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Let's say we have a flat object. We are asked to create some mechanism so that the part can rotate in the shown angles above. What mechanisms can be used?

enter image description here

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Gimbals are the classic solution for this: https://en.wikipedia.org/wiki/Gimbal And if you don't need any roll, you can omit one of the gimbal rings, in which case a pan/tilt mechanism is sufficient (often sold for photography.) You might look for a gimballed gyroscope toy and start with that. (Flight quality gimbals are expensive.)

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  • $\begingroup$ Link only answers are considered poor on this stack, due to link rot. $\endgroup$ – Solar Mike Jul 7 '19 at 18:47
  • $\begingroup$ (1) it's a Wikipedia link to a non-controversial subject, so I suspect it'll be there longer than anybody reading, and (b) even a dictionary will return something useful for the user if they know the name of the mechanism. YMMV $\endgroup$ – Catalyst Jul 7 '19 at 18:50
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    $\begingroup$ 1 and 2 or A and B? why mix? $\endgroup$ – Solar Mike Jul 7 '19 at 19:07
  • $\begingroup$ @SolarMike He has not yet come up with number 2. I guess the number one has two subsegment:) $\endgroup$ – Sam Farjamirad Jul 7 '19 at 19:42
  • $\begingroup$ @SamFarjamirad he started with (1) then used (b) ... $\endgroup$ – Solar Mike Jul 7 '19 at 19:44
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You can mount your head part on a neck globe with two pins protruding out and screw that into a sphere socket like a kids doll neck.

This spherical socket is threaded in a pitch that spirals around the sphere with the slope of 30 degrees over a half a turn and the two pins slide back and forth in this thread.

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