Design of the planetary gear unit

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Planet gear train assembly comprises a sun gear rotating at 5,000 revolutions per minute. The gears meshed onto the planetary ring rotate around a central axis, their pitch circles engaging with each other's teeth in an evenly spaced arrangement. This mechanical advantage enables transfer of rotational motion and torque from the sun gear to the planetary output shaft at 1,250 revolutions per minute. Consequently, a force multiplication ratio of four results due to gear ratio calculated by dividing final velocity, n_f=5,000, divided by planetary speed, n=2,500 rpm; torque amplification of seven is generated since output Torque T_out=T*T in=T-Out is the calculated torque when taking account the pitch diameters as calculated above and factored by angular velocities and efficiency ratio at desired mechanical system working range.