Researches On The Rigid-flexible Coupling Problem And The Dynamic Modeling Theory Of Multi-link Spatial Flexible Manipulator Arms

In this dissertation, the rigid-flexible coupling problem of the flexible multibody system and the dynamic modeling theory of multi-link spatial flexible manipulator arms are studied.In the flexible multibody system dynamics, the traditional zero order approximate coupling model applies mechanically the supposes of small deformation in structure dynamics, but ignores the high order coupling term between the large displacement rigidbody motion and the small displacement elastic deformation. When the large overall motion of the system is at high speed, the result of the zero order approximate coupling model will be divergent. So, scholars pay more attention to the rigid-flexible coupling problem, and a more accurate model, which is called the first order approximate coupling model, is proposed. The coupling effect between the large rigidbody motion and its own deformation is considered in the first order approximate coupling model. But it uses the supposes of small deformation in the modeling to simplify the dynamical equation, and can’t deal with the large deformation problems. Thus, a more accurate model, which is called the first order coupling model, is proposed based on the theory of the first order approximate coupling model in this dissertation.To study the modeling theory of the rigid-flexible problem, a hub-beam system with large overall motion is researched in the dissertation. Both the transversal deformation and the longitudinal deformation of the flexible beam are considered. And the non-linear coupling term, also known as the longitudinal shortening caused by transversal deformation, is considered in the total longitudinal deformation. The approach of assumed modes is used to describe the deformation of the beam. The first order coupling dynamical equations of the system are established via employing the second kind of Lagrange’s equation. The high order quantities of the non-linear coupling term, which are omitted in the first order approximate coupling model, are retained in the equations. Thus, the dynamical equations can be used not only in the small deformation problems, but also in the large deformation problems. Based on this theory, the model can be extended to the hub-variable section beam system and the hub-beam system with a payload on the arbitrary position of the beam.The natural frequencies of the hub-beam system with large overall motion are studied though the transversal bending vibration analysis based on the first order approximate coupling model. For convenience of discussion, dimensionless parameters are used in the dynamical equations. The divergence mechanism of the zero order approximate coupling model is explained from the angle of the natural frequencies. Then, the influences of the position, mass, rotary inertia of the payload and the structure change of the variable section beam on the natural frequencies of the system are studied.The dynamic characteristics of the hub-beam system with large overall motion are studied based on the first order coupling model. The differences among the first order coupling model, the first order approximate coupling model and the zero order approximate coupling model are compared. And the applicability of the first order coupling model under large deformation situation is verified.Based on the theory of the first order coupling model, the dynamic modeling theory of the multi-link spatial flexible-link flexible-joint manipulator arms is investigated. The system considered here is an n-flexible-link manipulator driven by n DC-motors through n revolute flexible-joints. The flexibility of each flexible joint is modeled as a linearly elastic torsional spring, and the mass of the joint is also considered. For the link’s flexibility, both the stretching deformation, bending deformation and the torsional deformation are included. The complete governing equations of motion of the system are derived via the Lagrangian equations. In the modeling the nonlinear description of the deformation field of the flexible link is adopted, and thus the dynamic stiffening effects are captured. Based on this model, a general-purpose software package for dynamic simulation of multi-link spatial flexible manipulator arms is developed. Several illustrative examples including a planar single-link flexible manipulator, two multi-link spatial flexible manipulators, a planar flexible fold link, and a flexible curve link are given to validate the algorithm presented and to indicate that the dynamic stiffening effects, the torsional effects, the flexibility of the structure all have significant influence on the dynamics of the manipulator.