This paper introduces three algorithms which are essential for the practical, real-time implementation of continuum robots. Continuum robots lack the joints and links which compose traditional and high-degree-of-freedom robots, instead relying on finite actuation mechanisms to shape the robot into a smooth curve. Actuator length limits shape the configuration or joint space of continuum manipulators, introducing couplings analyzed in this paper which must be understood to make effective use of continuum robot hardware. Based on the new understanding of the configuration space uncovered, this paper then derives the workspace of continuum robots when constrained by actuator length limits. Finally, a tangle/untangle algorithm correctly computes the shape of the distal segments of multisection tendon-actuated continuum robots. These contributions are essential for effective use of a wide range of continuum robots, and have been implemented and tested on two different types of continuum robots. Results and insight gained from this implementation are presented