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

The design process

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

• Trace Here: 3 × 3 in. The original goes here.
• Draw Here: 9 × 9 in. The whole copy has to land inside it.
• Pivot holes: 5 across, 11 down. Each one grips a 7 mm nylon bushing tight. A bushing pressed into the hole you pick is one way to make your pivot. See attaching to the rig.
• Measure the real board. These sizes come from the board's drawing. Check them with a ruler before you rely on them.

Attaching to the rig: one hand only

• One pivot, held still. It can turn, but it can't slide, lift, or rock. The pivot is the one point that never moves.
• A bushing in a pivot hole is one way. The holes are made to grip a 7 mm nylon bushing. Link 1 turns on the outside of it.
• Your own pin or peg works too, like a printed peg sized to press into a hole. Fit-test it first. The board's holes are sized for 7 mm, not for whatever your printer makes.
• A clamp works if your pivot still lands where your pivot math says.
• No changes to the board. No glue, no tape, no new holes. It comes off clean so the next team can use the rig.
• Keep link 1 from riding up. When you push the stylus, link 1 wants to lift off the pivot. A cap, a collar, or a screw and washer on top stops it.

The two ends: your stylus and your pencil

The tracing insert and your stylus

• One hand on the stylus. That's the only hand on the pantograph. You hold the stylus, push it around the groove, and the rest of the machine follows. Nobody touches the pencil.
• It's also a joint. Two links meet at T, so the stylus is the pin they both turn on. Treat it like your best joint: measured, fit-tested, and the tightest clearance you can get without binding. Play here shows up 3× in the copy.
• Make it something you can hold. A handle that stands up above the links, fat enough to pinch, so your fingers grip it without bumping a link.
• Hold it low. Push near the links, not at the top. The higher you push, the more a stylus tilts, and a tilted stylus puts the tip somewhere other than under T.
• Keep it straight up. A thin link gives the stylus only 1/8 in of wood to lean on. A longer sleeve, a printed boss, or a collar above and below the links stops it leaning.
• Fit the tip to the groove. Measure the groove's width and depth with calipers. The tip needs a clearance fit: loose enough to slide, snug enough not to wander side to side. Any play between tip and groove shows up 3× bigger in the copy.
• Mind the corners. A fat tip rounds off the hexagon's corners. A thinner or pointed tip follows them.
• Set the height. The tip rests in the groove, and the links ride above the insert without dragging. The stylus length decides that gap.
• What it's made of is up to you. A bolt with a rounded tip, a standoff, a dowel, or a printed peg could all work. It just has to sit exactly at T and not wiggle.

The pencil holder

• Point exactly at D. The center of the pencil is the drawing point. In your sketch, D is the center of the holder's hole, on the line from O through T.
• Straight up. A leaning pencil draws to one side of D, and the lean changes as the links move. A tall sleeve (a printed tube or a few stacked layers of wood) keeps it straight.
• Pressure with no hand. The easiest way is gravity. Let the pencil slide up and down in a clearance-fit sleeve, so its own weight holds the point on the paper. Add weight on top if it skips. A rubber band or a spring works too.
• Not too much. Too much pressure drags, the links bend, and the stylus gets hard to push. Too little and it skips. Test both.
• Sliding or fixed. A pencil clamped tight can lift off the paper wherever the board isn't flat. A sliding pencil follows the paper, but any side play in its sleeve shows up in the copy. Keep that play small.
• A thin line. A sharp point or a mechanical-pencil lead draws a thin line, and a thin line is easier to measure for your accuracy report.
• Easy to swap. You'll sharpen or change the pencil. Don't make it something you have to take apart.
• Measure your pencil. Pencils aren't all the same size. Size the sleeve from the one you'll use on test day.

How a pantograph makes it 3×

Why it works

It's not the only layout

• The arms don't have to be equal. OA and AD can be different lengths. The rule still works.
• The tracer or pencil can sit on a longer link instead of at a joint, as long as it's still on the line from O.
• Swap the tracer and pencil and it shrinks. Put the pencil at T and the tracer at D, and you get a copy 3× smaller. That's what last year's did.
• Every layout gets the same test: O, T and D on one line, and OD = 3 × OT. Show it with your own link lengths.

Check it in Onshape before you cut

• Sketch the links as lines, with a point at every hole. Fix point O.
• Constrain the parallelogram: BT parallel to AC, TC parallel to BA.
• Dimension with variables: for example #OA and #AD, and #OA / 3 for OB.
• Drag T around. D should follow. Measure OT and OD in three different positions. OD ÷ OT should be 3 every time.

Picking your pivot hole

• Measure how far holes 3 and 4 are from the ideal point on the real board.
• Work out where your copy lands from each. Then pick the hole that keeps the whole copy inside Draw Here.
• Write it in your notebook: the hole, the distance, and where the copy's center lands.

Reach: can the pencil get everywhere?

