Statics analysis of an extensible continuum manipulator with large deflection

Abstract Statics modelling is critical to posture deformation analysis and shape control under external loads, especially large deflections. This paper presents a novel statics modelling method to discuss the shape deformation of an extensible continuum manipulator (ECM) under an external tip load. According to the equivalence of the elastic bending potential energy, the ECM is simplified as an equivalent-fixed-guided beam (EFGB) with the corresponding equivalent bending stiffness. Subsequently, a large deflection statics model of the EFGB is established based on the continuous beam theory, and a solution is calculated by employing the elliptical integral algorithm. Further, based on the large deflection statics model, several shape simulations under different external tip loads of the ECM are discussed, especially the shape deformation of the vertical posture. In addition, the statics experiments of the ECM are performed to validate the presented statics modelling method by comparing the shape deformation under different directions of the external tip load between the theoretical and experimental value. The experiments and the contrast demonstrate that the results match with the theoretical solution well, and that the proposed statics modelling method is efficient and precise for predicting the shape deformation of the ECM.