Abstract: Digitized precision measurement technology is one of the key technologies in the digitized manufacturing technology. The three-coordinate measuring machine as digitized testing equipment for geometric size is extensively used in the machinery manufacturing, and the technological progress in scientific research and machinery manufacturing industries put forward more new requirements for the three-coordinate measuring machine. With the increasing application of flexible three-coordinate measuring machine, users are not only concerned with the structure and principle of the measuring machine, and the computation of measuring coordinates, but also more concerned with the accuracy analysis of the measuring machine and the factors that affect the accuracy. Based on the theoretical analysis of flexibile three-coordinate measuring system, the leapfrog type coordinate transformation method is derived so as to solve the problem of measuring large-size parts. The leapfrog method is discussed, the mathematical model of coordinate transformation is built, the coordinate transformation relationship between new and old coordinate systems after leapfrog, and the general coordinate transformation formula after n times of leapfrog are derived. After importing the norms and condition numbers of vector and matrix, the calculation formula of measuring error and the coordinate transformation formula after leapfrog are given. Based on this, the repeated affect of leapfrog ball position and leapfrog step on the large-size measuring accuracy is analyzed, and the best positioning of leapfrog ball and the best step of each time of leapfrog are indicated.

Key words: Coordinate transformation, Flexible three-coordinate measurement, Leapfrog position, Leapfrog step