System mode approach for analysis of horizontal vibration of 3-D two-link flexible manipulators

This paper deals with the system mode analysis of horizontal vibration for 3-D two-link flexible manipulators. For the analysis, we formulate and solve a set of partial differential equations which represent vibration mixed with bending and torsional moment. The inclusion of torsional vibration complicates the analysis, but the results are more precise and realistic. We obtain a number of geometrical and dynamical boundary conditions depending on manipulator configuration. There are two possible boundary conditions at the rotary joint: clamped and pinned with spring condition. We perform a examination and comparison between the two joint conditions. Numerical and experimental tests show the validity and effectiveness of the proposed analysis and modelling.