Kinetostatic Modeling of Retractable and Prismatic Spring Body for Continuum Climbing Robots in Discontinuous Terrains

There are few studies on the mechanics of the retractable backbone for continuum climbing robots, especially the non-circular cross-section. The retractable non-circular structure endows the robot with more compact structure, adjustability in initial stiffness, and dexterous mobility in narrow space. Consequently, a retractable prismatic spring backbone is proposed. Aiming at rectangular helical characteristic and coupling deformation, the backbone is equivalent to an elastic beam, whose equivalent stiffness is solved by the projection principle of the micro-segment deformation. Then the finite piecewise method and continuous differential method are used to establish its mechanical model. The piecewise method uses linear superposition principle to decouple the compression and bending deformation, and the rotation angle is solved by using the projection principle of the bending deformation. The continuous method uses the Cosserat-rod theory to establish the variable-curvature mechanics based on the equivalent beam, whose boundary-value problem is solved by gradually extending the integral region. Finally, two theory methods are in good agreement with FEA and experiment results; the continuous method has higher accuracy and piecewise method has lower computation cost; a multipurpose continuum climbing robot composed of the spring backbone, rotatable joint and flexible claw is applied to inspection in enclosed equipment.