S16. Hypocycloid Straight-line Mechanism
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A point on the circumference of a circle rolling on the inside of another circle generates curves called hypocycloids. When the diameter of the rolling circle is one half that of the outer circle the curve traced by a point on the circumference of smaller circle is an exact straight line. This principle is used to design a planetary gear pair that when rotated by a crank in the rear it moves the slider in a vertical motion.

This 1:2 planet and ring gear pair also represents the centrodes of a double slider mechanism shown in S-2. The sliding motion of a link moving in two crossed slots is equivalent to pure rolling of the 1:2 gear pair in S-16.