Modeling of flexible shaft for robotics applications

Reducing moving mass and effective inertia is essential for achieving safe human–robot collaboration. This can be achieved either by employing remote actuation, which moves the mass of actuators away from the moving elements of the robot, or by elastic actuation, which decouples the inertia of the actuator from the inertia of the robot’s link. Flexible shafts, being torsionally compliant slender long shafts, offer a combination of remote and series elastic actuation over an obstacle. Modeling such transmission is complicated due to its three-dimensional deformation in torsion, bending, and helical buckling. This paper proposes an algorithm for estimating the polar moment of inertia and stiffness of the flexible shafts using their physical dimensions of length and diameter. Using an inertia-spring–damper model, the stiffness parameters are estimated experimentally for nine flexible shafts with variable diameters and lengths in straight and bent configurations. The proposed algorithm is validated with experimental stiffness values for variable diameters and lengths in straight configuration. For bent configuration, an empirical formulation is provided to incorporate the bending deformation effect till a bending angle of 45∘.