Engineering & Architecture

Guidance

The board, the one-hand rule, the stylus and pencil holder, the scale math, picking your joints, and the accuracy report. Keep this page open while you sketch, model, and test.

The one idea

A pantograph is a parallelogram with two long arms. However you move it, three points stay on one straight line: the pivot, the tracer (your stylus), and the pencil. And the pencil always stays the same number of times farther from the pivot than the tracer.

Make that number 3, and every line you trace comes out 3× longer. Everything else on this page is about making that true on paper, then keeping it true in real wood with real joints that wiggle, and then proving with measurements how close you got.

The design process

Same six steps as every project in this class. This page is in the same order.

The six steps of the engineering design process in a row: define the problem, research and brainstorm, pick a solution, prototype, test and evaluate, communicate. A loop arrow runs from test and evaluate back to prototype. 1 DEFINE THE PROBLEM 2 RESEARCH & BRAINSTORM 3 PICK A SOLUTION 4 PROTOTYPE 5 TEST & EVALUATE 6 COMMUNICATE repeat until it works
Steps 4 and 5 are a loop. Cut, assemble, trace, measure, fix, cut again.
  1. Define the problem. Read the brief. In your notebook, write the problem, your goal, and every rule in your own words.
  2. Research and brainstorm. Learn how the scaling works, compare ways to join the links, measure your parts, and sketch several layouts, each with its stylus and pencil holder. See what to research and the design questions.
  3. Pick a solution. Compare your best layouts and joint methods against the rules and the target, pick one, and write down why.
  4. Prototype. Model it in Onshape, do a fit test cut, then cut your links.
  5. Test and evaluate. Trace, measure the scale, fix, and record every version. On test day, write your accuracy report.
  6. Communicate. A team presentation, 4 minutes or less, about your own solution, with your accuracy report.

The board you attach to

Every team attaches to the same base board. You can't change it, so your pantograph has to fit it.

The base board, 18 by 12 inches, seen from above. On the left, a grid of pivot holes five across and eleven down. In the middle, a 3 by 3 inch Trace Here box. On the right, a 9 by 9 inch Draw Here box. Both boxes are centered top to bottom, and their centers are 6.75 inches apart. TRACE HERE 3 × 3 in DRAW HERE 9 × 9 in 6.75 in center to center PIVOT HOLES 18 in 12 in
The base board from above. Draw Here is exactly 3× the size of Trace Here. Both boxes sit on the board's centerline, and so does the middle row of pivot holes.
The testing rig from above: a white board with a grid of pivot holes, a grey printed insert in the small trace box, a large wooden draw area, and a wood pantograph attached to one hole
The testing rig. Pivot holes on the left, the tracing insert in Trace Here, and Draw Here on the right. This pantograph is pivoting on a bushing in one of the holes.

Attaching to the rig: one hand only

This is the biggest rule in the project. Your pantograph is pinned, clamped, or fastened to the rig. Then the only hand on it is the one on the stylus. Not your other hand on the pivot, not your partner holding the board. The machine makes the 3× copy all by itself.

If you have to hold something down to make it work, the pantograph isn't done yet.

The let-go test · do it on every version

Fasten it to the board and take your hands off. Then put one hand on the stylus and trace the whole insert. Nothing lifts, slides, or rocks at the pivot, and nobody touches anything else. If it fails, fix the attachment before you fix anything else. Play at the pivot shows up 2× in the copy.

The two ends: your stylus and your pencil

Most teams spend their time on the links and leave these two for the end. Then they tape a pencil on and use a loose screw as a stylus, and the copy comes out wavy. These are the only two parts that touch the drawing. Plan them in your first sketches, model them in Onshape, and test them like any other part.

The two ends of a pantograph, cut in half. Left, the stylus at T: a fat handle on top, a shaft passing through two stacked links with a collar above and below them, and a rounded tip riding in a groove of the tracing insert. The links sit well above the insert. Right, the pencil at D: a pencil sliding in a tall sleeve that rises from the link, with a weight on top of the pencil, and its point resting on the paper. The link sits above the paper. STYLUS AT T PENCIL AT D insert link B–T link T–C 1 2 3 4 5 paper on Draw Here link A–D 1 2 3 4 5 1a handle you can pinch, held low 2both links turn on the stylus: your tightest fit goes here 3collars keep the links on 4tip sized to the groove 5links clear the insert 1tall sleeve keeps it straight up 2pencil slides: its weight holds the point down 3add weight if it skips 4point exactly at D 5link clears the paper
Both ends, cut in half. Gaps drawn much bigger than real. Left: the stylus is also the pin for the joint at T. Right: the pencil slides in a tall sleeve, so its own weight keeps the point on the paper. One way to do each, not the only way.
Where play hurts most

stylus × 3    pivot × 2    pencil × 1

If your stylus can wiggle 0.5 mm in its hole, the copy can be off by 1.5 mm. The same wiggle at the pencil costs only 0.5 mm. Spend your tightest fit on the stylus.

