Geometric constraint-based modeling and analysis of a novel continuum robot with Shape Memory Alloy initiated variable stiffness

Continuum robots exhibit promising adaptability and dexterity for soft manipulation due to their intrinsic compliance. However, this compliance may lead to challenges in modeling as well as positioning and loading. In this paper, a virtual work-based static model is established to describe the deformation and mechanics of continuum robots with a generic rod-driven structure, taking the geometric constraint of the drive rods into account. Following this, this paper presents a novel variable stiffness mechanism powered by a set of embedded Shape Memory Alloy (SMA) springs, which can make the drive rods become 'locked' on the body structure with different configurations. The resulting effects of variable stiffness are then presented in the static model by introducing tensions of the SMA and friction on the rods. Compared with conventional models, there is no need to predefine the actuation forces of the drive rods; instead, actuation displacements are used in this new mechanism system with stiffness being regulated. As a result, the phenomenon that the continuum robot can exhibit an S-shaped curve when subject to single-directional forces is observed and analyzed. Simulations and experiments demonstrated that the presented mechanism has stiffness variation of over 287% and further demonstrated that the mechanism and its model are achievable with good accuracy, such that the ratio of positioning error is less than 2.23% at the robot end-effector to the robot length