Reduced Models for the Static Simulation of an Elastic Continuum Mechanism

In this paper, two approaches are established and compared that simulate the static deformation of a tendon-driven, elastic continuum mechanism (ECM). The mechanism at hand is made out of silicon and deforms in a large workspace as a results of any externally applied wrench. This yields high dexterity and high mechanical robustness for the system, but also the commonly used kinematic model is not suitable any more. The discussed models in this paper are essentially different. At first, the finite element method (FEM) is used to discretize the mechanism along its centerline. A nonlinear material law is setup and identified for the axial direction and it could be shown that the established model matches the real system very closely. The second model is more abstract. Here, a polynomial relationship is setup between the Cartesian pose of the mechanism and the associated wrench necessary to achieve this deflection. A comparison between the two models show, that the FEM model is slower but more accurate and therefore useful for offline computations whereas the polynomial model seems more suitable for real-time control approaches, with an acceptable accuracy and an efficient computation.