The mathematical model of the single-link flexible manipulator with tip mass that considered in this subsection is shown
in Fig. 1. The flexible manipulator is clamped to a rigid hub whose radius is a. Here, u is the joint angle while w and u are the transverse and axial displacements of the flexible manipulator, respectively.
It should be noted that u represents the axial shortening caused by the large bending deformation and s is the coordinate along the deformed configuration of the flexible
manipulator.
In the experimental setup , a brass plate of length 475 mm, width 50 mm, and thickness 1 mm was used as the flexible manipulator whose tip mass weighed 36 g.
The equations of motion for the flexible manipulator