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This paper presents the intrinsic capability of full-wrench estimation of multisegment continuum robots with multiple flexible backbones. Intrinsic-full-wrench estimation refers to the ability of continuum robots to also serve as force and moment sensors by using measurements of axial loads on their backbones. This end-effector-as-sensor approach fulfills the rapidly increasing needs for miniature-robotic-surgical tools with haptic sensing ability subject to various limitations, such as size, magnetic resonance imaging (MRI) compatibility, sterilizability, etc. A performance index for the intrinsic wrench-sensing capability is introduced and evaluated to show how this index can serve as a design guide for continuum robots that provide force sensing.