Interactive Visualization of Line Congruences for Spatial Mechanism Design

This paper presents a framework for generating, representing, and interacting with the line congruences associated with four general finite poses. These line congruences are the solution space of spatial 4C mechanisms which will guide a moving body through the four prescribed poses. Hence, the contributions of this paper are applicable to developing interactive tools for designing spatial 4C mechanisms for four pose motion generation. Moreover, the strategies employed to address this difficult interactive visualization challenge are presented. The goal here being to facilitate future works which address other interactive visualization challenges. First, a methodology for generating a parameterized representation of the line congruences is reviewed. This is followed by strategies for visually representing the line congruences which are appropriate for both workstation and immersive virtual reality computer graphics. Next, strategies and supporting algorithms for interacting with the line congruences to obtain solution mechanisms with fixed links or coupler links in desired regions of the workspace are presented. The result is an intuitive interactive visual design methodology for generating and interacting with the line congruences associated with four general finite spatial poses for spatial 4C mechanism design. It is our desire that this effort, albeit focused upon the challenge of creating computer-aided design environments for spatial 4C mechanisms, will facilitate as well as motivate other efforts to address the inherent visualization and interaction challenges in designing three dimensional mechanical systems.