Cycloid Machine 3d Model with laser cut files.

cyclographs create intricate and visually appealing geometric patterns by combining cycloidal motion with various gear ratios and pen placement. Here's how it works:

Components:
1. A circular disc with multiple holes or slots around its edge.
2. Gears or wheels, which are meshed together and connected to the circular disc.
3. A pen or pencil, which fits into one of the holes or slots in the circular disc.
4. Paper placed on a flat surface.

How it works:

1. Place the circular disc on a piece of paper.

2. Choose a hole or slot on the disc for the pen or pencil to go through.

3. Start rotating the circular disc by turning a handle or manually spinning it. This action causes the pen or pencil to move in a cycloidal path.

4. As the circular disc rotates, the interconnected gears cause the pen or pencil to move in a coordinated way, creating a combination of circular and linear motion. The pen or pencil traces a path on the paper.

5. The specific patterns created depend on the size and shape of the holes or slots on the disc, the placement of the pen or pencil, and the gear ratios between the wheels.

6. By adjusting these parameters or changing the pen or pencil location during the process, you can create a wide variety of intricate and colorful spiral patterns.

Spirographs are often used for artistic and recreational purposes, and they can produce mesmerizing designs that vary based on the user's creativity and choices. They are popular as a creative tool for children and adults alike and are a fun way to explore mathematical concepts related to geometry and harmonograph-like motion.