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One of the key design parameters in tendon-driven continuum robots is the number of tendons and the tendon loading distribution. A load model is also helpful for avoiding slack in tendons that causes control inefficiency and inaccuracy. A quasistatic model of n-tendon continuum robots is derived using the Euler-Lagrange formulation. The model is employed to derive an analytical loading model for equidistant tendon tensions for any given beam configuration within the workspace. The model accounts for the bending and axial compliance of the manipulator as well as tendon compliance. Features of the proposed model are discussed and some of the potential applications are explained. Based on the proposed model, a slack avoidance algorithm with analytical formulation is developed to dynamically optimize the tendon loads while preventing slack in tendons for a given configuration. The proposed model is experimentally validated in a multitendon continuum robot system for four case studies of three- to six-tendon arrangements in open-loop control architecture. A stereo vision-based three-dimensional reconstruction system measures the beam configuration and properties for each of the threeto six-tendon continuum robots. The effect of number of tendons on the tension loads in n-tendon continuum robots is studied. A quantitative dimensionless relationship between the number of tendons, the maximum tendon loads, and the bending angles is developed that may be used as a design tool for tradeoff among the complexity and required force and size.

An Analytical Loading Model for $n$ -Tendon Continuum Robots