• The far corner. The far corners of Draw Here are about 15 to 16 in from holes 3 and 4. The pencil has to get there without the elbow at A going perfectly straight. A straight elbow locks up.
• The near edge. The near edge of Trace Here is only about 1.5 to 2.2 in from holes 3 and 4. The tracer has to reach it without the arms folding flat onto each other.
• The limit. No link longer than 18 in. Check your arm lengths against both ends before you commit.
• Try it in your sketch. Drag T to all four corners of Trace Here. If D can't follow, your arms are too short or too long.

Picking your joints

• Try two before you pick. Build one joint each way on scrap and turn it. Which one wiggles least? Which stays together?
• Pick, test, accept. No method is perfect. Pick one, measure how much it varies, and design for that. Then write down how much play you're living with and what it does to the copy.
• Write down why. "We picked printed bushings because the bolts wore the holes out" is a reason. "They looked cool" isn't.

Measure first

Every part varies

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.

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

Fits: every joint needs one

• A bit longer than the stack. Add up the wood at each joint. Whatever the links turn on (a bushing or a printed sleeve) has to be a little longer, so the screw clamps it, not the links. If it's shorter, the screw squeezes the wood and nothing turns.
• Bare bolt and nut? The nut can't be tight, or nothing turns. Set it just loose enough, and keep it there with a lock nut or two nuts tightened against each other.
• Links that cross sit on different layers. Plan which link is on top at every joint, and draw the stack in your notebook.

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

Laser-cut holes aren't the size you draw

• Cut a fit strip first. One scrap strip with a row of holes, each a little bigger than the last (0.1 mm steps work), around your measured part size. Engrave the drawn size next to each hole.
• Try your biggest and smallest parts in every hole. Find the one that turns freely on the biggest with the least wobble on the smallest. That's your clearance hole. Find the one that grips. That's your press-fit hole.
• The laser varies too. Cut your chosen hole size three times, in different spots on the sheet, and try your part in each. If they don't all match, that's more variation to plan for. Cut your real links from the same sheet as your strip when you can.
• Put it in a variable. In Onshape, #hole = the clearance size from your strip. Size every turning hole with it. If the fit is wrong, you change one number.
• Kerf Compensation is one of the Onshape add-ons on Making Parts. If you use it, cut your fit strip with it too, so the strip tests what you'll really cut.

What to research

• How pantographs work and where they're used: copying drawings, engraving, sign making. Write down your sources.
• Backlash, and how machines keep it small. Start with Backlash (engineering).
• Fits: clearance, transition, and interference. Use your notes from class.
• Joint methods: at least two from picking your joints. How do real machines join moving links?
• Tolerance and variation: why no two parts are exactly the same size, and how engineers design for it.
• Percent error: how to work it out. You'll need it for your accuracy report.
• Your parts: every measurement in the table above, 5 of each.
• Last year's pantograph on the overview. What would you keep, and what would you change?

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

• Start from your line sketch. The distance between two holes is the link length from your scale math. The outline around the holes is yours to shape.
• Dimension hole center to hole center, never from the end of a link.
• Use variables: #OA, #AD, #hole from your fit strip, and #t for the wood thickness you measured.
• One part per link, named with its version: link1_v2.
• Assemble it with mates and drag it through the trace box before you cut. Look for links that hit each other.
• Lay the parts flat for the laser. See Making Parts for how to submit a file.

Checking your scale

• Trace something with a straight line in it. A square or a letter works well.
• Measure the line on the original, in millimeters. More digits make a better check.
• Measure the same line on the copy.
• Divide: copy ÷ original. 3.00 is perfect. 2.85 to 3.15 is within 5%.
• Check two directions, one across and one up and down. If they're different, something is out of line.

The accuracy report

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.

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

• Average the errors, not the scales. In the example, the scales average out to exactly 3.00, which looks perfect. It isn't. Too big and too small cancel out. The average error, 1.1%, is the honest number.
• Find the pattern. In the example, both up-and-down measurements came out short, and the across ones were fine. Something only goes wrong in one direction. Maybe the pivot rocks that way, or a joint has play in that direction. That's your next fix.
• 5% or less, on average, is the target for the final product score.

Put this in your presentation

• The copy, next to the original, with the features you measured marked.
• Your table: original, expected, copy, and % error for every measurement.
• Your average and worst error.
• The pattern, and your best guess at the cause, using what you know about your joints and their play.

Test and evaluate

Change tracking

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

Your notebook and Google Classroom

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

• Brainstorms: photos of your sketch pages.
• Research: photos of your research and measurement pages.
• Onshape screenshots: your line sketch, your links with the variable table showing, and the assembly.
• Final product: the pantograph fastened to the board, from above, and close-ups of your stylus and pencil holder.
• Accuracy report: your test-day copy with the measured features marked, and your table of errors.

Each of you submits.

The presentation

Show these four

• Brainstorms: your sketches, which layout and joint method you picked, and why.
• Onshape screenshots: your line sketch, your links with the variables, and the assembly.
• Prototypes: every version, what failed, and what you changed.
• Accuracy report: your test-day copy, your table of measurements and errors, the average and the worst, and what you think caused it. See the accuracy report.

• Both of you present. You're scored on your own, so be ready to explain any part of the pantograph, not just the part you built.
• Your Classroom photos are most of your slides already.

Tuning: problems you will have