Planetary Gear Mechanism – Trajectory of the Pitch Point and a Point Outside the Pitch Circle #gear

In a planetary gear system, analyzing the trajectory of a pitch point and a point outside the pitch circle provides insight into the gear’s dynamic behavior, especially in a fixed reference frame (non-rotating observer):

1️⃣ Pitch Point:
This is the theoretical contact point between the sun gear and a planet gear;

Since the planet gear both rotates about its own axis and revolves around the sun gear, the pitch point traces a compound curve;

The resulting path is typically an epicycloid, formed by a point on a circle rolling around another fixed circle.

2️⃣ Point Outside the Pitch Circle (e.g., tooth tip):
Such a point experiences both self-rotation (around the planet gear's axis) and orbital rotation (around the sun gear’s axis);

Its trajectory becomes an epitrochoid, which is more complex than a simple epicycloid;

If the point is near the tooth tip, the trajectory appears like a looped, petal-like path, especially when plotted over one full revolution.

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