Making a groove/slot in 1st component for 2nd component which have complex movement and shape

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First of all SORRY FOR MY ENGLISH. Let me explain the problem: for example i need to rotate cylinder from 90 deg to 0 deg with cutting a some box to make a groove for moving cylinder:
Its very easy to do! BUT how to make a groove path for rotating object which have complex shape? For example like this:
Of course some of fusion experts can say something like: "you need to make a shape's max points projections, rotate this projections around axis, make a sweep or a loft, cut box with that sweep,...blablabla,...but what if this object with complex shape also rotating in 2 directions while "grooving" the box? or sliding while rotating? (i even cant create a picture for this situation....cuz im new)
Even by math calculations its very hard to make a "cutting path" for complex movement of complex shape. So my question is "how to cut a one component by second, which have COMPLEX shape and COMPLEX movement? probably by simulating joints movement? by some other fusion-360 instruments?".
Please help!