Dynamic stability analysis of a flexible four-bar mechanism and its experimental investigation

Abstract

This paper presents a method for stability analysis of a closed-loop flexible mechanism by using modal coordinates. Mode shapes of a flexible four-bar mechanism are defined as those of individual links (single-link modes). Based on these single-link modes, the flexible four-bar mechanism has time-invariant mode shapes and its governing equations of motion become decoupled, regardless of mode-crossing. Therefore the stability of the flexible mechanism can be analyzed efficiently for each mode. Floquet theory is employed to check the stability of the mechanism. The experimental study of a flexible four-bar mechanism is also presented to verify the proposed method. The experimentally-determined bending strains and critical speeds are compared with numerical results obtained from the proposed method. The experimental and analytical results show a fairly good agreement.