Use Pivot Point Center
Command entry:Main toolbar (Use Pivot Point Center), on Use Center flyout

The Use Pivot Point Center option, available from the Use Center flyout, lets you enable rotation or scaling of one or more objects around their respective pivot points. When Auto Key is active, Use Pivot Point Center is automatically chosen and no other option is available.

The axis tripods show the centers that are currently being used.

NoteThe transformation center mode is set on a transform-by-transform basis, so select the transform before you select the center mode. If you do not want the center setting to change, turn on Customize menu Preferences General tab Reference Coordinate System group Constant.

Applying a rotation with the Pivot Point rotates each object around its own local axis.

Rotating Multiple Linked Objects

When rotating a chain of linked objects (that is, a hierarchy) with Use Pivot Point Center active, the rotation is applied equally to each object in the chain. This results in a accumulated rotations, which makes it easy to animate such effects as fingers curling.

Hierarchy before rotation (parent at bottom)

Hierarchy rotated