Screen/Cursor-Alligned Object Interaction/Controls

So, I'm trying to replicate a similar effect to the levers, drawers and wheels in games like Myst, where the player can (within a declaired radius/area) move a lever (for example) around a pivot point with a min and max rotation by grabbing it (using left-click, or a trigger) and moving the cursor/camera in the direction the lever can move.

My main question about achieving these is: how does one translate screen-centre/cursor position to a movement-restricted object in Unity?

Here's a video of the effect I'm after (although I may have the cursor togglable locked to centre screen).

http://kylebriggs.co.uk/wp-content/uploads/2018/08/Myst-IV-Revelation-8_19_2018-5_18_06-PM.mp4

 

First figure out if the user is interacting with the object using a raycast.
Then you could project the objects Pivot to Screenspace (https://docs.unity3d.com/ScriptReference/Camera.WorldToScreenPoint.html) and get the angle change of user input to pivot. Apply that value to your objects rotation.

 

I would approach this from the opposite direction -- translate your world space object motion into screen space. Define a world space "motion path" that the player's "hand" needs to take. When the player first interacts with the object, translate that path into screen space and calculate the motion there in 2D. Should simplify the problem considerably.