Analysis of Geometric Obstacles in the Assembly of Complex Products: A Lattice-Theoretic Approach

The article discusses analysis of geometric obstacles in computer-aided assembly planning. An important concept of a geometric situation is introduced. This is such a connected and coordinated set of parts that requires a test of freedom from geometric obstacles. The axiom of geometric heredity is formulated and two algebraic models of a complex technical system are proposed. It is shown that the set of all assembled fragments of the product, which are free from geometric obstacles, forms a lattice. This makes it possible to solve the problem of geometric analysis of assembly processes by algebraic methods