This paper deals with generally routed, pre-bent cable-driven continuum robots (CCR). A CCR consists of a flexible backbone to which multiple disks are attached. Cables are passed through holes in the disk, and when pulled, the flexible backbone and the CCR can attain different shapes based on their routing and backbone configuration. An optimization-based approach, using minimization of strain energy, is shown to give good results for the pose and motion of the CCR and to determine contact with external objects. The pose, motion, and the contact obtained from the model are shown to match very well with experimental results obtained from a 3D-printed CCR. An algorithm is proposed to generate the pre-bent backbone for a CCR which on actuation can attain the desired shape. Using the algorithm, three 3D-printed CCRs with pre-bent backbones are fabricated and these are used to demonstrate a compliant gripper that can grip a spherical object similar to that done by tentacles, and another three-fingered gripper with straight backbone CCRs is used to orient a square object gripped at the end.
