I want an object's axis always to face an empty while subject to a clamp constrain. Any suggestions on how to do that?

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The "Clamp To" constraint and the "Track to" constraint can co-exist on the Object Constraints panel. Place the "Clamp To" above the "Track To", so that the track targeting happens from the newly clamped location.

In this example, the object's location is clamped along a path defined by a Bezier Curve, and its X axis targets an Empty.

Clamp To and Track To

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