1. The envelope of moving line on the hypocycloid plane may be an epicycloid or cardioid and the...

2. Based on the principle of the formation of hypocycloid, a kind of stepless gear speeder has been designed.

3. Based on hypocycloid characteristics and transmission principles, a new kind of hypocycloid energy transformation mechanism was proposed.

4. Recommends a method to calculate node coordinates on hypocycloid using straight line to approach curve with equal errors. So that the NC programming and the machining can be completed.

5. It has a lot of properties, Cycloid, hypocycloid and epicycloid are plane curves .

6. In this paper the authors present a new recurrence algorithm for super ellipse, para ellipse, hypocycloid and special kind of curves.

7. Hypocycloidal drive, designed based on formation and engagement theory of the hypocycloid, is a new drive with great use value.

8. The method is very simple and the result is accurate enough. It suits different batch production of hypocycloid gears.

9. The result provide the theoretical rational for further study of the hypocycloid energy transformation mechanism.