Abstract: A flexible appendage for use as a robot arm, controllable medical instrument, or simply a toy, has flexibly coupled segments defining an open lumen, and flanges protruding laterally of the axis. The flanges have passages for control lines spaced laterally from the axis. Each control line is fixed to a segment and can be pulled through the other segments from the proximal end. The control lines shorten a lateral side of the appendage to controllably bend it. Resilient couplings between the segments, leave open the lumen for passage of conduits or tools. The couplings can be helical springs wound with turns which abut at rest, such that the couplings elongate on the outside of a bend but do not compress on the inside, thereby maintaining the overall length of the appendage. The control lines are distributed around the axis, and can be arranged in ranks for controlling groups of the segments at different distances from the proximal end.