Numerical Analysis of Robotic Manipulator Subject to Mechanical Flexibility by Lagrangian Method

In this work, a systematic approach is presented for the development of dynamic equations of motion of a robot manipulator with mechanical flexibility. A simple structural lightweight rotating manipulator with joint elastic flexibility is considered for the mechanical flexibility study. The complexity of mathematical equations involved in mechanical flexibility is analyzed. The analytical approach helps the design for controls of flexible manipulator. A set of decoupled dynamic equations are derived incorporating both the structural and joint flexibility. The dynamic equations are compared with a detailed model, and the results are showing that equations are accurate for small joints. Also the results from the simulation show that in a flexible joint system, there is no rigid mode.