A wire-driven planar continuum manipulator is developed, and a mechanics model for the notched hyper-redundant manipulator is presented.Based on the idea of FEM (finite element method), the mechanics model of the proposed hyper-redundant continuum manipulator is divided into several mechanics models of sub-deformation units, which results in sub-mechanics modeling.In the proposed sub-deformation unit mechanics model based on the Timoshenko beam element, the coupling between sub-deformation units of the whole manipulator during deformation is also included.In addition, the lateral force caused by the interface contact between the wire and the continuum manipulator is considered, and its influence on the flexible manipulator shape is investigated.With the proposed mechanics model, the joint angles in the joint space and each sub-joint space can be mapped to the driving force.Finally, the proposed mechanics model is experimentally validated on two continuum manipulators with different notches, which illustrates the effectiveness of the proposed mechanics model.
 Robinson G, Davies J B C.Continuum robots--A state of the art[C]//IEEE International Conference on Robotics and Automation.Piscataway, USA: IEEE, 1999: 2849-2854. Webster III R J, Jones B A.Design and kinematic modeling of constant curvature continuum robots: A review[J].International Journal of Robotics Research, 2010, 29(13): 1661-1683.  Jones B A, Walker I D.Kinematics for multisection continuum robots[J].IEEE Transactions on Robotics, 2006, 22(1): 43-55.  Suzuki N, Hattori A, Tanoue K, et al.Scorpion shaped endoscopic surgical robot for NOTES and SPS with augmented reality functions[C]//5th International Workshop on Medical Imaging and Augmented Reality.Berlin, Germany: Springer, 2010: 541-550. Ding J N, Xu K, Goldman R, et al.Design, simulation and evaluation of kinematic alternatives for insertable robotic effectors platforms in single port access surgery[C]//IEEE International Conference on Robotics and Automation.Piscataway, USA: IEEE, 2010: 1053-1058. Lock J, Laing G, Mahvash M, et al.Quasistatic modeling of concentric tube robots with external loads[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems.Piscataway, USA: IEEE, 2010: 2325-2332. Trivedi D, Lotfi A, Rahn C D.Geometrically exact models for soft robotic manipulators[J].IEEE Transactions on Robotics, 2008, 24(4): 773-780.  Webster III R J, Okamura A M, Cowan N J.Toward active cannulas: Miniature snake-like surgical robots[C]//IEEE/RSJ International Conference on Intelligent Robots and Systems.Piscataway, USA: IEEE, 2006: 2857-2863. Xu K, Simaan N.An investigation of the intrinsic force sensing capabilities of continuum robots[J].IEEE Transactions on Robotics, 2008, 24(3): 576-587.  Han S M, Benaroya H, Wei T.Dynamics of transversely vibrating beams using four engineering theories[J].Journal of Sound and Vibration, 1999, 225(5): 935-988.  Luo Y H.An efficient 3D Timoshenko beam element with consistent shape functions[J].Advances in Theoretical and Applied Mechanics, 2008, 1(1-4): 95-106.