- 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 follower traces a 5 cm square while the pencil produces a recognizable scaled copy with each corner within about 5 mm of its expected position.
Learning goals
- Identify how hand motion at the tracing pointer produces scaled pencil motion.
- Construct and explain a guided planar translation system.
- Measure how the pencil pivot position changes performance.
- Diagnose losses caused by pivot looseness 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.
- Use four equal-width cardboard strips and paper fasteners, measuring every pivot from the same strip end.
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 a blunt tracing point and keep the pencil tip facing the paper, not toward hands or faces.
Orient the build
Place the build so hand motion at the tracing pointer is on your left and scaled pencil 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
Step 1
Prepare the drawing board
Tape source and output paper to a rigid board that cannot slide.
Mark the planned fixed-pivot location away from both sheets.
Step 2
Match four links
Select straight links and verify repeated holes align when stacked.
Label them A through D for consistent assembly.
Step 3
Build the first parallelogram
Join links A and B to the fixed pivot and connect their free ends through link C.
Leave every pivot free but controlled.
Builder checkpoint: After build the first parallelogram, the first subassembly should stay aligned when handled gently.
Step 4
Complete the moving frame
Attach link D so opposite sides remain parallel through the working range.
Move the empty linkage before adding tools.
Watch for: If this stage binds or drifts, inspect base movement before adding more parts.
Step 5
Place tracer and pencil
Mount the tracer at one selected hole and the pencil at a corresponding farther hole.
Keep both tips vertical to the paper.
Step 6
Set contact pressure
Adjust the pencil holder until it marks without lifting the linkage.
Let the tracer glide rather than dig into the source.
Builder checkpoint: After set contact pressure, operate the build slowly and confirm that scaled pencil motion begins without binding.
Step 7
Trace a square slowly
Follow each side and pause at corners while the pencil copies the path.
Keep the fixed base from rotating.
Step 8
Measure scale error
Compare corresponding side lengths and diagonal lengths in both squares.
Tighten loose pivots and repeat the largest-error corner.
Builder checkpoint: At the final checkpoint, The follower traces a 5 cm square while the pencil produces a recognizable scaled copy with each corner within about 5 mm of its expected position.
See the engineering
Why it works
- Input
- hand motion at the tracing pointer
- Output
- scaled pencil motion
- Motion
- guided planar translation
- Energy losses
- pivot looseness, link flex, pencil drag, base movement
Why this works
Geometric similarity
Parallel links keep corresponding triangles similar, so distances from the fixed pivot scale by a nearly constant factor. The pencil follows the tracer path at that geometric scale.
Look for: Compare the tracer-to-pivot and pencil-to-pivot distances, then measure corresponding sides in both drawings.
Where the energy goes
Efficiency and losses
The ideal model leaves out pivot looseness, link flex, pencil drag, base movement. 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 looseness becomes visible or audible.
Math bite
Predict the copy scale
Formula: scale factor = pencil radius / tracer radius
- Pencil distance from fixed pivot = 180 mm
- Tracer distance = 90 mm
Substitute: scale factor = 180/90 = 2
Result: A 5 cm traced side should become a 10 cm copied side.
Every corresponding length should ideally double.
Joint clearance, link bending, and pencil angle create drawing error.
Make it behave
Test, troubleshoot, and tune
Controlled test
Start here: Trace a taped 5 cm square at a slow steady hand speed.
Success looks like: The copied square has four recognizable corners and side lengths within 5 mm of the prediction.
Measure: Source and copy side lengths plus diagonal mismatch.
Change: the pencil pivot position
Keep constant: source shape, tracer position, link set, base, and hand speed
- 1:1 position
- about 1.5:1 position
- about 2:1 position
| Symptom | Likely cause | Confirm it | Fix |
|---|---|---|---|
| The copy is curved instead of straight | A link bends or a pivot shifts | Trace one ruler edge and watch the frame | Brace the link and lock the fixed pivot |
| Corners become loops | Pivot play continues after the tracer changes direction | Rock each joint while stopped | Add collars or shorter pins without squeezing |
| The pencil skips | Holder pressure is too light or the board is uneven | Draw a slow circle and inspect gaps | Lower the pencil and flatten the paper |
| Scale changes across the page | The parallelogram is assembled incorrectly | Check opposite link lengths and parallel edges | Rebuild with matched center-to-center distances |
Choose your tradeoff
Low-friction pivots improve feel, but loose pivots enlarge corner error. Keep links stiff and the pencil light; changing hole positions changes scale and available drawing area at the same time.
Keep experimenting
Try another version
One-to-one copy
Place tracer and pencil at equal pivot radii.
Mirror drawing
Rearrange the working side and observe reversed output.
Calibration grid
Trace a grid and map scale error across the workspace.
Build together
Classroom and access options
Classroom version
Teams can compare the pencil pivot position while keeping source shape, tracer position, link set, base, and hand speed. 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 a thick marker in a wide holder and raised source outlines made from string or glue once fully dry.
Reflect on the design
- How did the pencil pivot position change the measured result?
- Where did pivot looseness affect the build most strongly?
- What evidence shows that geometric similarity explains the motion?
- Which change would improve scaled pencil motion without creating a new problem?
Glossary
- Geometric similarity
- Parallel links keep corresponding triangles similar, so distances from the fixed pivot scale by a nearly constant factor.
- Input
- The action or energy supplied to a system; here it is hand motion at the tracing pointer.
- Output
- The useful response produced by a system; here it is scaled pencil 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 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.