Research On Recursive Dynamics Of Mechanical Multi-body Systems With Open And Closed Loop Based On Lie Groups And Lie Algebras

With the development of modern science and technology,engineering objects which composed a large number of objects have emerged. New methods are needed to study various complex mechanical systems, such as vehicles, serial and parallel mechanisms, robots, aviation and space flights. The aim of Multi-body system dynamics is to research the forward, reverse, and hybrid problems of large-scale systems. It contains the dynamical problems of rigid body mechanics, analytical mechanics, computa-tional mechanics, material mechanics and bio-mechanics. Multi-body system dynamics is oriented to the areas of aerospace engineering, mechanical engineering and automobile, bionic artificial limbs. It is a high-technology discipline after many years of practical application.A unified recursive multi-body dynamics theory, algorithms and applications of open and closed loop mechanical systems are studied in this paper. It aims at fast and efficient recursive modeling, optimization-based design and simulation of dynamic control problems of multi-body systems. It contains the problems of comparing and selecting of modeling method, serial systems expanding to tree topology systems, free flying systems and the systems with active and passive joints, the recur-sive closed-loop system dynamics and the efficient flexible multi-body dynamics. The software sys-tems and control simulation of such problems are described.First, a detailed comparison between three classic O(N) recursive dynamics methods of spatial op-erator algebra method, articulated body inertia method and Lie Groups and Lie algebraic method is investigated. From the core algorithm of the basic theory and recursive process of inverse and forward dynamics, it can be concluded that these methods use different principles reaching the formations of efficient recursive dynamics algorithms. Screw theory is the fundamental to form a highly efficient recursive dynamics. Comparing with the results of dynamical software SimMechanics, it can be veri-fied the correctness of the algorithm. The theoretical calculation is studied from the addition and mul-tiplication times required for the recursive algorithm. The actual computation time are compared be-tween the O (N3) methods and O (N) method.Then on the basis of chain systems, recursive dynamics described of Lie groups and Lie algebras are extended to tree topology systems, free flying systems and the systems with active and passive joints. Based on natural orthogonal complement and decoupling of natural orthogonal complement, the recursive dynamics for the closed loop systems are discussed. Gaussian elimination method is used to solve the inverse and forward dynamical problems. Dynamics method based on six-bar presses were optimized. The finite segment and the finite element model are investigated to solve the flexible multi-body system. Combined with recursive dynamics algorithm presented earlier, a recursive finite segment method for flexible multi-body system dynamics is studied. Two types of space deployable mecha-nisms– the hinged deployable mechanism and three-dimensional deployable mechanism are analyzed. The deploying process of one satellite antenna model is given. The three-dimensional deployable mechanisms based on Bennett are discussed. Dynamical simulation results of plane four-bar linkage and spatial four-bar linkage are given.At last, three parts is proposed to solve multi-body system dynamics simulation program design and control problems. Mathematica symbolic analysis software is used to establish the system of sym-bolical model. By NETLINK of VB.NET, the user interface achieves a seamless connection with Mathematica. With Matlab, the program to achieve numerical calculation, simulation and control is developed. By automatically programming C code and S-Function, Mathematica and Matlab are con-nected together. Discusses are made to the dynamics-based control algorithm. The simulation results are given comparing the PID control method and force/displacement hybrid control law for a space-floating Stanford robot.