Guidance is offered for understanding and using the Legendre transformation and its associated duality among functions and curves. The genesis of this paper was encounters with colleagues and students asking about the...Guidance is offered for understanding and using the Legendre transformation and its associated duality among functions and curves. The genesis of this paper was encounters with colleagues and students asking about the transformation. A main feature is simplicity of exposition, while keeping in mind the purpose or application for using the transformation.展开更多
The problem of finished surface being not first-order continuous commonly exists in machining sculptured surfaces with a torus cutter and some other types of cutters. To solve this problem, a dual drive curve tool pat...The problem of finished surface being not first-order continuous commonly exists in machining sculptured surfaces with a torus cutter and some other types of cutters. To solve this problem, a dual drive curve tool path planning method is proposed in this article. First, the maximum machining strip width of a whole tool path can be obtained through optimizing each tool position with multi-point machining （MPM） method. Second, two drive curves are then determined according to the obtained maximum machining strip width. Finally, the tool is positioned once more along the dual drive curve under the condition of tool path smoothness. A computer simulation and cutting experiments are carried out to testify the performance of the new method. The machined surface is measured with a coordinate measuring machine （CMM） to examine the machining quality. The results obtained show that this method can effectively eliminate sharp scallops between adjacent tool paths, keep tool paths smooth, and improve the surface machining quality as well as machining efficiency.展开更多
文摘Guidance is offered for understanding and using the Legendre transformation and its associated duality among functions and curves. The genesis of this paper was encounters with colleagues and students asking about the transformation. A main feature is simplicity of exposition, while keeping in mind the purpose or application for using the transformation.
基金National Natural Science Foundation of China (50875012)National High-tech Research and Development Program (2008AA04Z124)+1 种基金National Science and Technology Major Project (2009ZX04001-141)Joint Construction Project of Beijing Municipal Commission of Education
文摘The problem of finished surface being not first-order continuous commonly exists in machining sculptured surfaces with a torus cutter and some other types of cutters. To solve this problem, a dual drive curve tool path planning method is proposed in this article. First, the maximum machining strip width of a whole tool path can be obtained through optimizing each tool position with multi-point machining （MPM） method. Second, two drive curves are then determined according to the obtained maximum machining strip width. Finally, the tool is positioned once more along the dual drive curve under the condition of tool path smoothness. A computer simulation and cutting experiments are carried out to testify the performance of the new method. The machined surface is measured with a coordinate measuring machine （CMM） to examine the machining quality. The results obtained show that this method can effectively eliminate sharp scallops between adjacent tool paths, keep tool paths smooth, and improve the surface machining quality as well as machining efficiency.
