Theory and Practice of Point Line Kinematics

点线运动学理论与实践

• 批准号: 0219859
• 负责人: Kwun-Lon Ting
• 金额: $ 24.34万
• 依托单位: Tennessee Technological University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2006-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0219859&HistoricalAwards=false
• 关键词: Theory; Practice; Point; Line; Kinematics

This grant provides funding for the development of a theory on point-line kinematics and its applications on the analysis, characterization, synthesis, and control of point-line motion. A point-line operator based on geometry and Clifford algebra will be developed to express a point-line transformation. Subsequently, this transformation will allow a point-line to be considered as an independent rigid element having a completely specified motion without invoking rigid body transformation. Based on a principle similar to the point-line operator, the theory will be extended to include line displacement and rigid body motion, in which parameters responsible for causing incompletely specified motion can be removed or added as needed. Issues on the synthesis for finite and infinitesimal point-line motions will be investigated. The results will be applied to enhance the design capability of spatial mechanisms and manipulators. The project will also explore for the first time the full configuration space concerning the tool path generation in five-axis numerical control machining for interference avoidance.If successful, the results will lead to the first point-line kinematics theory comparable to the well-developed rigid body kinematics theory. In addition, it will lead to a unified kinematics theory for lines, point-lines, and rigid bodies. It allows one to understand and treat a point-line motion by viewing the point-line as an integrated rigid element in a way similar to that of points or rigid bodies. It will lead to a mathematical language such that the characteristics of point-line motions can be rigorously articulated. It will serve as a catalyst and foundation for advancements in kinematics, robotics, computer-aided geometric design, and manufacturing technology. Because many tool operations such as numerical control machining, drilling, screwing, riveting, cutting, probing, insertion, and electric wire discharge machining are basically point-line operations, the project's results will enhance the capability of making improvements on the motion synthesis, control, and quality of these operations. It is also recognized that because of the fundamental nature of the subject, the impact may extend to other aspects of science and engineering.

这笔资金用于开发点-线运动学理论及其在点-线运动的分析、表征、合成和控制方面的应用。提出了一种基于几何和Clifford代数的点线算子来表示点线变换。随后，此变换将允许将点-线视为具有完全指定运动的独立刚体元素，而无需调用刚体变换。基于与点-线算符类似的原理，该理论将扩展到包括线位移和刚体运动，其中导致不完全指定运动的参数可以根据需要删除或添加。关于有限和无穷小点线运动的综合问题将被研究。研究结果将用于提高空间机构和机械手的设计能力。该项目还将首次探索五轴联动数控加工中刀具轨迹生成的全构形空间。如果成功，将产生可与成熟的刚体运动学理论相媲美的第一个点-线运动学理论。此外，它还将导致直线、点线和刚体的统一运动学理论。它允许人们通过将点-线视为一个完整的刚体元素来理解和处理点-线运动，其方式类似于点或刚体的运动。它将导致一种数学语言，这样点-线运动的特征就可以被严格地表达出来。它将成为运动学、机器人、计算机辅助几何设计和制造技术进步的催化剂和基础。由于数控加工、钻孔、螺丝、铆接、切割、探头、插入、电火花线切割等许多刀具作业基本上都是点线作业，项目成果将提高这些作业的运动综合、控制和质量改进的能力。人们还认识到，由于该学科的根本性质，其影响可能延伸到科学和工程的其他方面。