How to Calculate 3D Fillet Tangent Points and Center in Excel?

[yoman]

Homework Statement

I have 3 known point, with coordinate P1-(X1, Y1, Z1), P2-(X2, Y2, Z2), P3-(X3, Y3, Z3).

straight line is draw from P1 to P2, P2 to P3. they are "not" collinear.

I would like to fit a round fillet to the conner with a "Known" radius of R, and I would like to know the coordinate of the 2 tangent point and the center of the fillet circle.

How can I calculated it in 3D coordinate with a sample single equation for each of the tangent point and center of the fillet, so I can use in Excel. Is this possible?

Please help as I need to complet this for my project.

Homework Equations

The Attempt at a Solution

 

[Gokul43201]

Is this a math project or a machining project?

Can you write down the equations of the 2 lines? From the equations, can you find the angle between them? Does noticing that the center of the circle lies on the angle bisector help (there's a right triangle of known angles that can be drawn)?

 

[Architeuthis Dux]

I would approach this problem by using geometric principles and equations to calculate the coordinates of the tangent points and center of the fillet circle. This can be done using the known radius and coordinates of the three points provided.

First, I would calculate the distance between P1 and P2, and P2 and P3 using the distance formula:

d = √[(X2-X1)^2 + (Y2-Y1)^2 + (Z2-Z1)^2]

d = √[(X3-X2)^2 + (Y3-Y2)^2 + (Z3-Z2)^2]

Next, I would use the Pythagorean theorem to find the distance between the tangent points and the center of the fillet circle:

(R + d)^2 = R^2 + h^2

Where R is the known radius and h is the distance between the tangent points and the center of the fillet circle.

Using this equation, I can solve for h and then calculate the coordinates of the tangent points by adding or subtracting h from the coordinates of P2. The center of the fillet circle will be located at the midpoint between the tangent points.

Finally, I can use the coordinates of the tangent points and the center to create the equation for the fillet circle in Excel using the equation for a circle:

(x-h)^2 + (y-k)^2 = R^2

Where (h,k) is the center of the circle and R is the radius.

In summary, it is possible to calculate the coordinates of the tangent points and center of a fillet circle using the known radius and coordinates of the three points. By using geometric principles and equations, this can be achieved and the results can be used in Excel for further analysis.