Interference-Free Insertion of a Solid Body Into a Cavity: An Algorithm and a Medical Application

Abstract

This article presents a novel algorithm for efficiently computing an interference-free insertion path of a body into a cavity and shows its practical use in the insertability analysis of custom orthopedic hip implants. The algorithm is designed to handle tightly fit, very complex three-dimensional bodies requiring fine, complex, coupled six-degree-of-freedom motions in a preferred direction. It provides a practical method for efficiently handling the geometric complexity of tight-fit insertions. The algorithm computes an insertion path consisting of small interference-free body motion steps. It formulates local, linearized configuration space constraints derived from the shapes and computes suc cessive motion steps by solving a series of linear optimization problems whose solution corresponds to the maximum allowed displacement in a preferred direction satisfying the constraints. It either finds a successful insertion path or a stuck conftgura tion. We demonstrate the algorithm with EXTRACT, a program for analyzing the insertability of cementless custom orthopedic hip implants. EXTRACT computes interference-free insertion paths for tightly fit implant and canal shapes described with 10,000 facets to an accuracy of 0.01 inch in 30 minutes on a workstation. It has been successfully tested on 30 real cases provided by a medical equipment manufacturer.