Educational Application of the AutoDyn7 (CADyna) Program in Advanced Dynamics Course at the Pusan National University in Korea

In this study, general purpose multibody dynamics codes AutoDyn7 (AUTOmobile DYNamics in G7) and CADyna (the NT version of the AutoDyn7) are introduced for the application to education in multibody dynamics. In the Auto-Dyn7 program, an efficient and systematic formulation for rigid and flexible bodies is derived using the velocity transformation technique. The Rapid-App for GUI (Graphic User Interface) builder and the Open Inventor for 3D graphic library have been employed to develop these programs in Silicon Graphics workstation. Several special purpose modules of the AutoDyn7 program are introduced to analyze vehicle dynamic characteristics. The NT version of the AutoDyn7, named CADyna, is also developed. The pre-processor for user input is developed with Visual C++ and the post-processor is developed with OpenGL and TeeChart for animation and graph.

Velocity Transformation Matrix of a Revolute-Spherical Massless Link

Since the contribution of lightweight components in the total energy of a system is small, the inertia effects are sometimes ignored via replacing them to massless links. A massless link, which is sometimes called as a composite joint, connects two adjacent bodies keeping the relative degrees of freedoms. For a revolute-spherical massless link, one edge is connected to an adjacent body with a revolute joint and the other edge is linked to another body with a spherical joint. Using velocity transformation technique, it is possible to combine the generality of Cartesian coordinates in modeling and the efficiency of relative coordinates in simulation. In this paper, velocity transformation matrix of a revolute-spherical massless link is formulated and implemented as a joint module in a vehicle dynamic analysis program. Numerical examples are presented to verify the formulation.

A Systematic Formulation for Dynamics of Flexible Multi-Body Systems Using the Velocity Transformation Technique

An efficient and systematic formulation for dynamics of spatial multi-body systems with flexible bodies is presented using the velocity transformation technique. The Cartesian variables are expressed in terms of the relative and elastic variables. Using the resulting kinemtic relationships, the velocity and acceleration transformation equations are derived and used to transform the equations of motion from the Cartesian coordinate space to the relative coordinate space. In order to reduce the number of elastic coordinates, elastic deformations are represented by the vibration normal modes obtained from the finite element analysis. The Euler parameters are used as the rotational coordinates since they are convenient for algebraic manipulation and have no singular condition. The formulation is illustrated by means of two numerical examples.

Spatial Dynamics of Deformable Multibody Systems With Variable Kinematic Structure: Part 2—Velocity Transformation

In Part 1 of these two companion papers, the spatial system kinematic and dynamic equations are developed using the Cartesian and elastic coordinates in order to maintain the generality of the formulation. This allows introducing general forcing functions and adding and/or deleting kinematic constraints. In control applications, however, it is desirable to determine the joint forces associated with the joint variables. On the other hand the use of the joint coordinates to formulate the dynamic equations leads to a complex recursive formulation based on loop closure equations. In this paper a velocity transformation technique applicable to spatial multibody systems that consist of interconnected rigid and deformable bodies is developed. The Cartesian variables are expressed in terms of the joint and elastic variables. The resulting kinematic relationships are then employed to determine the joint forces associated with the joint variables. A spatial robot manipulator that manipulates an object is presented as a numerical example to exemplify the development presented in this paper.