Planetary gear system and gears therefore

In a planetary gear system having a first ring gear, a pair of planet gears, means supporting said planet gears for coaxial rotation in unison and for rotation about the axis of said first ring gear with one of said planet gears in intermeshing engagement with said first ring gear, a sun gear journaled for coaxial rotation relative to said first ring gear and in intermeshing engagement with the other of said planet gears, and a second ring gear journaled for coaxial rotation relative to said first ring gear and in intermeshing engagement with said other planet gear, said first ring gear and said one planet gear forming one set of gears, said sun gear, said other planet gear and said second ring gear forming another set of gears, the improvement wherein each gear in at least one of the sets is engaged with another of the gears in said one set along a line of action in accordance with the equation:

• Y=-(.chi..sub.p tan.phi..sub.o +.chi..sub.p.sup.3 b)
• wherein:
• .phi..sub.o is the pressure angle;
• y is one rectangular coordinate of a point on said line of action;
• .chi..sub.p is the other rectangular coordinate of said point;
• and b has a value other than zero.