An adapter clamp for clamping an adapting tube. The adapter clamp includes: an adapter tube; a first resilient ring placed in the inner circumferential surface of the adapter tube and including elastic material for expanding inward and clamping to the outer surface of the adapting tube; a hollow adjustment ring configured to be threaded to the inner surface of the adapter tube to generate a displacement force; and a compression ring providing minimum friction resistant for translating the displacement force from the threading hollow adjustment ring to a longitudinal compressing displacement of the first resilient ring, causing an inner surface of the first resilient rings to fit to the outer surface of the adapting tube. The adapter clamp also includes a second resilient ring placed in the inner circumferential surface of the adapter tube; and a spacer placed on the inner circumferential surface of the adapter tube.