Meshing Sets of Somsky Gears

d Outer gear radius
a Sun gear radius
b Planet pair 1, smaller planet radius
c Planet pair 2, smaller planet radius

Somsky gears are sets of meshing gears that obey the Somsky condition: the sum of the diameters of three gears spanning an outer gear must equal the diameter of that outer gear. With this condition met, the central or "sun" gear has significant freedom of motion. This freedom of motion allows us to mesh two distinct pairs of Somsky planet gears around the sun gear, and this page computes the locations of the gears given the input values.

There are almost always multiple solutions; the "spread" and "narrow" buttons permit you to explore the different solutions. The minimum gap between gears is displayed as "mingap". The offset of the center of the sun gear with respect to the center of the outer gear is displayed as "offset".