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.