The tracing insert and your stylus

On test day you don't trace a drawing on paper. A 3D-printed insert drops into the Trace Here box. Its shapes are grooves cut into the plastic. Your pantograph needs a stylus: a point at T that rides in a groove, so you can push it around each shape.

Onshape model of a square plastic plate with a groove around the edge, a circular groove, and a hexagon-shaped groove in the middle
The tracing insert in Onshape. It fits the 3 × 3 in Trace Here box. Your stylus follows the grooves.
A pantograph stylus at the tracing joint, with its tip in a groove of the insert
A stylus that works: a handle to pinch, the two links turning on it, and a tip that sits in the groove.

The pencil holder

Nobody touches the pencil, so the holder does three jobs on its own: keep the point exactly at D, keep it straight up, and keep it pressed on the paper.

A pantograph pencil holder with the pencil standing straight up and its point on the paper
A pencil holder that works: straight up, point on the paper, link clear of the paper.

How a pantograph makes it 3×

This example is 2×, not 3×. It's a pantograph that doubles, so you can see how it works without being handed your answer. Four links, six holes. O is the pivot on the board. T is the tracer. D is the pencil.

A 2 times pantograph made of four links. Link one runs from the pivot O up to the elbow A, with a hole B halfway along. Link two runs from A down to the pencil D, with a hole C halfway along. Two short links join B and C to the tracer T, so B, A, C and T form a parallelogram. O, T and D sit on one straight line, and D is twice as far from O as T is. O pivot B A C T tracer D pencil OT OD = 2 × OT 2× EXAMPLE yours is 3×, not 2× OB = OA ÷ 2 BT = AD ÷ 2 B-A-C-T is a parallelogram: BT ∥ AC and TC ∥ BA
A 2× pantograph. B is halfway along link OA, and link BT is half as long as AD. B, A, C and T make a parallelogram, so O, T and D always stay on one line, with D twice as far out.
The scale rule · scale k

OB = OA ÷ k    BT = AD ÷ k

Then finish the parallelogram: AC = BT and TC = BA. If you did, then OD = k × OT in every position. The example uses k = 2. Yours is 3.

Why it works

Triangle O-B-T and triangle O-A-D have the same shape. The parallelogram keeps BT parallel to AD, and OB is 1/k of OA. So every side of the small triangle is 1/k of the big one, and they share the corner at O. Same shape, same corner, so T sits on the line from O to D, 1/k of the way out. Move the tracer anywhere, and the pencil makes the same move, k times bigger.

It's not the only layout

Check it in Onshape before you cut

Picking your pivot hole

Where you put the pivot decides where the copy lands. The copy is always 3× as far from the pivot as the original, along the same line. Pick the wrong hole and your copy runs off the edge of Draw Here, even if the scale is perfect.

Work it out on the centerline. Say the pivot is x inches left of the center of Trace Here. The center of the copy lands 3x from the pivot. For it to land in the center of Draw Here, the gap between the two box centers, 6.75 in, has to equal 3x − x.

A slice along the board's centerline. From left: the board edge, the five pivot holes in the middle row, the Trace Here box, and the Draw Here box. The ideal pivot point sits 3.375 inches left of the Trace Here center and 10.125 inches left of the Draw Here center, between the third and fourth holes. board edge TRACE HERE DRAW HERE ideal pivot between holes 3 and 4 x = 3.375 in 3x = 10.125 in 3x − x = 6.75 in
2x = 6.75 in, so x = 3.375 in. The ideal pivot sits 3.375 in left of the Trace Here center, in the middle row. No hole sits exactly there: it falls between holes 3 and 4, counting from the board edge.
Move the pivot, move the copy

copy moves 2 × as far as the pivot, the opposite way

A pivot 0.3 in too far right puts the copy 0.6 in too far left. Same rule up and down: one row off the middle moves the copy almost 2 in.

Reach: can the pencil get everywhere?

