A clamping system of universally interchangeable clamping components and accessories for use with standard healthcare equipment or patient healthcare procedures. The clamping system includes a support rod, a slip-coupling and a mounting bracket from which depends a short perpendicular post, which bracket may be permanently affixed to any piece of furniture. The slip-coupling is a tubular body defining a receiving bore for close passage of the perpendicular post at a first end, and a through bore passing at a right angle to the receiving bore at the opposite end. A set screw is removably threaded through the tubular body and attached to an oversized knob head for easy manual rotation to tighten and release the set screw. The support rod passes through the through bore and from which other slip-couplings or a secondary slip-coupling are mounted. The rod is vertically oriented relative to the appliance to provide support for horizontally mounted secondary slip-couplings from which accessories depend, such as a removable tray, an arm rest, an elbow rest, a handle bar and veterinary limb clamp. A slotted bar serves as a horizontal appendage to which a secondary slip-coupling is attached to hold an I.V. pole.