A new type of high-performance fewer teeth difference planetary driving part called filtering gear reducer is briefly introduced.The main factors of effecting the idle stroke error are analyzed

and the formula of return difference is derived towards a pair of cylindrical gear pair

and then the return difference of filtering gear reducer is calculated with the method of probability statistics.The calculation and test of prototype is carried out and the correctness of the formula for gear transmission return difference is verified by comparing calculation result with experiment result.The correlation factor influencing on idle stroke error of filtering gear reducer is analyzed

and some improvement methods are proposed.