A transmission or backend mechanism for a medical instrument connects four cables to three motorized degrees of freedom. The transmission employs a first drive mechanism attached to first and second cables and a second drive mechanism attached to third and fourth cables, where each mechanism can include a capstan or a lever system that pulls in one cable while simultaneously feeding out another cables. A third drive mechanism has a first pivot about which a portion of the first drive mechanism rotates, a second pivot about which a portion of the second drive mechanism rotates, and a third pivot about which the third drive mechanism rotates. Rotation of the third drive mechanism about the third pivot pulls in at least one of the first and second cables and feeds out at least one of the third and fourth cables.
