Elimination Methods for Spatial Synthesis

Many spatial, dimensional, position-synthesis problems lead to finite sets of solutions. In this paper, four such problems are presented. Two of these problems are solved using multihomogeneous resultant theory. The other two problems are solved using elimination strategy to obtain a solution based on rank reduction of a rectangular matrix of the form (A — λB). In the latter case, the appearance of linearly dependent equations during the elimination process is fully analyzed.