Influences of generic payload and constraint force on modal analysis and dynamic responses of flexible manipulator

Abstract

This article presents the dynamic modeling and nonlinear analysis of two-link flexible manipulator with generic payload whose center of gravity is different than the point of attachment with the link. The manipulator is driven by harmonic joint motions and subjected to a constraint force at the terminal end due to its interaction with working environment. Hamilton’s approach is adopted to dynamically model the multi-link manipulator for longitudinal and transverse vibrations incorporating the nonlinearities associated with axial stretching. The resulting set of eigenfrequency equations are solved numerically with subsequent generation of eigenspectrums. Further, this paper investigates the resonant behavior of manipulator links for the subharmonic and primary resonance conditions due to end follower force and revolute joint motions, respectively. The resonant responses show the jump phenomenon and existence of multi-valued solutions at pitchfork and saddle-node bifurcation points. The numerical and graphical results thus obtained, clearly indicate the significant influence of variation of system configurations and generic payload on eigencharacteristics and nonlinear responses, and hence must be given consideration during dynamic modeling of a manipulator in order to attenuate undesirable vibrations.

Keywords:

• Two-link manipulator
• generic payload
• pulsating force
• modal analysis
• nonlinear stability