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# Linear Interpolation Principle

Oct 15, 2019

Deviation calculation formula

One, Linear equation Linear discriminant deviation discriminant If F=0, it means that M point is on the AB line;

If F>0, it means that the M point is above the AB line;

If F < 0, it means that the M point is below the AB line.

Two, For the convenience of control, the two cases of F=0 and F>0 are discriminated as one way of F≥0. When F≥0, the tool must be above the AB line, or on the AB line, as shown by the M1 point in the figure. At this time, the tool is only closer to the AB line when feeding in the +X direction. Therefore, according to this discrimination result The computer outputs a pulse in the X-axis direction, causing the tool to advance by a pulse equivalent distance in the +X direction to reach the M2 point.

The new discriminant is: If F2<0, the M2 point is judged to be below the AB line, then one step should be fed in the +Y direction: Deviation calculation formula, only the addition and subtraction in the formula, as long as the deviation of the previous point is added or subtracted from the projection of the oblique line length equal to the constant in the coordinate direction (Xe-X0), (Ye-Y0) Obtain the deviation value of the new coordinate point. The deviation of the machining starting point A is known, that is, F0 = 0, so that as the machining point advances, the deviation of the new machining point can be obtained by adding or subtracting the deviation of the previous point and the projection of the length of the oblique line in the coordinate direction.

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