## Introduction: Hand-drawn Photocopying Machine Tinkercad Challenge

With current technology, copying an image is an easy task with the use of photocopiers or computers. In the past, copying images were usually hand-traced. What if someone wanted to copy and scale an image to make it bigger? Doing this by hand would have been very difficult by hand and would need the help of a drawing tool.

Before computers, many machines were purely mechanical. A machine that consisted of 4 connected linkages was all that was necessary to copy and scale drawings. This machine was called a pantograph.

This instructable will first describe how a pantograph works and its real-life applications. Next, a Tinkercad video tutorial will walk-through the process of making a simple pantograph. This instructable will finish with an open-ended Tinkercad design challenge to create a practical, 3D-printed pantograph.

Assignment Learning Objectives:

• Geometry (ratios and similar triangles)
• Computer Aided Design(Tinkercad and working with coordinate systems)
• Engineering Design (linkage design and 3D-Printing)

## Step 1: Pantograph Applications

Historically, the pantograph was used for drawing and drafting purposes. Before computers existed, creating photocopies of an image were often hand-traced. To operate a pantograph, this tool would be anchored on a table at one point (bottom right circle). An image would be traced by manually moving a stylus tip and a second, larger copy would be created using an attached pen/pencil/marker. The GIF above shows the operation of a pantograph by tracing and scaling a triangle.

This mechanical machine has found uses in other applications. The second image shows an scissor lift, which uses the pantograph mechanism for raising and lowering the height of a platform. This same scissor design is commonly found in consumer goods such as extendable wall mounted mirrors and lamps.

## Step 2: How Does a Pantograph Work?

In this pantograph, there are 4 connectors of the same length and an anchor point (point A) fixed to a table. There are four pivot joints located at points B,D,E, and F, which join two connectors at each point. Point B has a stylus attached and is manually moved by the user to trace an image. Point C has a pencil holder attachment and follows the same motion as Point B.

There are 3 rules that always remain true for pantographs. These rules are true even if the pantograph position is changed as seen from the transition between the first and second image.

1. Collinear Points: Points A, B, and C are always collinear, meaning an imaginary straight line connects all three points.
2. Similar Triangles: Triangles ABF and ACE are similar triangles. If a person changes the pantograph position, the ratios of the two similar triangles remain the same.
3. Parallelogram: Points B,D,E, and F form a parallelogram. This parallelogram fixes the motion of all 4 connecting beams and is the reason why rules 1 and 2 are always true.

From the first image, it can be seen that the green connector (line BF) bisects the bottom red connector (line AE). This means that the ratio of the two triangles is 1:2 as the dimensions of the yellow triangle will be half the dimensions of the purple triangle. In the second image, a person has manually moved point B, and all 4 connectors moved automatically. The similar triangle ratio between the two triangles remains the same because the green line still bisects the red line.

The last image shows the similar triangles with the scissor jack example. This is to show that the 3 rules are still true for the scissor arm extension.

## Step 3: Tinkercad Walkthrough Part 1: Create Components

Steps 3 to 5 will be video tutorials of designing a pantograph using Tinkercad. A Tinkercad account is necessary for this project as well as understanding the basics of Tinkercad.

In this first step, we will create two connectors (one red and one green) and an anchoring component. The two connectors are rectangular linkages that are 41 cm long. The red connector will have snap connectors while the green connector will have snap sockets. The anchoring component is cylinder with a snap socket to connect to a red connector.

This first step teaches students how to create and dimension objects. The ruler is utilized in these steps for accurately positioning objects using a coordinate system. Individual steps are described in the subtitles in the walk-through videos.

## Step 4: Tinkercad Walkthrough Part 2: Assemble Connectors

In this next step, we assemble all of our components to create a pantograph. This step is helpful for learning how to align objects in Tinkercad and to visualize our pantograph before we print it.

## Step 5: Tinkercad Walkthrough Part 3: Build Stylus and Pencil Holder

Lastly, we finish our design by drawing in the stylus and pencil holder attachment. The stylus is a built-in point to trace over an image. The pencil holder is used to hold a standard pencil with the help of a small screw.

After this step is completed, the connectors are finished and ready to be exported for printing. The image above shows the 5 components needed to be printed.

## Step 6: Assignment Problem

After going through the steps of making this pantograph, we want to print it and we notice a problem! After exporting the objects and uploading to our 3D printer (the Makerbot Replicator 2), we notice our connectors are too large to print. The largest object length we can print is 28.5 cm, so we need to modify our connectors to be less than this length.

One quick fix is to shrink our connectors by reducing the length by roughly half and keeping everything else the same. However, if we do so, we also reduce the overall size of the pantograph. This means we may only be able to trace small images, which is not ideal.

Our assignment problem is this: Without reducing the size of the original pantograph, design a new pantograph using objects that can be printed with our Makerbot printer (part lengths must be less than 28 cm). Show a snapshot of your unique pantograph design, a snapshot of all the unique connectors (including a 41 cm red connector as a reference object), and exported STL files for 3D printing. Hints: look at toys or real life examples that use shorter beams to create longer beams (Lego, K'nex, jigsaw puzzles, wood joints, etc.)

Students are encouraged to think of practical designs that would be useful. Examples of practical modifications would be to create a clip-on pencil holder and stylus or to design a better clamping mechanism for the anchor point. Three example solutions to this problem are shown.

## Step 7: Student #1 Solution

The first approach was to add a second snap/socket mate to each of the connectors. Connecting two yellow connectors together was the equivalent of one longer rigid connector. The overall pantograph designed was even larger than the original design with the use of smaller connectors.

## Step 8: Student #2 Solution

The second solution followed the design of the scissor jack. This unique solution has the added flexibility of changing the scaling ratio of the pantograph, by moving the pink and red beams to different positions.

## Step 9: Student #3 Solution

The last solution decided to not design a drawing tool, but an extending arm instead. This student showed the application of a extending mirror mount.

## Step 10: Wrap Up

This assignment introduces an engineering design application that uses similar triangle ratios. The assignment problem required some creative thinking and was intended for more senior students. For younger age groups, a simpler problem could focus strictly on geometry where students can be asked to design a pantograph of a specific scaling ratio.