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Abstract Cable-driven continuum robots that consist of a flexible backbone and are driven by applying tension and displacement on the cables are of interest for use in unstructured environments. Previous work has explored methods to alter the stiffness along the length of the robot via the introduction of additional cables beyond those used for actuation. The introduction of these tendons on the robot would allow the operator to adjust and increase the stiffness value at different locations by prescribing and removing a fixed pretension on the stiffening tendons. This paper presents a continuum mechanism for robotics applications with continuously variable output stiffness. The new method introduces a nonlinear compliance at one side of the tendons that can be adjusted using a lead screw. The nonlinear compliance is provided by a soft hemispherical contact surface that is inspired by the Hertzian contact theory. Through the provided adjustment mechanism, the mechanism output stiffness can be continuously varied without any active control loop. The stiffening cables and adjustable stiffness mechanism allow for the stiffness to be adjusted between a range of 6x to 11x of the stiffness in the case of only actuating cables. The stiffening of a higher-order mode showed a reduced effect, allowing for stiffnesses in the range of 1.5x to 2.2x of the stiffness in the case of only actuating cables.