Directly Visualizing Spatial Freedom from Geometric Models

Abstract

When two parts are in contact, their relative freedom of motion is restricted according to the geometry of their contacts. Rela tive freedom tells us how one part is allowed to move relative to another. Although a determination of relative freedom was solved by Ohwovoriole in the last decade, a graphical tool to visualize and represent relative freedom remained to be devel oped. The relative freedom of a polyhedral object exhibiting different types of contacts has been derived based on screw theory. The contacts are modeled as a set of essential wrenches normal to a contact plane. An algorithm to identify essential wrenches is developed. A twist field of a contact contains all possible twists that are reciprocal or repelling to the essen tial wrenches representing the contact. The relative freedom is represented by a set of freedom twists in space, which are derived by intersecting all the twist fields. The result of our analysis is a means with which to graphically visualize and algorithmically determine relative freedom.

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