A clamping assembly for adjustably connecting a device to a rail, including a clamp body, rail interface mechanism, and support mechanism for the device. The rail interface mechanism attaches to rails of various heights and thicknesses with a single user control activation. The rail interface mechanism includes at least one flanged fixed upper jaw, a rail clamp control comprised of a threaded vertical axle terminating in a pm end, a flanged lower jaw constrained to slidable vertical motion along an internal face of the clamp body by the pin end of the vertical axle, and two angled wedges that can be extended and retracted horizontally.
