In this paper, a novel mathematical framework is introduced for modeling deformation behavior of Tendon-Driven Continuum Manipulators (TD-CMs) featuring discontinuous cross-sectional geometries (i.e., having flexural patterns). Leveraging this framework, we also introduce the concept of design space by which the deformation-behavior space of a TD-CM can intuitively be analyzed via its geometrical design parameters. To thoroughly evaluate the performance of the proposed modeling framework, we have conducted various simulation studies and experiments.

In this paper, we present an analytical modeling approach to address the problem of tension loss in a generic variable curvature tendon-driven continuum manipulators (TD-CM) occurring due to the tendon-sheath distributed friction force. Despite the previous approaches in the literature, our presented model and the iterative solution algorithm do not rely on a priori known curvature/shape of the TD-CM and can be implemented on any TD-CM with constant/ variable curvatures with a continuous neutral axis function. The performance of the proposed modeling approach in predicting the distributed tendon tension and tension loss has been evaluated via simulation and experimental studies on a TD-CM with planar bending. Results demonstrate the outstanding and accurate performance of our novel modeling and the proposed solution algorithm.