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.

该项目旨在创建一个几何驱动的运动学近似框架，为可制造性设计提供统一的处理，解决制造中的运动学问题，例如雕刻表面的多轴加工、零件配合和装配规划、齿轮设计和制造，任务驱动机器设计的任务规范，以及 CAD/CAM 集成中的自由加工特征建模。主要任务是开发 NURBS（非均匀有理 B 样条）运动的计算运动几何，并探索其在工程设计中形状生成和询问过程中刚体运动的分析、合成和微调中的应用，其中几何和运动之间的相互作用起着至关重要的作用。将从刚体位移的射影几何和运动学几何的角度充分探讨NURBS运动的计算、算法和微分几何。将利用 NURBS 运动的算法几何，研究制造中常用刀具形状的轨迹和扫掠体积，以实现单参数和多参数 NURBS 运动。这将催生第一个单参数和多参数 NURBS 运动的计算运动几何的综合理论。此外，研究结果将代表第一个真正基于运动学的免测量 5 轴刀具路径全局规划方法，该方法将全局表面近似问题与局部刀具位置生成的逐步过程完全解耦。通过生成用于学习空间可视化和推理以及探索几何与运动之间相互作用的工具箱，虚拟设计和制造的研究活动与教育和推广活动相结合。预计这些软件工具将对本科生和高中生特别有吸引力，创建一种从根本上严谨的设计游戏方法，同时提供体验式学习。