Using Nonlinear Recursive Formulation on Dynamic Analysis of Multi-body Systems

• Main Authors: Chu Duc Nhat, 朱德日
• Other Authors: Yunn-Lin Hwang
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/9xwg9j

碩士 === 國立虎尾科技大學 === 電機工程研究所 === 100 === Using nonlinear recursive formulation method for the dynamic analysis of multi-body systems is presented. The first part is used for the dynamic analysis of open-loop mechanical systems that consist of a set of interconnected deformable bodies. The second part is used for the dynamic analysis of a closed-loop flexible kinematic mechanical system. At first, the configuration of each body in the system is identified using a coupled set of reference and elastic co-ordinates. The absolute velocities and accelerations of child bodies in the open-loop system are expressed in terms of the absolute velocities and accelerations of the parent bodies and the time derivatives of the relative co-ordinates of the joints between the bodies. The dynamic differential equations of motion are developed for each link using the generalized Newton-Euler equations. The relationship between the actual joint reaction and the generalized forces combined with the kinematic relationship and the generalized Newton-Euler equations are used to develop a system of loosely coupled equations which has a sparse matrix structure. Using matrix partitioning and recursive projection techniques based on optimal block factorization, an efficient solution for the system acceleration and joint reaction forces is obtained. It also allows a systematic procedure for decoupling the joint and elastic accelerations. Secondly, the kinematic and force models are developed using absolute reference, joint relative, and elastic coordinates as well as joint reaction forces. This nonlinear recursive formulation leads to a system of loosely coupled equations of motion. In a closed-loop kinematic chain, cuts are made at selected auxiliary joints in order to form spanning tree structures. Compatibility conditions and reaction force relationships at the auxiliary joints are adjoined to the equations of open-loop mechanical systems in order to form closed-loop dynamic equations. Using the sparse matrix structure of these equations and the fact that the joint reaction forces associated with elastic degrees of freedom do not represent independent variables, a method for decoupling the joint and elastic accelerations is developed. Unlike existing recursive formulations, this method does not require inverse or factorization of large nonlinear matrices. It leads to small systems of equations whose dimensions are independent of the number of elastic degrees of freedom. The application of dynamic decoupling method in dynamic analysis of closed-loop deformable multi-body systems is also discussed in this study. The use of the numerical algorithm developed in this investigation is illustrated by several numerical examples in this study. Keywords: Nonlinear recursive formulation, Open-loop deformable multibody, Generalize Newton-Euler equations, Closed-loop, Primary joint, Auxiliary joint.