Nonlinear Spring-Damping Modeling for Cable-Driven Bionic Fingers: A Pressure-Dependent Approach - Bayram, Osman; Koroglu, Onur; Toprak, Bilge; Gur, Emre; Iscan, Mehmet (IEEE, 2025)
In this study, a novel nonlinear spring and damping equations are proposed for a cable-driven bionic finger model to accurately capture the nonlinear elastic properties of the tendon. Unlike previous studies, the proposed model employes instantaneous changes in the cross-sectional area of the cable resulting in nonlinear spring and damping coefficients, while internal pressure distributions are utilized to generate the normal forces acting on bionic fingers. The nonlinear friction model as well as damping ratio is derived from vertical forces in relation to the Poisson coefficient, enabling an in-depth analysis of internal pressure on normal forces. To assess the performance of the present study, the experiments are conducted with different sinusoidal input forces, yielding different transient behavior of spring-damping coefficients at different frequency. The results indicate that joint position changes are measured at 20.19%, whereas they reached 91.33% in the constant one. Despite minor variations in elongation and internal stresses, the final angular displacement is determined at 2.32 radians for the proposed model, while the constant-one reaches 4.55 radians. Additionally, the energy consumption on mass and damping-related components can efficiently suppressed and separated from efficient force generation incorporating acceleration and damper losses into the model to achieve more realistic representation. For the complex controller designs in bionic finger systems, the proposed flexible cable model is a candidate to track reference angle value by simplifying the control rule design. By presenting these new features, the proposed study attains a significant contribution to modelling techniques.
Keywords: nonlinear modelling; second order system; frequency response; system dynamic; control theory; Computer Science; Robotics