In this work, a systematic method based on graph theoretic concepts is presented that allows setting up a general mechanism's governing equations and analyzing transmission performance for a wide range of parametric and topological variations. The algorithms and methods described in this work are designed to be both fully automatic — requiring minimal supervision from an analyst for successful execution, robust — capable of handling instantaneous bifurcations and end-of-stroke conditions, and numerically efficient — through the application of numerical reduction strategies, custom sparse matrix methods and vectorization.
In the first primary section, the focus is on automatic, graph-theoretic methods for setting up a mechanism's constraint equations and solving the dynamic equations of motion. A multibody system's constraint equations, i.e. the Jacobian matrix, plays a central role in the equations of motion, and is almost never full-rank, which complicates the solution process even for relatively simple systems. Therefore, Generalized Coordinate Partitioning (GCP), a numerical method based on LU decomposition applied to the Jacobian matrix is applied to find the optimal set of independent, generalized coordinates to describe the system. To increase the efficiency of the GCP algorithm, a new general purpose graph-partitioning algorithm, referred to as "Kinematic Substructuring" is introduced and numerical results are provided. Furthermore, a new numerical implementation of solving the equations of motion, referred to as the "Preconditioned Spatial Equations of Motion" is presented and new sparse matrix solver is described and demonstrated in several numerical examples.
In the second primary section, it is shown how a simple numerical procedure applied to a mechanism's constraint equations can be used as a measure of transmission performance. The metric, referred to as "mobility numbers" provides an indication of a joint's ability to affect a change on a mechanism's overall configuration and is directly related to a mechanism's instantaneous mobility. The relationship between mobility, transmission and manipulability is discussed. Unlike many other measures of transmission performance, mobility numbers are normalized and bound between 0 and 1, and can be computed simply and efficiently from the Jacobian matrix using LU and QR matrix decomposition methods. Examples of applications of mobility numbers are provided.
Finally, in the last section, aspects of software design, including external and internal storage formats and memoization programming methods are discussed.
|Commitee:||Cheng, Harry H., Velinsky, Steven|
|School:||University of California, Davis|
|Department:||Mechanical and Aerospace Engineering|
|School Location:||United States -- California|
|Source:||DAI-B 78/10(E), Dissertation Abstracts International|
|Subjects:||Mechanical engineering, Computer science|
|Keywords:||Complex mechanisms, Computational dynamics, Constrained dynamics, Engineering software design, Mobility analysis|
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