Abstract
The locations of components in mechanical assemblies are determined by reconciling various constraints among the components that arise from physical, geometric and kinematic relationships, human factors, maintenance concerns, etc. Among them some constraints require that particular spatial relationships between components be maintained exactly, i.e., equality constraints. In general the equality constraints can be expressed as systems of equations. However the systems of equations deduced from the equality constraints are mostly ill-determined so that special numerical attentions are required. This paper proposes a numerical treatment for ill-determined systems in mechanical assemblies. It utilizes singular value decomposition and Newton-Raphson methods in corporation with minimum weighted deviation criteria. The treatment was implemented on an assembly modeler for automatic packaging task.
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Kim, J.J. A numerical treatment for III-determined systems in mechanical assemblies. KSME Journal 9, 472–482 (1995). https://doi.org/10.1007/BF02953645
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DOI: https://doi.org/10.1007/BF02953645