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, U{sub}a and U{sub}g, representing material and geometric properties (also axial and flexural stiffness) respectively, are used to nondimensionalize the equations of motion. The effect of variation of U{sub}a and U{sub}g on the dynamics of a planar flexible manipulator is brought out using numerical simulations. It is shown that above a certain U{sub}g value (approximately 45 m/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 U{sub}a is prominent only if U{sub}g is small. The natural frequencies are seen to be varying in a nonlinear manner with U{sub}a and in a linear manner with U{sub}g.
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