## Collision point of 2 cylinders

Geometric formulae, word problems, theorems and proofs, etc.

### Collision point of 2 cylinders

I'd like to ask for some help to solve a problem from real manufacturing world.

I have 2 cylinders A, and B.

- Cylinder A has dia Da=207.525 mm and Length La=50. mm The top face of the cylinder is in plane x,y,z=0, the bottom end of the cylinder is in Z=-50.

- The other cylinder diameter is Db=90.0 mm, with length Lb=200 mm

- The axes of the cylinder B is parallel with the axes of the cylinder A in plain x,y, and it is on distance H=140.96mm.

- In plain X,Z the axes of the Cylinder B is in angle=74.25622 deg with the axes of the Cylinder A. The center of the B cylinder axes is in X=0, Y=140.96 mm all the time. This cylinder can slide in Z axes only in plus or minus direction.

Becasue the cylinder B is Cylinder A center distance=140.96 is closer than the sum of radiuses of both cylinders (207.525+90)/2=148.7625mm), so they will collide at some point.

Imagine the cylinder A is fixed, (X=0, Y=0, Z=0)and thats the center of the coordinate system. The cylinder B is moving from plus Z area down to minus direction. (with const. x=0,y=140.96). At some point the surface of the cylinder B will collide with cylinder A top face in plain x,y, z=0.

I'd like calculate the collision point. I want to know in plain X,Z the Z distance from the center of B cylinder axes x=0,y=140.96 Z=?), also the collision point with the cylinder A(X=?, y=? z=0).

I want to generate a formula for this situation for different cylinder diameters and center distance.

I'd appreciate any help.
Thanks
zalb8991

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Joined: Tue Oct 22, 2013 5:36 pm