How to Make a Geometric Drawing Machine TUTORIAL

DIY Drawing Motorcar

Objective:
Create a drawing machine to brand circuitous mathematical patterns. Explore the scientific discipline on how gears motility.

Have you ever played with a Spirograph? These drawing devices tin can create beautiful patterns and are fun to tinker with. If you lot have patience and some time, y'all tin build your own drawing machine just by using just cardboard, mucilage, and newspaper. You can use the drawing machine to investigate the math of curved figures!

Difficulty to build: Challenging (ages 10-12)/Medium with help (ages eight-12)
Difficulty to utilise: Medium (ages 8-12)/Easy with assist (all ages)

Download and Impress (PDF): DIY Drawing Machine

Hither are the materials you volition need to go started.

Materials:
– 10" Paper plate or something else circular
– xiv ten 14" Paper-thin pieces (2)
– A large piece of corrugated paper-thin – Yous can make your own corrugated cardboard past advisedly separating the flat layer of a corrugated box from the bumpy inner layer. The size you volition need vary slightly, but it will be roughly 3 times as long equally the distance around the rim of each of your circles.

– Mucilage – craft glue, school glue, or hot glue (be sure an adult knows if you are using hot glue, exist conscientious of burns)
– Pair of scissors
– Pen, pencil, or marker
– Paper
– Cardstock or plastic lids of assorted sizes
– Awl, hole dial, or nail

Note: You can use unlike sized objects than nosotros list here. If you do, that volition affect the size and circumference of your circles, and the length of the corrugated cardboard strips that yous need to put around them.

Commencement your project similar this.

Process:
Part One: The drawing machine base
1. Trace effectually the outside edge of a paper plate onto 2 separate pieces of cardboard. If you don't take a paper plate, you can use a java can or other circular object.

2. Cut along the lines you lot traced so both pieces of cardboard wind up having a circular hole cut through them. These will course the inner ring of your cartoon machine base.

3. Place the two pieces of paper-thin with circular cutouts side-by-side, and spread mucilage on ane of them. Then sandwich them together and so the round cutouts are aligned.

4. Cut a strip of corrugated paper-thin long enough to encircle the inner cutting out circle, and slightly higher (wider) than the peak of the two pieces of paper-thin that you glued together. The dimensions will vary depending on what you used to trace your circle onto the cardboard.

5. Mucilage the corrugated cardboard strip along the interior of the circular cut out so that the smooth side is attached to the cardboard template and the bumpy side points toward the middle of the circumvolve, similar the teeth of a gear.

6. If you used craft glue or school glue, you will need to let your project dry thoroughly. If you lot use hot glue, you will not need as much drying time. (Always be certain an adult knows you are using hot mucilage, and be careful, since it can cause severe burns).

Function 2: The drawing machine inner gear

1. While your template is drying, you will make the additional parts of your cartoon machine. Take a smaller square of cardboard, and an object with a circular surface that is smaller in diameter than the newspaper plate, or whatsoever you used to brand the template for the inner band.

Here is an example of what yous could create.

2. Trace effectually the object, so y'all accept a circumvolve that has a smaller circumference (outside measurement) than the first two circles you drew and cut out. Cut out this circumvolve.

3. Cut another strip of corrugated cardboard, long enough to become around the outside of this smaller circle. Glue it onto the edge of the circle, with the smoothen side attached to the circle's border and the bumpy side pointing out. Attempt different materials, and run across what works best. Is it easier to cutting out two circles and attach the corrugated cardboard between them, like an water ice foam sandwich? We had the best luck using a large, screw-on plastic lid from a jar of mixed basics, and attaching the corrugated paper-thin to the outside rim. This will exist your inner gear.

4. Poke a pigsty slightly off-eye in the top of the inner gear. The hole will demand to be big enough to fit the tip of a marker, pen or pencil through it. Experiment with the size until you lot are able to fit a writing musical instrument through the hole and make marks on paper underneath. This might accept a few tries. Keep tinkering, and don't give up!

5. Record a big piece of newspaper to the underside of your drawing machine base of operations. You may desire to tape or weight down your drawing motorcar base to the table.

6. Place the inner gear inside the inner ring on the drawing auto base. Put a pen, pencil, or mark into the hole in the superlative of the inner gear, and motility it so the corrugated cardboard lines up with the corrugated cardboard on the interior of the cartoon machine base circumvolve template (similar the teeth of a gear).

7. Employ 1 paw to hold your writing implement steady, while using the other hand to move the smaller circle around the inside of the larger circle template. What exercise you notice happening on the paper?

viii. Go on tracing your smaller circle around and around the larger circumvolve template, until you have created a geometric blueprint. Then you tin can use different colored markers or pencils and trace around the template once more, making even more complex patterns.

