The earliest example of a gear train dates to at least 2,000 B.C. when Chinese engineers built a chariot that used a complex planetary mechanism made of wooden gears to let a dragon head continuously point south when driven around (Ref. 1). In Greece, a surprisingly advanced Antikythera gearbox mechanism, incorporating at least 37 precisely crafted bronze gears, was built years later, between 205–60 B.C. (Ref. 2).

More than a billion people around the world unite to ring in the New Year, their eyes set upon the glittering New Year’s Ball in Manhattan. Thousands are gathered at Times Square — the famed “Bow Tie” of Midtown — braving the December cold and peering through glasses with numerically shaped frames. Millions more tune in from their various screens at home.
With so much riding on its descent, the Ball, along with the mechanical and electrical systems responsible for its operation, must operate like clockwork.

Today, gearboxes are inevitable in numerous applications requiring high power density including wind turbines, electric vehicles, cranes, robotics, etc. A combination of high-ratio gearboxes with high-speed, low-torque motors is often used to achieve high power density. Planetary gear trains (PGTs) help achieve a high gear ratio in a compact arrangement. Several configurations of planetary gears are widely studied in this article where the gear profiles used in these studies are primarily involute.