distance travelled to cutpoint

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I have two circumscribe circles shown above that represent different diametered saw blades. The saw blade is used to cut a tube as you can see (kinda rectangular small one in the picture). I am trying to determine three important values.

First, the difference in travel distance that the blade must travel to hit the object (tube) if you change the size of the blade from big to smaller (assuming the center of the blade is always fixed). This difference is shown as DELTA in the picture.

Second the X distance of the cutpoint (where blade hit object) to center of the blade (X2)

Third the Y distance of the cutpoint (where blade hit object) to center of the blade (Y2)

Could someone please show me a mathematical formula that relates to the diameter or radius would represent these values. Thanks in advance.

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Orc General
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If you consider the part to be cut as a rectangle (neglecting the radiused edge), you can draw a right trangle between the circle center, the contact point and horizontal and vertical lines that meet. The vertical line has length Y2, the horizontal line has length X2 and the hypotenuse is the radius of the sawblade, R. The relation is simply the pythagorean theorem:

X2 = sqrt(R^2 - Y2^2)

If you figure the X2 dimension for each sawblade using this equation, then your "delta" is just the difference between these two numbers.

Don Kansas City

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