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 long colored flags and an angle guide with raised marks.
Reflect on the design
- How did the shaft angle change the measured result?
- Where did cross-pin friction affect the build most strongly?
- What evidence shows that cross-axis coupling explains the motion?
- Which change would improve rotation of a second intersecting shaft without creating a new problem?
Glossary
- Cross-axis coupling
- Two perpendicular pivots in a central cross allow the yokes to change angle while remaining rotationally linked.
- Input
- The action or energy supplied to a system; here it is rotation of one angled shaft.
- Output
- The useful response produced by a system; here it is rotation of a second intersecting shaft.
- 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.