How do I maintain the world pitch, roll or yaw of child objects?

Question

I've got an application where I'm trying to display an object in 3D, with information provided by real-world accelerometers and inclinometers - sensors that pick up the angle of the equipment, relative to ground. The trouble comes when I want to show this 'world pitch' or 'world roll' on an object that is a child of another. I'd think that there is a trivial solution to the problem, but for the life of me, I can't figure out what it is.

Let's say I've got a robot arm with several pieces - "LowerArm", "Elbow", "UpperArm" and "Hand". "Hand" is the child of the "UpperArm", and "UpperArm" is the child of "Elbow". I'd like to place "Hand" at 0 degree pitch, relative to world-space, no matter how I move the parent objects. If I grab my "LowerArm", and rotate it 90 degrees, the hand should still lay 'flat', relative to the ground; in local coordinate space, it should moved 90 degrees, to compensate.

I want it to remain attached; so it should continue to follow the other parts, in terms of roll and yaw. If I twist the arm, the hand twists with everything else - it just maintains that 0 degree world pitch. Observe the yellow object, in the below example:

How can I do this? I would have thought that there was some kind of trick, with matrices or quaternions, that could resolve it; but I've had no luck, so far. It's hard to figure out what the new 'forward' vector should be.

Answer 1

A user over at UnityAnswers gave me the solution to the problem.

Assuming you've got a variable named 'worldPitch', you can do the following (Unity C# code), although ...

Vector3 forward = Vector3.Cross(transform.parent.right, Vector3.up);
Vector3 up = Vector3.Cross(forward, transform.parent.right);
transform.rotation = Quaternion.LookRotation(forward, up) * Quaternion.Euler(new Vector3(worldPitch, 0, 0));

You can extend this to other orientations (ie. roll, pitch or yaw) by adjusting the axes.

http://answers.unity3d.com/questions/1360796/child-object-world-rotation-on-a-single-axis.html?sort=newest