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Continuum manipulators have been widely adopted for single-port laparoscopy (SPL). A novel continuum manipulator with uniform notches which has two degrees of freedom (DOFs) is presented in this paper. The arrangement of flexible beams makes it own a higher load capacity. Its kinematic model is coupled with the mechanical model. The comprehensive elliptic integral solution (CEIS) is more practical in the actual deformation of the flexible beams. Based on that method, kinematics modeling is established from the driven space to the Cartesian space. The friction coefficient is an important factor which can affect the kinematic modeling. Therefore, an experimental platform is established to obtain the friction coefficient. The kinematic modeling is verified through the prototype. Experimental results show that the model has high precision.