Calculating the arc with tool nose compensation

[myhäje]

Consider the tool path in the image, displayed in blue, using tool nose compensation. How do you compute the uncompensated tool path, which is red arc?

Likewise, if we don't use tool nose compensation (red arc), how can I derive the start and end points and the radius for the blue arc?

Example: If the nose radius was 0.8 and the blue arc was start=(0,0), end=(5,5), radius=5, what would be the values for the red arc?

[txcncman]

I do not get the red arc/blue arc scenario. They are 2 different arcs. The red arc has a smaller radius than the blue arc. The centers of the red arc and blue arc will be different points.

With tool nose compensation on, the arc tangent points on the part and the actual part radius is programmed with R or the incremental distance from the starting point of the radius to the center of the radius is programmed with I, J, K.

With tool nose compensation off, the quadrant points of the tool tip is programmed and the part radius minus or plus the tool radius is programmed with R or the incremental distance from the starting point of the radius to the center of the radius is programmed with I, J, K.

[myhäje]

As the circle in the image sweeps along the blue arc, the red arc is be drawn by the corner point. If we know the parameters of the blue arc (start, end, center point, radius etc.), what's the formula for getting the red arc? This is pure geometry/algebra but I'm not that good at math.

[vegipete]

The radius of the red arc + the radius of the cutter = the radius of the blue arc.

In your drawing, the center of the red arc is 1 cutter radius right and down of the center of the blue arc.