Shortest path between 2 planes with fixed radius arc in 3D space.

[Arwex]

Hi,

Take a look at my pictures below. What I'm interested to know is how to find the shortest path between two planes that starts and ends with fixed radius arcs. The arcs should be perpendicular (tangent?) to the planes, and tangent to the straight section of the path. I am able to sketch it up with a 3D modeling software but would like to know how to calculate it given the angles between the planes, minimum center distance or with x, y and z offsets. Is this possible at all? Hopefully someone at least can point me in the correct direction.

Thanks in advance!

 

[metastable]

I suspect there is no solution for some pairs of planes the way you’ve worded it so perhaps the solution you seek isn’t “well defined.”