Brick-compatible mechanisms

Chebyshev Walking Linkage

Use a compact four-bar geometry to create an approximate straight foot path during part of each crank cycle.

This leg uses fewer links than a Jansen mechanism. The endpoint cannot stay perfectly straight, but a carefully chosen geometry makes one section flat enough to act like a walking stroke.

Difficulty
Advanced
Build time
120-180 min
Estimated cost
$0-$25
Age range
13-18
Workspace
A clear table about 90 cm wide

The finish line

What you will build

The foot point traces a repeatable loop whose working section deviates by less than about 8 mm from a straight reference over 8 cm of travel.

Learning goals

  • Identify how rotation of a short crank produces foot point with near-straight stance motion.
  • Construct and explain a rotary-to-planar walking path system.
  • Measure how the foot-point location on the coupler changes performance.
  • Diagnose losses caused by pivot clearance and link 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.
  • Cut links from laminated cardstock and use brass paper fasteners for a large tracing 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.
  • Use as an unloaded kinematic model and keep hands clear of crossing links.

Orient the build

Place the build so rotation of a short crank is on your left and foot point with near-straight stance motion 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

  1. Step 1

    Prepare the proportion set

    Measure every center-to-center length from one scale and label each link.

    Do not round different links independently.

  2. Step 2

    Build the ground base

    Place two reinforced pivots at the specified spacing on parallel walls.

    Check the base against a ruler line.

  3. Step 3

    Attach the input crank

    Mount the shortest link at the first ground pivot with a slow handle.

    Mark its starting angle.

    Builder checkpoint: After attach the input crank, the first subassembly should stay aligned when handled gently.

  4. Step 4

    Attach the rocker

    Mount the output link at the second ground pivot in the chosen branch.

    Keep both moving links in separate planes.

    Watch for: If this stage binds or drifts, inspect foot drag before adding more parts.

  5. Step 5

    Join with the coupler

    Connect crank and rocker free ends with the measured coupler.

    Verify all pivots remain free.

  6. Step 6

    Add the foot point

    Extend or mark the specified coupler location with a blunt tracer.

    Keep the marker perpendicular to paper.

    Builder checkpoint: After add the foot point, operate the build slowly and confirm that foot point with near-straight stance motion begins without binding.

  7. Step 7

    Check full rotation

    Turn through 360 degrees in 30-degree steps and inspect locks or collisions.

    Correct geometry before tracing.

  8. Step 8

    Trace the path

    Hold the base fixed and draw one closed cycle.

    Use a ruler to measure straight-section deviation.

    Builder checkpoint: At the final checkpoint, The foot point traces a repeatable loop whose working section deviates by less than about 8 mm from a straight reference over 8 cm of travel.

See the engineering

Why it works

Input
rotation of a short crank
Output
foot point with near-straight stance motion
Motion
rotary-to-planar walking path
Energy losses
pivot clearance, link flex, frame movement, foot drag
Chebyshev Walking Linkage concept diagram with labeled input, output, and motion arrows.
The rotary-to-planar walking path motion path, with the main efficiency losses called out.

Why this works

Approximate straight-line linkage

A chosen four-bar proportion shapes the coupler point path so one section approximates a line. The rest of the cycle returns the point in a curved loop.

Look for: Trace the endpoint and compare the stance section with a ruler line rather than judging by eye.

Where the energy goes

Efficiency and losses

The ideal model leaves out pivot clearance, link flex, frame movement, foot drag. 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 pivot clearance becomes visible or audible.

Math bite

Measure straightness error

Formula: maximum deviation = largest |measured height - reference height|

  • Reference line height = 40 mm
  • Largest measured height = 47 mm

Substitute: deviation = |47 - 40| = 7 mm

Result: The working path departs from straight by at most 7 mm.

Smaller error is useful, but foot travel and clearance also matter.

Marker thickness and pivot play add measurement error.
Brick-building meme reading: Chuck Norris does not build LEGO; he roundhouses the bricks into sculptures.
It is an approximate straight line, which is engineering for confidently almost straight.Image supplied by the site owner.

Make it behave

Test, troubleshoot, and tune

Controlled test

Start here: Trace one unloaded foot cycle at slow hand speed.

Success looks like: The path closes and its selected stance section stays within 8 mm of a ruler line.

Measure: Straight-section length and maximum vertical deviation.

Change: the foot-point location on the coupler

Keep constant: link lengths, ground spacing, frame, crank start, and marker

  1. inner point
  2. reference point
  3. outer point
Troubleshooting guide
SymptomLikely causeConfirm itFix
The crank locksLengths or assembly branch are incorrectMove to the lock without force and compare geometryReturn to verified proportions and uncross links
The trace does not closeA pivot or base shiftsMark every ground point before a second cycleBrace and retain all pivots
The line section is strongly curvedFoot point or link scale is wrongMeasure point position from pivot centersCorrect the coupler point and lengths
Links scrapeThey occupy the same depth layerWatch overlaps through the cycleAdd spacers and separate planes

Choose your tradeoff

Judge path quality from measurements, not appearance. Change only the foot-point location first; altering core link proportions can remove full crank rotation.

Keep experimenting

Try another version

Easier

Pinned paper model

Explore the path on a flat sheet with no rigid frame.

Performance

Foot-point sweep

Trace three points on the same coupler.

Advanced

Compare walkers

Overlay this path with a Jansen leg trace at the same scale.

Build together

Classroom and access options

Classroom version

Teams can compare the foot-point location on the coupler while keeping link lengths, ground spacing, frame, crank start, and marker. 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 high-contrast link colors and raised ground-pivot labels.

Reflect on the design

  1. How did the foot-point location on the coupler change the measured result?
  2. Where did pivot clearance affect the build most strongly?
  3. What evidence shows that approximate straight-line linkage explains the motion?
  4. Which change would improve foot point with near-straight stance motion without creating a new problem?
Glossary
Approximate straight-line linkage
A chosen four-bar proportion shapes the coupler point path so one section approximates a line.
Input
The action or energy supplied to a system; here it is rotation of a short crank.
Output
The useful response produced by a system; here it is foot point with near-straight stance motion.
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 guides

Sources 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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