Design and kinematics analysis of a tendon-driven surgical continuum arm

LU Jia-jia1,2, FENG Xian-ying1,2, DU Fu-xin1,2, YUE Ming-jun1,2, QU Liang-cheng1
(1.School of Mechanical Engineering, Shandong University, Jinan 250061, China;
2.Key Laboratory of High Efficiency and Clean Mechanical Manufacture of Ministry of Education, Shandong University, Jinan 250061, China)

Abstract: Aiming at the problem that the kinematic analytical solution cannot be obtained in the existing continuum robotic arm and its kinematic model, a tendon-driven continuum arm was presented with two bending degrees of freedom (DOFs), and its forward kinematics and inverse kinematics were studied. Based on the constant curvature hypothesis and combined with the modified DenavitHartenberg (DH) method, the mapping from the tendons' lengths to the arm end position was derived and the forward kinematic analytical solution was obtained. By extracting the arm backbone curve, the inverse kinematics was established using the geometric analysis method and the mapping from the arm end position to the tendons' lengths was derived. What's more, the partial inverse kinematics closedform solution was obtained. Finally, the proposed model was validated by an experiment. The results indicate that the average position error of the proposed kinematics model is no more than 2.56 mm, which accounts for less than 2.57% of the total arm length, and therefore the model can be well used for the end position control of continuum arm.
Key words: continuum arm; kinematics analysis; constant curvature; closed-form solution