A cam transforms rotary motion into linear motion, or vice versa. The shape of the rotating cam determines the path of the reciprocating linear motion.

This project starts with a 3D wave machine and 2D and 3D cams that were derived from it. The wave machine was developed by a group of teachers in Singapore who participated in a FabLab Academy. The 2D and 3D cams were developed by Glen Bull of the Make-to-Learn lab. The 3D wave machine consists of a camshaft that rotates a number of cams to produce a wave.

The video below was taken by Glen Bull. It features the wave machine, the cams, and a Snap! Cam Explorer, which he also developed. Glen uses these objects-to-think-with to demonstrate the characteristics of one of the cams of a wave machine.

YouTube Video: https://youtu.be/SGUw28h-D1c?si=0F0PgwQY8pMnOeSW

Link to Snap! Cam Explorer

When these objects-to-think-with were recently introduced at an in-person conference, the following question was posed: *Is the 2D cam really generating a sine function?* My collaborators, Allison and Enrique, and I were tasked with discerning some mathematical concepts that could be taught using these objects. We began to explore the space of possibilities, but we couldn’t resist engaging with the “sine function” question.

We re-posed it to ourselves in a form that we could use in our own teaching of mathematics, so that we could determine the object’s potential for supporting instruction: *Is the 2D cam really generating a sine function? Use whatever tools you wish to determine the answer. Include justifications for your claims.*

Allison constructed this GeoGebra investigation to answer the question. Hopefully, you can tell that it’s a GeoGebra analog of the 2D cam explorer. We’re still working on our investigation to answer the question. Or maybe we just don’t want to give so much away that we deny you the opportunity for your own investigation.

So what do you think? What other concepts do you imagine being embedded in these designs? What else does this get you wondering about?