A NUMERICAL TREATMENT FOR ILL-DETERMINED SYSTEMS IN MECHANICAL ASSEMBLIES

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, mainte nance concerns, etc. Among them some constraints require that particul ar spatial relationships between components be maintained exactly, i.e ., equality constraints. In general the equality constraints can be ex pressed as systems of equations. However the systems of equations dedu ced from the equality constraints are mostly ill-determined so that sp ecial numerical attentions are required. This paper proposes a numeric al treatment for ill-determined systems in mechanical assemblies. It u tilizes singular value decomposition and Newton-Raphson methods in cor poration with minimum weighted deviation criteria. The treatment was i mplemented on an assembly modeler for automatic packaging task.