Continuum robots present the great dexterity and compliance as dexterous manipulators to accomplish complex positioning tasks in confined anatomy during minimally invasive surgery. Tendon actuation is one of the most popular approaches, which is to insert the tendon to eccentrically go through and interact with the flexible backbone to accomplish compliant bends. However, hysteresis of tip trajectory of tendon actuated dexterous manipulators (TA–DMs) has been observed during the loading and unloading procedure, which is mainly caused by the hindered friction at discrete interactions between the actuation tendon and conduits. This paper aims to propose a general friction model to describe the interactions and friction profile at the multiple discrete contact points for tendon actuated dexterous manipulators under the history-dependent tendon tension. The friction model was integrated into the beam theory to describe the hysteresis and loading history-dependent behavior by solving the profiles of tendon force, normal force, and friction force, as well as the deflection of the dexterous manipulator. Experiments were carried out to validate the effectiveness of the proposed friction model. Results indicate that the friction model can successfully describe the discrete interaction and predict the deflection of dexterous manipulator subject to the different tendon loading histories. Furthermore, the effects of discrete friction to the tendon force propagation and the loading history-dependent behavior are discussed.

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