Research on Coordinate System Transformation in Flexible Rope FEA

摘要

This paper focuses on the transform relationships between each element and between elements with inertial system under different attitude coordinate system in the finite element multi-body system mechanical analysis of the flexible rope process. It mainly research the attitude coordinate transformation matrix between the of flexible rope Micro-element and inertial system under the four coordinate system which are the direction cosine coordinates, finite rotation four element coordinates, Euler angle coordinate and Cardan angle coordinates, and the relationship between the connecting base on the element type and inertial reference based. It generally takes the rope as the flexible body in the dynamics and kinematics analysis process. The analysis method is mainly the finite element analysis method. It divides flexible rope into a number of micro line which is looked as ideal rigid body. Then it uses the multi-body system dynamics theory to do kinematics and dynamics analysis of every micro-element. Kinematics analysis of flexible rope is the inverse problem of gesture analysis that direction cosine matrix of rigid body is known, solving rigid body attitude coordinate. If coordinates of each element is determined, the dynamic attitude of flexible rope can be determined, which is the core of the kinematics analysis. Therefore, primary problem of gesture inverse analysis is how to get the direction cosine matrix. For the two elements associated with each other, under the different attitude coordinate system, the direction cosine matrix expressions are different. The relation of element and inertial coordinate system is also different. So, this paper aims to study the coordinate transformation matrix between the attitude of flexible rope Micro-element and inertial system and the relationship between the connecting base and inertial base, under the direction cosine coordinates, finite rotation four elements coordinate, Euler angle coordinate and Cardan angle coordinate.