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This article presents a useful measuring system for the simultaneous measurement of six-degrees-of-freedom motion errors of a moving stage. The system integrates a miniature fiber coupled laser interferometer with specially designed optical paths and quadrant detectors, capable of measuring six-degrees-of-freedom motion errors. Using this model, the proposed measuring method provides rapid performance, simplicity of setup, and preprocess verification of a linear stage. The experimental setups and measuring procedures, and a systematic calculated method for the error verification are presented in the paper. The system’s resolution of measuring straightness error component is about 25nm. The resolution of measuring the pitch and yaw angular error component is about 0.06arcs. With the comparison between the HP calibration system and the proposed system in the measuring range of 120mm, the system accuracy of measuring straightness error and angular error is within the range ±0.6μm and ±0.3arcs.

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This paper presents the sliding-mode control of a three-degrees-offreedom nanopositioner (Z , x , y ). This nanopositioner is actuated by piezoelectric actuators. Capacitive gap sensors are used for position feedback. In order to design the feedback controller, the open-loop characteristics of this nanopositioner are investigated. Based on the results of the investigation, each pair of piezoelectric actuators and corresponding gap sensors is treated as an independent system and modeled as a first-order linear model coupled with hysteresis. When the model is identified and the hysteresis nonlinearity is linearized, a linear system model with uncertainty is used to design the controller. When designing the controller, the sliding-mode disturbance (uncertainty) estimation and compensation scheme is used. The structure of the proposed controller is similar to that of a proportional integral derivative controller. Thus, it can be easily implemented. Experimental results show that 3-nm tracking resolution can be obtained.

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A new spindle error measurement system has been developed in this paper. It employs a design development rotational fixture with a built-in laser diode and four batteries to replace a precision reference master ball or cylinder used in the traditional method. Two measuring devices with two position sensitive detectors (one is designed for the measurement of the compound X-axis and Y-axis errors and the other is designed with a lens for the measurement of the tilt angular errors) are fixed on the machine table to detect the laser point position from the laser diode in the rotational fixture. When the spindle rotates, the spindle error changes the direction of the laser beam. The laser beam is then divided into two separated beams by a beam splitter. The two separated beams are projected onto the two measuring devices and are detected by two position sensitive detectors, respectively. Thus, the compound motion errors and the tilt angular errors of the spindle can be obtained. Theoretical analysis and experimental tests are presented in this paper to separate the compound errors into two radial errors and tilt angular errors. This system is proposed as a new instrument and method for spindle metrology.