Tendon driven continuum robots have attracted a significant amount of attention in the last decade. As a result several discrete and continuous modeling approaches have been explored in order to understand their behavior. The following article proposes an analytical model describing the influence of frictional effects between the tendon and its conduit in tendon driven continuum robotic manipulators. Existing constant curvature models ignore internal device friction completely and treat it as a negligible effect. This results in an assumption that the tendon tension is always constant along the length of the continuum manipulator. While this assumption is reasonable for small articulation angles, internal device friction can significantly change internal tension distribution deteriorating performance of constant curvature models at high articulation angles. The proposed model departs from the constant tension assumption and predicts a tension distribution along the tendon. From the tension distribution a curvature distribution is determined. It is observed that the proposed nonlinear friction model performs better than the existing linear elastic constant curvature model. Following this, a consequence of internal device friction: hysteresis effects are predicted. An algorithm that estimates tendon tension distribution given applied tendon tension history is proposed.
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