Cable-driven continuum manipulators have gained considerable attention due to their high dexterity and inherent structural compliance, making them a popular research topic. However, previous studies have overlooked the kinetostatics of these manipulators, which can result in a multi-solution problem. This issue is critical as having multiple equilibrium states can lead to erroneous estimations of the manipulator's profile. To address this issue, the kinetostatic model is presented and simulations based on both the interval analysis method and the commonly used floating-point optimization algorithm are conducted under the same actuating forces and external loads. Results show that there are multiple solutions to the kinetostatics of cable-driven continuum manipulators with constant cross section or variable cross section. This paper fills a gap in the current literature and offers valuable insights for researchers in the field of cable-driven continuum manipulators.

Continuum manipulators have shown a wide range of applications due to their inherent compliance and dexterity. At present, the cross-sectional dimension of these manipulators is often kept constant, which facilitates the design, fabrication and modeling processes. The famous piecewise-constant-curvature (PCC) assumption is widely used in the kinematics and motion control. By contrast, most natural creatures that have continuum structures usually exhibit variable cross sections, such as the elephant trunk and the octopus tentacle. Inspired by these creatures, variable cross-section continuum manipulators have been proposed in literature. For variable cross-section, the PCC assumption is no longer valid. In fact, the manipulator’s kinematics and statics are coupled, which should be considered and solved together. This paper establishes the general kinetostatic model of variable cross-section continuum manipulators, and performs experimental validations under various actuating and loading situations. Results showed that the proposed model has satisfactory accuracy in predicting the manipulator profile under various actuating and loading situations. The average root-mean-square error of the proposed model was 1.67 mm, and even the maximum error did not exceed 2.6 mm, according to all the 51 groups of tests on three 100 mm long prototypes. Furthermore, results also indicated that Type-1 manipulator (only varying the spacer dimension) has larger deflections and tends to be "softer" than Type-2 manipulator (only varying the backbone cross-sectional area). Results of this paper could be helpful for the design and analysis of variable cross-section continuum manipulators.