Picking your joints

How you join the links is your call. There's no single right answer, but every method has a catch, and every part you can buy or make comes out a little different each time. Compare at least two methods, pick one, and write down why.

Three ways to join two stacked links, cut in half. Left, an M3 bolt and nut: the bolt passes straight through holes in both links, with a washer on each side and two nuts locked together underneath, so the links turn on the bolt's threads. Middle, a nylon bushing: the bushing passes through both links with an M3 bolt through its middle, washers on each side and a nut underneath, so the links turn on the outside of the bushing. Right, a 3D-printed bushing in two halves: the top half has a flange and a sleeve that passes through both links, and the bottom half has a flange and a peg that presses up into the sleeve, so the links turn on the sleeve. BOLT AND NUT links turn on the threads NYLON BUSHING links turn on the bushing PRINTED BUSHING links turn on the sleeve link 1 link 2 link 1 link 2 link 1 link 2 top half bottom half + cheap, nothing to make − threads wear the wood − nut loosens as it turns: lock nut, or two nuts + smooth, made to turn + fits the board's holes − set sizes and lengths, and they vary by bag + any size you want + flanges hold links on − varies more than bought parts: test-fit every one
Three ways to join two links, cut in half. Gaps drawn much bigger than real. They aren't the only ways. You can also mix them: your best joint at the stylus, a cheaper one somewhere else.
MethodLinks turn onWatch out forWhat varies
M3 bolt and nutThe bolt's threadsThreads chew the wood hole bigger over time. A plain nut works loose as the joint turns.Thread size, and the laser-cut hole
M3 bolt through a nylon bushingThe outside of the bushingThe bushing has to be a bit longer than the wood stack. Only the lengths in the bag.Bushing outside size and length, bag to bag
3D-printed bushing, top and bottomThe printed sleeveThe halves have to press together and stay. Printed holes come out small, pegs come out big.Every print. Check the tolerance blocks at each printer for clearance numbers.
Your own ideaYou decideRun it by Mr. Hubbard before you build it.Measure it and find out

Measure first

Every hole you draw is sized from a real part. Don't trust the number on the bag, or the number in your Onshape model for a printed part. Measure with calipers, measure 5 of each, and write them all in your notebook.

PartThe spec saysWhy you need it
M3 bolt, thread Ø3 mmThe hole, if links turn on the bolt. Or the bushing's inside, if it passes through one.
Nylon bushing, outside Ø7 mmIf you use them: every hole a link turns on, and the board's pivot holes
Nylon bushing, inside Ø3 mmThe M3 bolt goes through it
Nylon bushing, length3, 5, 8, 13 or 20 mmHas to match the stack of links at each joint
Printed bushing or pinWhatever you modeledMeasure what came off the printer, not your model
Plywood thickness1/8 in (3.2 mm)"1/8 in" plywood is often thinner. Last year's sheet was 0.11 in.
Pencil or lead ØMeasure itThe pencil holder
Insert groove, width and depthMeasure itYour stylus tip
Nylon bushings in a row by length, with calipers measuring one
The nylon bushings, by length, if you use them. Measure the outside, the inside, and the length.

Do the math on the width. A link can be 1/2 in (12.7 mm) wide. A 7 mm hole leaves less than 3 mm of wood on each side. Keep holes away from the ends, and give the wood around them a rounded end.

Every part varies

The laser cutter is accurate, but not perfect. Store-bought bolts and bushings aren't all exactly the same size. Printed parts vary even more. You can't make that go away. What you can do is measure it, design for it, and know what it does to your copy.

  1. Measure 5, not 1. Five of each joint part you'll use, with calipers, in the same spot on each.
  2. Write down the smallest, the biggest, and the average.
  3. Size the hole for the biggest. A clearance hole has to fit every part in the bag, not just the one in your hand. Find it on your fit strip.
  4. Check the play with the smallest. That's the most wiggle you'll get. Write it down.
  5. Decide if you can live with it. Put your best-fitting parts where play hurts most: the stylus first, then the pivot.
Part12345SmallestBiggestAverage
Bushing, outside Ø (mm)6.967.026.937.056.996.937.056.99

An example, not real measurements. Yours will have a row for every joint part.

How much play are you living with?

worst play = hole size − smallest part

Say the hole that fits the biggest bushing measures 7.10 mm. Worst play is 7.10 − 6.93 = 0.17 mm. At the stylus that's up to 3 × 0.17 = 0.51 mm in the copy. On a 192 mm line, that's under 0.3% error. You can live with that. Do this math for your own parts and put it in your notebook.

