Assembling objects through parts correlation
Pamela J. Vermeer · 1997
A solution is presented to the problem of assembling four solid objects by matching points and planes of pairs of the objects. This problem would be simple if the parts could be assembled by fixing one part and adding the others sequentially. In the situation we consider, however, after fixing one part, the remaining three parts must be positioned simultaneously. To do this requires solving an interlocked system of nonlinear equations with up to sixteen different solutions. Since we are interested in obtaining all possible positionings of the four objects which satisfy the given constraints, an analytic approach is taken to solve the resulting system of equations. In addition to the theoretical solution, results of an implementation of the solution are presented. 1 Introduction When designing a complex mechanism or structure, it is often easiest to construct the object component by component. The simpler individual components can then be pieced together by correlating geometric elemen...