How about one for you
A crane is working on a building site, see attached diagram.
The crane bob is moved in and out along the gantry (X) and of course up and down (Y). The crane top also rotates through an angle of (č)
The crane picks an item up from the ground at one end of the site and delivers it to the top of the construction (h) after turning through an angle and moving the crane bob from near the end of the gantry to near the centre of the crane tower (As in the diagram)
Describe the curve in 3D space that the crane bob travels in algebraic terms.
(I have not yet worked this one out either
)