Fits: every joint needs one

This is the part of the project that's about tolerance. A pantograph has several joints, and each one needs the right fit. Too tight and it binds. Too loose and the pencil wobbles.

Two joints cut in half. Left, a moving joint: a nylon bushing passes through holes in two stacked links, with a little gap around it. The bushing is a little longer than the two links together. An M3 screw runs through the bushing with a washer and nut at each end, clamping the bushing but not the wood. Right, the pivot: a bushing pressed tight into a hole in the base board, with link one sitting over it in a slightly bigger hole so it can turn. MOVING JOINT PIVOT ON THE BOARD link 1 link 2 1 2 3 base board link 1 4 5 how does link 1 stay on? your call 1link hole a bit bigger than the bushing: clearance, so it turns 2bushing a bit longer than the stack 3M3 screw clamps the bushing, not the wood 4board grips the bushing: press (interference) fit, done for you 5link 1 turns on the outside of the bushing: clearance
Two joints, cut in half, shown with nylon bushings. Gaps drawn much bigger than real. Left: links turn on the outside of the bushing, and the screw only holds the stack together. Right: the board grips the pivot bushing, and link 1 turns on it. The same fits apply whatever joint you pick.
JointFitWhy
Link turning on a bolt, bushing, or pinClearanceHas to turn freely, with as little play as you can get
Links turning on the stylusClearance, your tightestPlay here shows up 3× in the copy
Link 1 on the pivotClearanceSame as any moving joint. Play here shows up 2×.
Pivot in the board's holeInterference (press)The holes are made to grip a 7 mm nylon bushing. Fit-test anything else.
Part that should stay with one linkInterference (press)Optional. It becomes a pin, and the next link turns on it. Printed bushing halves press together this way.
Pencil in its holderYour callClearance if it slides down onto the paper. Tight if it's fixed. See the pencil holder.

Backlash: the wobble you can't see until it draws

Backlash is play in a joint: how far one part can move before the other one follows. Every joint with extra clearance adds a little. One loose joint might feel fine in your hand and still draw a wavy line.

The stylus matters most. Play at the stylus shows up 3× in the copy, because the links don't move until the slack is taken up. Next is the pivot: the copy moves 2× as far as the pivot moves (see above). Play at the pencil shows up 1×.

Laser-cut holes aren't the size you draw

The laser burns away a thin line of wood as it cuts. That line is the kerf. Holes come out a little bigger than you drew them, and parts come out a little smaller. How much depends on the laser and the wood, so don't guess. Test it.

A laser-cut fit strip with a row of labeled holes and a bushing in one
A fit strip. One cut, a few minutes, and you know your real hole sizes.

What to research

Questions you should consider

  1. Which hole is your pivot, and where does the center of your copy land?
  2. How long are your arms? Can the pencil reach the far corners of Draw Here, and the stylus the near edge of Trace Here?
  3. How does it fasten to the rig, so it works with only one hand on the stylus? Does it pass the let-go test?
  4. What is your stylus? What tip rides in the groove, how do the two links turn on it, and where does your hand hold it?
  5. What is your pencil holder? What keeps the point exactly at D, straight up, and on the paper when nobody is allowed to touch it?
  6. What keeps the links from dragging on the paper and the insert?
  7. Which joint method did you pick, and why? How much does it vary?
  8. Which links stack at each joint, and how long does each joint part need to be?
  9. Where could it wobble, and where could it bind?

Building it in Onshape

Checking your scale

A quick check for every version while you're still building. On test day you'll do the full accuracy report.

Example

76 mm ÷ 25 mm = 3.04    error = 0.04 ÷ 3 = 1.3%

A 25 mm line on the original came out 76 mm on the copy. That's 1.3% too big.

The accuracy report

On test day your pantograph draws the insert's shapes. Then you prove how good the copy is. Measure the original and the copy, work out the percent error, and put the results in your presentation. One measurement can be lucky. Six or more tell the truth.

  1. Draw the copy on test day: fastened to the rig, one hand on the stylus, nobody touching the pencil.
  2. Pick at least 6 features to measure. Use every shape, and for each one, measure across and up and down. For example: the square's width and height, the circle across and up and down, the hexagon across its flats and across its corners.
  3. Measure the original on the insert, with calipers, to the center of the groove. That's the path your stylus tip follows.
  4. Measure the same features on the copy, center of the pencil line to center of the pencil line, in millimeters.
  5. Work out the error for each one, then the average and the worst.
  6. Look for a pattern, and make your best guess at the cause.
Percent error · for each measurement

expected = 3 × original    % error = | copy − expected | ÷ expected × 100

The bars mean "ignore the sign." A copy 2 mm too big and a copy 2 mm too small are both 2 mm off. Then average all your % errors, and pick out the worst one.

