Principal vibration modes of a rigid-flexible manipulator

Flexible robotic arms have advantages such as reduced weight and more safety during interaction with human or the environment. In previous studies on flexible link manipulators, the frequency and mode shape of the flexible link are obtained from the flexible link as a beam under simplified boundary conditions, mainly cantilevered beam. This paper aims to examine the validity and capacity of a new model that is free of the presumption. The vibration modes of a planar two link manipulator with a rigid upper arm and a flexible forearm is studied using Lagrangian formulation and the Finite Element discretization, employing Euler-Bernoulli beam elements and lumped mass model. Experiments have been done on a laboratory rigid-flexible manipulator, concluding that the eigenvalues of the manipulator differs from that of a supported beam, and can be predicted more precisely by the proposed modeling method.