Dynamic stability analysis of a closed-loop flexible link mechanism

This paper presents an efficient and accurate stability analysis method for a closed-loop flexible mechanism. Based on single link modes, the modal properties of a flexible mechanism are derived from the second order perturbation method. Since the low mode shapes of the flexible mechanism become time-invariant, the equations of motion can be decoupled using these modes, regardless of the curve veering. Therefore the stability of the flexible mechanism can be analysed efficiently for each mode. Also the relationships between the instability conditions and the time-varying natural frequency are derived from in detail investigation on the monodromy matrix. In this proposed stability analysis method, unstable regions can be found out efficiently for each mode through doing the stability analysis only at a few speeds satisfying Omega = <(omega)over bar>(i)/m or Omega = <(omega)over bar>(i)/(m + 1/2) within the operating range of interest. Also the ranges of unstable regions are determined from the derived relations without doing the secondary stability analysis in the neighborhood of Omega = <(omega)over bar>(i)/m or Omega = <(omega)over bar>(i)/(m + 1/2). Numerical results of a flexible four-bar mechanism are compared with those from several existing methods to verify the numerical efficiency and accuracy of the proposed method. (C) 1996 Elsevier Science Ltd.