Natural Frequencies of a Manipulator with Rigid Tip Mass: the Case of Flexural-Flexuraltorsional Coupling

The characteristic (or frequency) equation of a flexible manipulator with a rigid tip mass is derived. The manipulator is modelled as an Euler-Bemoulli beam and it permits flexural (bending) deformation in two planes and torsional deformation. The position of the centroid of the tip mass may not necessarily be coincident with the elastic axis of the beam. This is represented by the use of offset coordinates. The natural frequencies of the manipulator are obtained by solving the characteristic equation. The results are compared to the results in the literature, where possible, and also to those obtained using a commercial finite element software ANSYS. The effects of the magnitude of the tip load, offset of the tip mass centre of gravity from its point of attachment, the length of the beam and slenderness ratio on the natural frequencies are examined.