Nonlinear Modeling of Flexible Manipulators Using Nondimensional Variables

Abstract

This paper deals with nonlinear modeling of planar one- and two-link, flexible manipulators with rotary joints using finite element method (FEM) based approaches. The equations of motion are derived taking into account the nonlinear strain-displacement relationship and two characteristic velocities, Ua and Ug, representing material and geometric properties (also axial and flexural stiffness) respectively, are used to nondimensionalize the equations of motion. The effect of variation of Ua and Ug on the dynamics of a planar flexible manipulator is brought out using numerical simulations. It is shown that above a certain Ug value (approximately ⩾45m∕s), a linear model (using a linear strain-displacement relationship) and the nonlinear model give approximately the same tip deflection. Likewise, it was found that the effect of Ua is prominent only if Ug is small. The natural frequencies are seen to be varying in a nonlinear manner with Ua and in a linear manner with Ug.