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During imaging or nanomanipulation with a sample-scanning AFM, two important errors, scanning size error and vertical cross coupling error, will be generated due to bend motion of the tube scanner, and these two errors are destructive to nanostructures quantitative analysis. To minimize the errors, a kinematics model of the scanner is presented, and according to the model the two errors are quantitatively analyzed, which shows that scanning size error is greatly affected by sample thickness and nominal scanning size, while vertical cross coupling error is greatly affected by probe tip offset to tube axis and nominal scanning size. Corresponding methods are proposed for minimizing the errors. Gratings imaging experiments verify the kinematics model and errors calculation formulas.