A Sparsity-Oriented Approach to the Dynamic Analysis and Design of Mechanical Systems—Part 2

Abstract

The work described herein is an extension of sparse matrix and stiff integrated numerical algorithms used for the simulation of electrical circuits and three-dimensional mechanical dynamic systems. By applying these algorithms, big sets of sparse linear equations can be solved efficiently, and the numerical instability associated with widely split eigenvalues can be avoided. The new numerical methods affect even the initial formulation for these problems. In this paper, the equations of motion and constraints (Part 1) and the force function of springs and dampers (Part 2) are set up, and the numerical solutions for static, transient, and linearized types of analysis as well as the model optimization algorithms are implemented in the ADAMS (automatic dynamic analysis of mechanical systems) computer program for simulation of three-dimensional mechanical systems (Part 2). The paper concludes with two examples: computer simulation of the front suspension of a 1973 Chevrolet Malibu and computer simulation of the landing gear of a Boeing 747 airplane. The efficiency of simulation and comparison with experimental results are given in tabular form.

A general on-the-fly algorithm for modifying the kinematic tree hierarchy

“…By the mid-1970s, solutions utilizing Lagrangian multipliers for joint constraints (Chace and Sheth, 1973;Orlandea et al, 1977) appeared. What is more, Orlandea's program (ADAMS) exploited matrix sparsity (sparse tableaux formulation) to improve performance.…”

Dynamic simulation of constrained mechanical systems using recursive projection algorithm

“…There are different formulations for the dynamic analysis of spatial mechanisms which vary in the system of coordinates used and in the way they introduce kinematical constraint equations (Denavit and Hartenberg, 1955, Sheth and Uicker, 1972, Orlandea et al, 1977, Nikravesh, 1988, and De Jalon, 1994. Each formulation has its own advantages and disadvantages depending on the application and the needs.…”

Multi-body dynamics: Historical evolution and application

“…In 1977 Orlandea et al [23] presented the ®rst practical solution methodology for large rigid multi-body dynamic systems, based upon Lagrangian dynamics for constrained systems. Their work culminated in the development of ADAMS, an acronym for automatic dynamic analysis of mechanical systems, the spread and increasing use of which in industry has acted as the main driving force for many developments that have since taken place.…”