Closed-Form Dynamic Model of Planar Multilink Flexible Manipulator

This paper develops a closed-form dynamic model of the planar multi-link flexible manipulator. The structural flexibility in the links is modeled using Rayleigh beam theory with clamped-mass boundary conditions. The solution of the Rayleigh beam equation is provided using the assumed mode method. The dynamic equations of motion are derived using the Lagrangian formulation. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The time-domain simulation results and analysis of the dynamic model are presented to show the effect of the payload on the mode shapes and frequencies and the dynamics of the system.