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Flexible manipulators become widely used in industrial and medical fields due to their high dexterity compared with traditional discrete manipulators. However, in existing kinematics models of flexible manipulators without extension ability, the inverse kinematic (IK) analytical solution including the end-effector position and pose cannot be obtained. In this paper, a design example of a class of n-tendon continuum manipulators is presented. Based on the constant curvature hypothesis, a unified solution for solving the coupling relationship among tendons is derived. Combined with the Denavit-Hartenberg (D-H) method, the Taylor Series and the quaternion, the forward and inverse models are established, and an approximate analytical solution to the IK is derived. Simulations show the proposed IK solution has a good performance in accuracy and efficiency. A two-dimensional plane experiment and a three-dimensional space experiment are implemented. The average position errors of the two validation experiments respectively account for less than 2.0% and 3.5% of the total manipulator length, and the average pose errors are respectively no more than 0.8° and 2.5°. [ABSTRACT FROM AUTHOR]

• An algorithm of dexterity evaluation for continuum robots based on IK is proposed. • An IK model for continuum robots is established using an oval curve equation. • Length distribution of the robot is optimized based on dexterity indices. Performance evaluation and inverse kinematics (IK) for continuum robots are always hard and time-consuming. In this paper, an efficient dexterity evaluation algorithm based on IK (DEAIK) for continuum robots is proposed. The IK model is established using an oval curve equation to improve computational efficiency. The relationship between length distributions and dexterity distribution is obtained by the simulation in this paper. Length distribution of the two-segment continuum robot is optimized under the guidance of the dexterity indices using the fruit fly algorithm. Theoretical analysis and numerical simulations demonstrate that the dexterity of the structure-optimized continuum robot is better than that of the traditional continuum robot. The simulation shows that the DEAIK algorithm is 3.68 times faster than the algorithm based on forward kinematics. The IK algorithm in this paper is 3 203 times faster than the IK algorithm based on the Levenberg-Marquardt algorithm in the same accuracy. This work is significant for designing a high-performance continuum robot. [ABSTRACT FROM AUTHOR]