Using sign algebra for qualitative spatial reasoning about the configuration of mechanisms

Abstract

This paper presents a novel approach to qualitative spatial reasoning about the spatial configuration of mechanisms that could be applied in the earlier phases of mechanism design. The basic idea in this approach is to predict all possible spatial configurations of a mechanism using sign algebra. This paper addresses spatial configuration problems of direction, position, and orientation of mechanisms. Spatial configuration matrices are introduced to describe and manipulate the spatial information of primitive mechanisms. Using these matrices, the overall spatial configurations of a complicated mechanism are constructed and then they are expressed by spatial configuration state matrices. These matrices are composed based on sign algebra and used to reason about all possible spatial solutions of a mechanism. The qualitative spatial reasoning proposed in this paper could provide useful prior information on the spatial configuration of mechanisms earlier in the conceptual design of mechanisms. The proposed approach is illustrated with a design example.