Abstract: Positioning accuracy is an essential index for judging the moving accuracy of precise linear stage, and conventional approach cannot reveal the positioning error transmission process precisely. This issue results in that the mathematical meaning is difficult to map the distribution law, and the requirements for micro displacement scale cannot be meet. A propagation approach of probability density function based on stream-of-variation theory is proposed. Through establishing the positioning error model in micro-scale displacement, the positioning error propagation law is revealed, and the function expression for characterizing the distribution pattern of positioning accuracy is derived, which is beneficial for following error prediction and compensation. Firstly, the mechanical structure of precise linear stage is analyzed. By comparing the error terms weight for positioning accuracy between micro and normal scale, the sensitive error terms and corresponding information is developed. Secondly, through adopting Homogeneous Transformation Matrix, the topology schematic of precise linear stage is established, and the positioning error propagation law is revealed. Thirdly, based on the stream-of-variation theory, the error model that from "part processes-mechanical error-assembly error-micro dynamic characteristic-micro displacement positioning accuracy" is established, and the mathematical relationship between positioning error and distribution law in micro displacement scale can be developed. The experimental results indicate that the trend that the error term weight for positioning accuracy changing with the displacement is in coincidence with the error model based on stream-of-variation theory, and the new approach is more accurate and closer to experimental results in micro-scale (0.01-1 mm).

Key words: precise linear stage, micro-scale displacement, positioning accuracy, stream-of-variation theory, probability density function