The position and pose of the tooth are difficult to be tested after the completion of the cutter or the reparation of the adapter.The traditional method is difficult to accurately locate the cutter tooth.Based on the fixed point coordinates provided by the inspection device,we deduce the blade in the benchmark and space state of composite transformation between two coordinate systems with middle coordinate system,obtain the expression form of transformation matrix,establish the spatial position and pose of the cutter,and solve the problem of the cutter tooth space positioning.The results show that the technology can be used for the space positioning of the tooth quickly,and can be used for the position and pose of the tooth after the cutter is made or the adapters are repaired.