The invention relates to a three-freedom-degree constant speed decoupling space robot active spherical wrist and a universal compliant control method. The offset mode that the included angles are formed among rotation plane normal and rotating shafts is adopted for both an upper hemisphere rotating body and a lower hemisphere rotating body. The intersection point of the two rotating shafts of the upper rotating body and the lower rotating body is the sphere center of hemispheres of the upper rotating body and the lower rotating body, the intersection point of the two rotating shafts coincides with the rotating center of an inner ball cage universal joint and the rotating center of an outer ball cage universal joint respectively, and then constant speed decoupling of three input movements is achieved; the output end of the outer ball cage universal joint is connected with a shaft neck of the upper rotating body through a bearing in a suspension mode, three absolute corner coded discs are connected with the upper rotating body, the lower rotating body, a motor conducting spinning motion, and the output end of a speed reducing system respectively, a six-dimensional ATI sensor is installed at the output tail end of the wrist, and a wrist universal compliant follow-up control mode is achieved by a rotating joint of an upper hemisphere, a rotating joint of a lower hemisphere and a joint conducting spinning motion through a system friction force compensation technology. The three-freedom-degree constant speed decoupling space robot active spherical wrist and the universal compliant control method are accurate in locating, stable in movement, and capable of avoiding oscillation phenomena of movement coupling and mechanical arms and effectively relieving mechanical interference in a spherical wrist full compliant mode.