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Tendon actuated multisection continuum arms have high potential for inspection applications in highly constrained spaces. They generate motion by axial and bending deformations. However, because of the high mechanical coupling between continuum sections, variable length-based kinematic models produce poor results. A new mechanics model for tendon actuated multisection continuum arms is proposed in this paper. The model combines the continuum arm curve parameter kinematics and concentric tube kinematics to correctly account for the large axial and bending deformations observed in the robot. Also, the model is computationally efficient and utilizes tendon tensions as the joint space variables thus eliminating the actuator length related problems such as slack and backlash. A recursive generalization of the model is also presented. Despite the high coupling between continuum sections, numerical results show that the model can be used for generating correct forward and inverse kinematic results. The model is then tested on a thin and long multisection continuum arm. The results show that the model can be used to successfully model the deformation.