Motion Equations Derivation of Flexible-Link Manipulators with Time- Dependent Link’s Length operated in Fluid Medium

Abstract

This article focuses on the derivation of the motion equations of flexible-links manipulator composed time-dependent link length in the fluid medium, necessitating the inspection of fluid-arms interaction during two simultaneous rigid and elastic motions. The system’s rigid motion consisting of rotational and reciprocating movements of links and the link’s oscillating motion due to their elasticity are both considered. These oscillations, which are posited to be small, are not exclusively a function of the excitations caused by the robot's motors, and the interaction between the manipulator’s links and the fluid medium also affects the links' deformation. Accordingly, the system oscillation, which is a function of the link length stemming from the changes in the rigid modes, becomes dependent on the mechanical features of the surrounding fluid and applied force/moment to the joints based on the fluid-robot interaction type. This interaction can impact the system's elastic and rigid modes. Although the equations are comparable to those developed in previous research that considered a time-varying structure, they include the effects of both the input to joints' motors and the mechanical characteristics of surrounding environment, leading to complex and non-conservative equations. With the aid of recursive Gibbs-Appell formulation, the dynamic equations of the system are calculated based on the defined algorithm and external forces. These equations are evaluated by changing the surrounding fluid's mechanical properties and the links' elasticity and examining the effect of system weight change in MATLAB. The results show that the effects of fluid-manipulator interactions on the links' deformation is greater than the effect of changing link elasticity. Thus, the deformation increases by 100% when the medium’s density changes from 0 to 100 kg/m.