LAGRANGIAN DYNAMICS OF CABLE-DRIVEN PARALLEL MANIPULATORS: A VARIABLE MASS FORMULATION

Abstract

In this paper, dynamic analysis of cable-driven parallel manipulators (CDPMs) is performed using the Lagrangian variable mass formulation. This formulation is used to treat the effect of a mass stream entering into the system caused by elongation of the cables. In this way, a complete dynamic model of the system is derived, while preserving the compact and tractable closed-form dynamics formulation. First, a general formulation for a CDPM is given, and the effect of change of mass in the cables is integrated into its dynamics. The significance of such a treatment is that a complete analysis of the dynamics of the system is achieved, including vibrations, stability, and any robust control synthesis of the manipulator. The formulation obtained is applied to a typical planar CDPM. Through numerical simulations, the validity and integrity of the formulations are verified, and the significance of the variable mass treatment in the analysis is examined. For this example, it is shown that the effect of introducing a mass stream into the system is not negligible. Moreover, it is non linear and strongly dependent on the geometric and inertial parameters of the robot, as well as the maneuvering trajectory.