Stiffness Evaluation of Continuum Robots Based on the Energy Method and Castigliano's Second Theorem

Mengxue Yang ¹ Zhicheng An ² Zechen Lin ³ Yuhang Wang ² Tongtao Pang ^2,4* Fuxin Du ^2,5*

• ¹ Beijing Tian Tan Hospital, Capital Medical University, Beijing, China
• ² School of Mechanical Engineering, Shandong University, Jinan, China
• ³ Shandong Institute of Medical Device and Pharmaceutical Packaging Inspection, NMPA Key Laboratory for Quality Evaluation of Medical Materials and Biological Protective Devices, Jinan, China
• ⁴ Qilu hospital of Shandong University dezhou hospital, Dezhou, China
• ⁵ Key Laboratory of High-Efficiency and Clean Mechanical Manufacture of MOE, Jinan, China

Continuum robots are studied and applied in neurosurgery due to their high flexibility and adaptability. The basic performance of continuum is mainly evaluated by stiffness, but there is no systematic and universal evaluation system. In this paper, a general experimental platform for continuum robots is designed, based on which the fundamental performance of the notched continuum robot used in neurosurgery is evaluated. The continuum stiffness evaluation method based on energy method and Castigliano's second theorem is proposed. By solving the internal force and energy of the notched continuum in sections, the stiffness model of single-segment and double-segment series continuum is established. The relationship between the stiffness of the continuum and the bending angle is obtained. The simulation and experimental results show that under the condition of small deformation angle, the spatial stiffness model obtained by strain energy basically conforms to the actual model, which verifies the correctness and rationality of the stiffness calculation method proposed in this paper. This paper is of significant importance to promote the performance evaluation and optimization of continuum.