# Stiffness evaluation of continuum robots based on the energy method and castigliano’s second theorem

## TL;DR

This paper introduces a new method to evaluate the stiffness of continuum robots used in neurosurgery using energy methods and Castigliano’s theorem.

## Contribution

A stiffness evaluation method for continuum robots based on energy method and Castigliano’s second theorem is proposed.

## Key findings

- A general experimental platform for continuum robots was designed and used to evaluate their fundamental performance.
- The proposed stiffness model aligns with actual models under small deformation angles, confirming its validity.
- The relationship between continuum stiffness and bending angle was established.

## Abstract

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.