Parametric global mode method for dynamical modeling and response analysis of a rotating and length-varying flexible manipulator

Rotating and Length-Varying Flexible Manipulators (RLVFMs) benefit from the ability to transform their length to adapt to complex and demanding workspaces but suffer from increased complexity in nonlinear dynamical characteristics and thus difficulties in modeling. To provide an in-depth understanding of the RLVFMs, this paper proposes a novel dynamical modeling approach for the RLVFMs, called the Parametric Global Modal Method (PGMM), and presents a framework to study their nonlinear responses. It is capable of addressing time-varying boundary conditions and describing the elastic deformation of all flexible components with only one set of modal coordinates. A low-dimensional dynamical model of a RLVFM is developed. The natural characteristic results obtained from the models developed by the PGMM and the finite element method (FEM) are compared for verifications of the PGMM. Via a convergence analysis of responses, the high precision of the model developed by the PGMM is verified to be achieved by using only the first two modes. On this basis, the dynamic responses and computational efficiency of the low-dimensional model are validated through experiments and finite element method (FEM) simulations. Moreover, the responses of the RLVFM under operations of rapid maneuvering are studied and a potential vibration control strategy for the RLVFM is preliminarily demonstrated. This work provides a new way of developing advanced dynamical modeling methods of reconfigurable and deformable multi-component mechanisms for their dynamical design, response analysis, and system control.