Closed-form solutions for the planar hard-magnetic soft beam with large deformations and its application to soft continuum robots

Hard-magnetic soft continuum robots (HMSCRs) have demonstrated a range of captivating applications due to their considerable advantages such as quick response and remote control. Accurate and efficient analytical solutions are crucial for the design and control of HMSCRs. In this work, an accurate closed-form analytical solution has been developed for solving both the forward and inverse problems of planar hard-magnetic soft beam (PHMSB) subjected to uniform magnetic fields and concentrated forces. The extension and shear deformations are considered herein, leading to more accurate results than those from the Euler–Bernoulli beam theory in the previous work. Moreover, the inverse problems associated with calculating the required magnetic fields can also be easily handled, but it is challenging for high-dimension numerical models. After validating the present method using the finite element method and experimental results in the literature, four HMSCRs including an inchworm-inspired crawling robot, steering robot, medical surgery robot, and soft grip robot are simulated for application. The effects of stretching and shear strains are essential for the beam with the small length-to-thickness ratio, which allows for the precise design of HMSCRs.