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I have 2 linked objects, and I want them to retain the same mesh data, but, on the object level, I want one to have a rotation different than that of the other one. e.g, I want object 1 to have no rotation (at the object level, at least), and I want the second one to be rotated 45 degrees on the z axis. Also, I want it so that when I rotate object 1, object 2 also gets rotated. So, if I rotate object 1 10 degrees on the z axis, then object 2 should be rotated 55 degrees. Is there any way to do this?

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This can easily be accomplished with a Copy Rotation constraint.

Create your first object, and Apply location and rotation. Then ALTD to make a linked duplicate. Then, in Object mode, rotate your second object on the Z axis.

Now, add a Copy Rotation constraint to the second object, targetting the first object. The trick is to map the World space of the first object to the Local space of the second object.

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In 2.8x, you can apply a Copy Rotation constraint and change the Mix option to Add. This will allow you to apply an offset rotation on the object who has the constraint applied.

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