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A new design of a machine has been developed which performs contactless actuation in four axis-three translational and one rotational-with high accuracy and controllability in 6-DOF. Remarkable on this concept is the contactless moving part, which enables completely free rotations on the z-axis. The components of the device are optimized especially regarding to the characteristics for micromachining. The optimization algorithm is based on the response surface approximation (RSA) combined with an evolution strategy (ES). The design and optimization process is supported by 3-D numerical simulations using the volume integral equation method (VIEM) coupled with the fast multipole method (FMM) for a fast and efficient computation.