CAREER: Geometric Singularities in Engineering Design and Manufacturing: A Generic Spacetime Approach

职业：工程设计和制造中的几何奇点：通用时空方法

• 批准号: 0644769
• 负责人: Horea Ilies
• 金额: $ 40万
• 依托单位: University of Connecticut
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-01 至 2013-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0644769&HistoricalAwards=false
• 关键词: CAREER; Geometric; Singularities; Engineering; Design

The research objective of this Early Faculty Career Development (CAREER) award is to develop a generic theoretical framework and computational algorithms for predicting, quantifying, and correcting potential malfunctions induced by geometric singularities, such as undesired loss of contact or changes in the prescribed motion of moving bodies in the presence of uncertainty. The research takes a new approach to the characterization of geometric singularities in the envelopes of families of both rigid and non-rigid moving shapes by reframing the problem in terms of the so-called "fold points" and "fold regions" in the neighborhood of these singularities. Based on this duality, the problem of detecting geometric singularities is recast into Point Membership Classification tests in the original d-dimensional Euclidean space, eliminating the need for envelope computations. In turn, this will result in improved detection and corrective capabilities of such potential failures. If successful, the results of this research will advance the state of the art in computer aided manufacturing, path planning, and geometric modeling by providing algorithms which will, for example, significantly improve on-line testing of tool paths and CNC codes for arbitrarily complex shapes and motions that will reduce under- or over-cutting in machining, improved swept volume calculations and improved collision detection. New curriculum will be developed and integrated into the mechanical engineering program. Outreach to an all women's college to encourage and actively recruit female students into mechanical engineering and collaboration with a successful existing K-12 outreach program will be performed as part of this project.

这一早期教师职业发展（职业）奖的研究目标是开发一种通用的理论框架和计算算法，用于预测，量化和纠正因几何奇异性而引起的潜在故障，例如在存在不确定的情况下，移动身体的处方运动的处方运动的不良接触或变化。这项研究采用了一种新的方法来表征几何奇异性在刚性和非韧性移动形状家族中的信封中，通过在这些奇异之处的所谓“折叠点”和“折叠点”和“折叠区域”来重塑问题。基于这种二元性，检测几何奇异性的问题是将原始D维欧几里得空间中的点成员分类测试重新铸造，从而消除了对信封计算的需求。反过来，这将导致这种潜在失败的检测和纠正能力的提高。如果成功的话，这项研究的结果将通过提供算法来推动计算机辅助制造，路径计划和几何建模，例如，这些算法将显着改善工具路径的在线测试，而CNC代码是任意复杂形状和运动的CNC代码，从而减少了加工的数量计算，从而减少了不足或改善的范围，从而减少了不足或过度的计算。新课程将开发并集成到机械工程计划中。将向所有女子学院推广，以鼓励并积极招募女学生参加机械工程，并与现有的K-12外展计划合作，将作为该项目的一部分进行。