Deterministic metrology of platform-type machine tools

The deterministic metrology problem for platform-type machine tools (PTMT) is solved using functional accuracy criteria: normal deviations of the points of the actual machined surface from the nominal surface. Accuracy calculation problems are formulated for typical sources of quasistatic errors: cumulative errors, cyclic deviations, backlash, etc. Spatial error calculations use the inverse kinematics solution and Jacobian matrix for the current position of the platform. Euler's angle matrix is used to formulate the PTMT inverse kinematics, and Plucker's coordinate technique is used to build the Jacobian and the normal at the current point of the machined surface. An interrelationship of all the mathematical models to one another is established through the Gaussian coordinates of the current point of the machined surface. Error modeling is carried out for typical setups for accuracy assessment: milling the cylinders and milling the planes.