Expedited Award for Novel Research: Geometric Representations of Functional Constraints Using Clifford Algebras

小说研究加急奖：使用克利福德代数的功能约束的几何表示

• 批准号: 8918325
• 负责人: John McCarthy
• 金额: $ 3万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-09-01 至 1990-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8918325&HistoricalAwards=false
• 关键词: Expedited; Award; Novel; Research; Geometric

Functional constraints in a manufactured assembly assure the proper relative movement of interconnected parts. Recent results in kinematics show that the Clifford Algebra of projective three space provides a convenient representation of these functional constraints as quadratic algebraic surfaces. A Clifford Algebra is a vector space with a product operation that contains information about the metric properties of the underlying space. In the case of three dimensions the Clifford Algebra also represents the group of spatial rigid displacements. In this research the investigator will derive the manifolds for six spatial functional constraints, show how this theory represents the planar mating of two "peg-in-hole" constraints as the intersection of hyperboloids. The goal of the research is to generalize these results to a formalism that prescribes geometrically the bounds of relative spatial position and orientation of two parts. This geometric prescription will facilitate assembly verification and tolerance verification.

制造装配中的功能约束保证了相互连接部件的适当相对运动。运动学的最新结果表明，投影三维空间的Clifford代数提供了一种方便的将这些功能约束表示为二次代数曲面的方法。Clifford代数是一个向量空间，其乘积运算包含有关底层空间度量属性的信息。在三维情况下，Clifford代数也表示空间刚性位移组。在这项研究中，研究者将推导出六个空间功能约束的流形，并展示该理论如何将两个“钉孔”约束的平面配合表示为双曲面的交集。本研究的目的是将这些结果推广到一种形式主义，这种形式主义规定了两个部分的相对空间位置和方向的几何界限。该几何配方便于装配验证和公差验证。