Disclosed is the shape of a curvature of two or more pathways for a device having moving parts that cause movement of an object along those pathways, such that the device can locate or hold the object. In the embodiment, an apparatus is described that centers and optionally locks an object at a desired location. The applications for such a device are varied and can range from chucking a workpiece of varying diameters in a lathe, to centering a drone on a landing zone, to medical and scientific devices to capture and center objects to study, to moving atomic level objects using an electromagnetic field. The scope of this disclosure is the mathematics that defines the mirrored curvatures of each curved pathway and the positioning of the curvatures relative to each other, and the relative movement of the mirrored curvatures to cause the desired effect.