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用单叶双曲螺旋管实现两个轴异面管道的光滑拼接 被引量:2

Employing Hyperbolic Spiral Pipe of One Sheetto Smoothly Blend Tubes Whose Axes is Non-coplanar
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摘要 讨论了用单叶双曲螺旋管实现两轴异面圆管道之间光滑拼接的问题,给出了光滑拼接所满足的条件:两轴异面管道的轴线与单叶双曲螺旋管的轴线在拼接点处满足位置连续:r(t_1)=M_1(x_1,y_1,z_1),r(t_2)=M_2(x_2,y_2,z_2),斜率连续:d_1=ε·r′(t_1),d_2=δ·r′(t_2)(ε,δ>0)及管道半径相同,同时得到了拼接曲面单叶双曲螺旋管的参数方程形式。并举出具体实例,以Maple数学软件为工具,给出拼接效果图。本研究对工业产品的外形设计具有重要的理论意义和实际的应用价值。 This paper discusses the problem of the smooth blending between two tubes whose axes are non-coplanar with the hyper- bolic spiral pipe of one sheet, and gives the smooth blending conditions: the axises of the two tubes whose axes are non-coplanar and the axis of hyperbolic spiral pipe of one sheet in splicing point meet position continuous: r( t1 ) = M1 ( xl , yl , zl ),r(t2) = M2 ( x2 , y2 ,z2), the slope continuous: dl -ε· r' (t1 ) ,d2 =δ· r'(t2)(ε,δ〉0), and the pipe radius is the same, at the same time, obtains smooth blending parameter surface. And citing specific examples, and using mathematical software Maple to draw the splicing effect pictures. This study has important theoretical significance and practical application value for the design of industrial products.
出处 《重庆师范大学学报(自然科学版)》 CAS CSCD 北大核心 2016年第2期108-112,共5页 Journal of Chongqing Normal University:Natural Science
基金 国家自然科学基金(No.11561052) 内蒙古民族大学科学研究基金项目(No.NMDGP1415)
关键词 轴异面圆管道 单叶双曲螺旋管 光滑拼接 two tubs whose axes are non-coplanar axes the hyperbolic spiral pipe of one sheet smooth blending
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