Computational Kinematic Geometry of NURBS Motions

NURBS 运动的计算运动学几何

• 批准号: 0500064
• 负责人: Qiaode Jeffrey Ge
• 金额: $ 27.11万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-04-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0500064&HistoricalAwards=false
• 关键词: Computational; Kinematic; Geometry; NURBS; Motions

This project seeks to create a framework for geometry driven kinematic approximation that will provide a unified treatment for design for manufacturability, addressing kinematic problems in manufacturing such as multi-axis machining of sculptured surfaces, part-mating and assembly planning, gear design and manufacturing, task specification for task-driven machine design, as well as freeform machining feature modeling in CAD/CAM integration. The primary task is to develop the computational kinematic geometry of NURBS (Non-Uniform Rational B-Spline) motions and explore its applications in the analysis, synthesis, fine-tuning of rigid-body motions in shape generation and interrogation process in engineering design where the interplay between geometry and motion plays a critical role. The computational, algorithmic and differential geometry of the NURBS motions will be fully explored from the perspectives of projective geometry and kinematic geometry of rigid body displacements. The trajectories and swept volumes of commonly used tool shapes in manufacturing will be studied for one- and multi-parameter NURBS motions taking advantage of the algorithmic geometry of NURBS motions. This will lead to the first comprehensive theory for the computational kinematic geometry of one- and multi-parameter NURBS motions. In addition, the results will represent the first truly kinematics based, global planning methodology for gauging-free 5-axis tool paths that completely decouples the problem of global surface approximation from the step-by-step process of local tool position generation. The research activities in virtual design and manufacturing are integrated with educational and outreach activities through the generation of a toolbox for learning spatial visualization and reasoning, and exploring the interplay between geometry and motion. It is expected these software tools will be particularly attractive to undergraduate students and high school students, creating a design game approach that is fundamentally rigorous while providing experiential learning.

This project seeks to create a framework for geometry driven kinematic approximation that will provide a unified treatment for design for manufacturability, addressing kinematic problems in manufacturing such as multi-axis machining of sculptured surfaces, part-mating and assembly planning, gear design and manufacturing, task specification for task-driven machine design, as well as freeform machining feature modeling in CAD/CAM integration.主要的任务是开发NURB（不均匀的理性B-Spline）运动的计算运动学几何学，并探索其在分析，合成，对形状产生中刚性运动的微调和工程设计中询问过程中的刚性运动的应用，其中几何学与运动之间的相互作用扮演着重要作用。 NURBS动作的计算，算法和差异几何形状将从投射几何形状和刚体位移的运动学几何形状的角度进行全面探索。将研究制造中常用的工具形状的轨迹和扫描量，以利用NURBS运动的算法几何形状来进行单参数NURBS运动。这将导致对单参数NURBS运动的计算运动学几何形状的第一个综合理论。此外，结果将代表第一个真正基于运动学的全球规划方法，用于测量无用的5轴工具路径，该方法完全将全球表面近似的问题与局部工具位置生成的逐步过程相比。虚拟设计和制造业中的研究活动通过生成学习空间可视化和推理的工具箱，并探索几何与运动之间的相互作用，与教育和外展活动融为一体。预计这些软件工具将对本科生和高中生特别有吸引力，从而在提供体验式学习的同时，创建了一种从根本上进行严格的设计游戏方法。