In the assumed mode models, the flexible displacements uj(h,t), vj(h,t), wj(h,t) are usually described by a truncated modal series, in terms of spatial mode eigen functions and time-dependent mode amplitudes, in each direction, where h = (x/lj), lj is the length of flexible link j, and nj is the number of modes used to describe the deflection of link j. It should be mentioned that for the flexible link with a revolute joint lj º aj, and for a flexible link with prismatic joint, lj º dj.

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