A math model on planar gear mechanism is built.The minimum volume of planar gear mechanism is chosen as optimization objective

and teeth number

face width

module of sun gear and planetary gear number are chosen as design variable

and tooth contact stress

tooth root bending stress and adjoining relation are chosen as restraint condition.The optimum results are solved applying Genetic Algorithm.By Monte Carlo method

robustness of planetary gear mechanism is analyzed

while design variable is as random variable of Normal distribution.Robustness analysis is include in probability distribution on objective and restraint condition.It is shown that planetary gear mechanism is not robustness when design variables are little varied.Precise of design variable is set up again

and robustness on planetary gear mechanism is improved and design requirment is attained.