Explore More:
Effort making holes at unlike points on your smaller circle or lid. When you put the pencil or marker through dissimilar holes, how does that alter the patterns you make?

Try using dissimilar sizes of lids or paper-thin circles to make your inner gear. How do different sizes of inner gears affect the pattern?

Try cutting your inner gears in different shapes. What will happen if y'all cut the inner gear in an oval shape? Volition it piece of work if the inner gear is a triangle or a pentagon?

Can you design a drawing auto that would let you lot coil the gear on the outside rim of a larger cut-out circle?

What exercise you notice nearly the finished patterns? How are they different? How are they the same?

If you make ring bases for your drawing machine in dissimilar sizes, then if you modify the size, you lot are making the ring base a variable. If you change the circumference of the ring base, how will that affect the number of bumps on the corrugated cardboard lining? How will it affect the gear traveling inside the ring?

You can try making unlike sized ring bases with unlike amounts of corrugated cardboard lining them. The corrugated cardboard acts similar the teeth of a gear. Try using different sizes of ring bases, and encounter how the smaller gear moves when it traces them, and how information technology changes the patterns it makes.

What's the Math?
A variable is a value that can change. Your drawing machine has two variables:

1. The radius of the small gear
ii.The distance of the point of your pen/pencil/marker from the border of the pocket-sized gear

The radius of a circle is the distance from the center of the circle to any point on the circumvolve (think of the spokes on a bike cycle). Imagine we could accept a circle and straighten it out into a line. The measurement of that line would be the circle'south circumference, or the altitude around its edge.

The radius of the ring template cut into your drawing motorcar base isn't a variable, considering it isn't irresolute. But you tin can create inner gears with dissimilar radii (the plural of radius), and yous can make holes in different places on your minor gear, to try placing your pen/marking or pencil at different points.

Increasing and/or decreasing the value of any one of these variables affects the results achieved past the tools.

If yous make different sizes of inner gears, their circumferences will be different. The number of teeth (bumpy corrugated cardboard edges) will besides modify. A larger inner gear traveling along the automobile base ring will comprehend the altitude in fewer rotations before it comes to its starting point.

We can practise this equally an investigation. Brand three different sizes of inner gears. Count the teeth (bumpy edges) on the outside border of each one.

Now, put a writing instrument into a hole made slightly off eye in the smallest inner gear. Trace information technology along the inner ring of the drawing machine base. How many rotations will the gear make before information technology gets all the way around the ring?

Now attempt the same thing with the middle sized gear. Finally, try with the largest gear. What do you notice? How does this modify the patterns you make?

Larger gears have a bigger circumference, then they require more corrugated cardboard. This makes more bumpy teeth.

Because bigger gears have a greater circumference, they tin can cover more distance in a unmarried rotation when they trace the inner ring. Changing the inner gear's radius will alter the number of points in the pattern that you make on the paper.

Can you design an investigation to encounter how making different holes for the writing instrument will touch your patterns? What practice you think volition happen? Brand a prediction, and then endeavour it.

Trigonometry is advanced math that gets into the formulas of these special curves. For now, it's fun just to experiment with changing variables and see how this affects the curves and the patterns they can make, but here are some bones trigonometry terms that relate to our cartoon machines.

Roulettes are special types of curves that are made when i curve is rotated around another past a fixed point.

Think about when you put your marker or pen into the hole in the smaller gear of your drawing machine. That is the stock-still bespeak. As y'all coil the smaller gear around the inside of the larger circumvolve, the path that the smaller gear takes makes special roulettes chosen hypotrochoids. The drawing machine y'all made creates these kinds of curves. If you were to create a drawing machine that allows the pocket-size gear to curl on the outside of a larger circumvolve, you can create types of curves called epitrochoids.

Ane famous type of trochoid is chosen a cycloid. This is the curve fatigued by a signal on the rim of a bike as it rolls along the ground. Galileo studied these curves and named them– they are used to shape arches, to design pendulum clocks, and to shape gear teeth.

The painting pendulum at ScienceWorks is a type of drawing machine called a harmonograph. It creates special kinds of curved figures called Lissajous figures. Here'southward a video of our big harmonograph.

Have a picture and share it with usa, then we can see what you made! For more engineering projects and science activities, subscribe to our newsletter! Take an adult transport it to online@scienceworksmuseum.org or share information technology using the hashtag #ScienceWorksOnline

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How to Make a Geometric Drawing Machine TUTORIAL

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