Abstract: The dynamic problem of the 3-TPS vertical—hor- izontal conversion hybrid CNC machine tool is studied by using the Lagrange method to analyze the dynamic behavior, study or realize the technology sectors, such as selecting and optimizing the structure parameters, control the machine, and so on. The Lagrange dynamic equation is firstly developed into a standard form expressed in the Cartesian space according to the machine’s structure feature. The machine tool is divided into three subsystems: The moving platform, the three limbs and the parallel locking mechanism according to the machine’s structure feature. Then the kintic energy and potential energy models of the three subsystems are deduced respectively. The dynamic equation expressed in the Cartesian space of the machine is founded on the base of that. To compute the terms of the dynamic equation, such as the inertia matrix M, the Coriolis centrifugal term V, the gravity term G, and so on, of the three subsystems, the recursion formulas are deduced according to the standard form of the Lagrange dynamic equation. The recursive algorithm to compute the terms is given finally. This dynamic model of the hybrid machine is of clear concept and the calculation is relatively simple. This can satisfy the needs of the machine’s control.

Key words: CNC machine tool, Dynamic, Hybrid, Lagrange equation