FeatureOriginal (mm)Expected 3× (mm)Copy (mm)Scale% error
Square, across64.0192.01933.020.5
Square, up and down64.0192.01892.951.6
Circle, across38.0114.01153.030.9
Circle, up and down38.0114.01122.951.8
Hexagon, across flats25.075.0763.041.3
Hexagon, across corners28.986.7873.010.3
Average1.1
Worst1.8

An example, not the real insert's sizes. Measure yours.

Put this in your presentation

A test-day copy with measured features marked and labeled, beside the tracing insert
A test-day copy, marked up for the accuracy report.

Test and evaluate

Change tracking

One row for every version, in your notebook. Write your guess at the cause before you fix it, even if it turns out wrong. Make one change per version when you can, so you know what made the difference. Give the Onshape parts the same version numbers.

VersionWhat failedOur guess at the causeWhat we changedScale (% error)
v1Copy came out too big.Hole B was placed from the end of link 1, not from hole O.Re-dimensioned hole center to hole center with #OA / 3.3.31 (10.3%)
v2Lines wavy. Pencil wiggles when the stylus stops.Too much play where the links turn on the stylus.Cut those two links with the next hole down on our fit strip.3.02 (0.7%)
v3Pivot lifts when we push the stylus. Needed a second hand on it.Nothing keeps link 1 from riding up the pivot.Printed a cap that presses onto the pivot above link 1.3.02 (0.7%)
v4Pencil skips on curves.Not enough weight on the pencil.Made the pencil slide in a printed sleeve and added a washer stack on top.3.03 (1.0%)

An example, not a real team's log. Yours will have more rows.

Your notebook and Google Classroom

Your notebook and your Classroom photos are where stages 1–4 of the rubric are scored from, and they're most of what you'll show in your presentation. Do it as you go. You can't photograph a prototype you already took apart.

In your notebook, in order and dated

  1. The problem. The goal and every rule in your own words, and which rule limits you most.
  2. Research and measurements. Your sources, and the measurement table filled in.
  3. Brainstorm sketches. Several layouts, each answering the design questions, with a sketch of the stylus, the pencil holder, and how it fastens to the rig.
  4. Joints. The methods you compared, which one you picked and why, and your 5-sample measurements with the worst-play math.
  5. The math. Your scale check, pivot hole, and reach, every step shown. Which layout you picked, and why.
  6. Fit tests. Your fit strip, and the hole sizes you chose.
  7. Every version. The change-tracking table, and each test tracing's measured scale.
  8. The accuracy report. Your test-day measurements, errors, average, and worst.

To the Google Classroom assignment

Each of you submits.

The presentation

Your team presents for 4 minutes or less. Everyone in the room already knows the challenge and the brief, so don't explain them. Spend every minute on your solution: what you tried, what you changed, and how accurate it turned out.

Show these four

Tuning: problems you will have

The copy is too big or too small. Your hole spacing doesn't match your math. Measure hole center to hole center on the real links. Check OB = OA ÷ 3 and BT = AD ÷ 3.

The copy comes out twisted or lopsided. T isn't on the line from O to D. Check that the opposite sides of your parallelogram are really equal.

Lines are wavy or wobbly. Backlash. Check the stylus first (play there shows up 3×), then the pivot (2×). Use the next tighter hole from your fit strip, or a better-fitting part from your five.

The pivot lifts, slides, or needs a second hand. It isn't fastened well enough. Add a cap or collar so link 1 can't ride up, and check the pivot's fit in the board. Run the let-go test again.

It's stiff or binds. Holes too tight, or a joint part shorter than its stack so the screw is clamping the wood. Go one hole up on your fit strip, or use a longer part. Check the stylus and pencil aren't leaning and dragging.

The pencil skips or draws faint. Not enough pressure on the paper. Let the pencil slide in its hole so its own weight holds it down, or add weight over it.

The copy runs off Draw Here. Wrong pivot hole. Every inch the pivot moves, the copy moves 2 in the other way. Redo the pivot math.

Before you send anything to the laser cutter, read Making Parts in the shop procedures. Wasted wood counts on your daily grading page score.