In the global machining industry, ultra-precision/ultra-high-speed machining has become a challenge, and its requirements are getting higher and higher. The challenge of precision grinding lies in the difficulty in ensuring the various dimensions and geometric accuracy of the final machined parts. This paper mainly uses the theory of a multi-body system to propose a “double accuracy” theory of manufacturing and measurement. Firstly, the grinding theory with an accuracy of 0.1 μm and the precision three-coordinate measuring machine theory with an accuracy of 0.3 μm are deduced. Secondly, the two theories are analyzed. Aiming to better explain the practicability of the “double accuracy” theory, a batch of motorized spindle parts is processed by a grinding machine. Then the precision three-coordinate measuring machine is used to measure the shape and position tolerances such as the roundness, the squareness, the flatness, and the coaxiality. The results show that the reached roundness of part A and B is 5 μm and 0.5 μm, the squareness is 3 μm and 4.5 μm, and the coaxiality tolerance is 1.2 μm, respectively.