## Possible Cycloidal Gear Curve Types with one Stationary Gear or Rack

When we roll a gear or rack along a fixed gear or rack, we can get particular curves that might be of interest to you.

### HYPO-CYCLOIDAL

If a gear rolls INSIDE a fixed gear, the motion that is generated is called * Hypocycloid Motion* and the curves are called HypoCycloid Curves.

Notes:

When the Curve is on the Pitch Circle of the rolling gear, the curve is called a **Hypocycloid**.

When it is outside, it is called a **Protracted Hypocycloid**.

On the inside, it is called a **Contracted Hypocycloid**.

### CYCLOIDAL

The fixed, large gear can be made bigger and bigger until it becomes a fixed straight rack gear, rather than a circular gear.

At that point, the rolling gear rolls along a stright line.

The curve that is on the pitch circle of the rolling gear is called a **Cycloidal**.

When it is outside the rolling circle it is called the **Protracted Cycloid**.

When on the inside it is called a *Contracted Cycloidal*.

### EPICYCLOIDAL

Then, we can contract the fixed-rack gear, but now with its centre on the opposite side to the rolling gear. We arrive at the Epicyclidal Motion, which is the motion of a gear that rolls around the outside of a fixed gear.

The curve that is on the pitch circle of the rolling gear is called a **Epicycloidal**.

When it is outside the rolling circle it is called the __Protracted Epiycloid.__

When on the inside it is called a *Contracted Epiycloidal*.

### EVOLVENT

If we then enlarge the rolling circle until it becomes a stright rack - we arrive at an evolvent motion, which is the rolling motion of the straight line over the fixed circle.

This is called an *Evolvent Curve*

The curve that is on the pitch circle of the rolling rack is called a **Evolvent**.

When it is outside the rolling circle it is called the **Protracted Evolvent**.

when on the insideit is called a *Contracted Evolvent*.

### PERI-CYCLOIDAL

Finally, we can contract the straight line so that it becomes a circle that surrounds the fixed circle, we get to the Pericycloidal motion.

The curve that is on the pitch circle of the rolling gear is called a **Pericycloidal**.

When it is outside the rolling circle it is called the **Protracted Periycloid**.

When on the insidee it is called a *Contracted Periycloidal*.