A pantograph is a four bar linkage based on a parallelogram that scales the movement of a point by a set factor.
For the sake of simplicity, the design is non adjustable but I have included linkage files for scale factors (SF) of 2, 3, 4, and Pi.
After putting the design through some tests, I found the margin of error to be consistently under 1%.
10x M3 x 8mm*
What to print
1x Link_2 (2x for SF of 2)
1x Link_3 (0x for SF of 2)
1x Pointer_1 (for joint closest to base)
For the sake of time, I printed the links with 0 top layers and only 2 bottom layers.
All parts except for Pin_1_Base can be printed without support material.
Overview and Background
The pantograph is a device that scales motion. As such, it is the perfect tool to provide a hands-on discovery of ratios and proportional relationships.
Lesson Plan and Activity
Ratio and Proportional Relationships Discovery
This activity is designed to help students understand what a ratio is and the concept of things being proportional.
Ask students to figure out how moving one pointer effects the other. They will likely realize that the points move similarly to each other, but not the same amount.
- Ask students to measure how far one point moves compared to the other. This should lead to the realization that the movements of the points are proportional to each other. By measuring the distance traveled by the two pointers for a given movement of the pantograph and dividing the larger distance by the smaller, students can calculate the scale factor (or ratio between pointer movement) of the pantograph.
Using Ratios and Proportional Relationships
This activity is designed to allow students to utilize their understanding of ratios.
Please note that students need to know the scale factor of the pantograph for this lesson. I recommend using the "Ratio Discovery" activity to accomplish this.
Please also note that "closer pointer" refers to the pointer that remains closest to the base while "further pointer" refers to the pointer furthest from the base.
Draw and label two points on a piece of graph paper (see second paragraph under the setup section).
Draw and label a third point where the further pointer lies when the closer pointer is on the first point .
Ask students to predict where the further pointer of the pantograph will lie when the closer pointer is on the second point (without using the pantograph of course). In order to solve this, students will first need to measure the angle and distance between the first and second point. Then, they should multiply the distance by the scale factor and draw a fourth point at the calculated distance along the measured angle from the third point.
- Have students check their work using the pantograph.
Aside from the pantograph itself, it is highly recommended to also provide graph paper, rulers, and protractors.
Mount the base to your work surface. I recommend doing this with tape (by putting a pice of tape across each of the two "legs" of the base).
I would also recommend taping some graph paper to your work surface such that it can easily be reached by both pointers of the pantograph. This makes it far easier to record and measure the pantograph's movements.
Students will likely also need rulers and possibly protractors for measurement.