CN1118704A - 最短线二十面体的高尔夫球表面凹坑图案 - Google Patents
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Abstract
一种在高尔夫球上布置表面凹坑图案的方法,包括建立带有60个相同三角面的以最短线展开的二十面体。最短线二十面体是通过建立一个与球面内接的二十面体而形成的。在二十面体上的每一个三角形中,通过平分二十面体三角形的三个边可以确定一个点,将所说的点投影到球体表面上就可以确定最短线汇聚点,将每个最短线汇聚点与每个二十面体三角形的顶点相连就可以使每个最短线汇聚点构成一个直角正四面体。
Description
本发明涉及高尔夫球表面凹坑图案,更确切地说涉及在以最短线展开的二十面体上构成的高尔夫球表面凹坑图案。
为了使高尔夫球具有均称的、可重复的飞行特性,利用多面体例如八面体、十二面体、二十面体等的球面设计开发了表面凹坑图案。将表面凹坑设置成使每个多面体中的凹坑图案相同或基本相同。多面体上的面或边的数量越多表示重复性水平越高。二十面体,即具有20个三角形表面的多面体是最常用的多面体而且该多面体为高尔夫球而布置了表面凹坑图案,其包含由20个球面三角形构成的重复部件。
美国专利No.4,560,168中描述了一种二十面体的表面凹坑图案。将表面凹坑设置在球面二十面体的三角形中,使表面凹坑不与穿过三角形各边中点的六个大圆相交。模型分割线可对准一个大圆,而其它的大圆则提供能增加图案对称性的虚分割线。
美国专利No.4,142,227中描述了一种十二面体的表面凹坑图案,其包含10个不与表面凹坑相交的大圆。然而,球的表面上带有12-30个矩形光秃贴片或无凹坑区。
美国高尔夫球协会(USGA)依据USGA对称性实验来测试高尔夫球。使用一个自动摆动器击打高尔夫球使之绕一个轴旋转,然后再对其击打使其绕与第一轴相垂直的轴旋转。如果球是对称的则两次击打之间的差值不能超出某一距离。如果能够增加精确重复部件的数量,就能够建立表面凹坑图案来改善对称性和飞行特性的重复性。
英国专利No.377,354描述了一种二十面体表面凹坑图案。在图5中将每个二十面体球面三角形分成六个直角球面三角形。图5没有针对分割线采取任何措施,而且在分割线处图案是不对称的。
美国专利No,4,915,389还描述了一种二十面体表面凹坑图案,其中将每个二十面体的三角形分成六个直角三角形。该图案不带有任何分割线,并且将凹坑设置在所有大圆上。用无心磨床形成球面,并将凹坑加工到该表面上。
美国专利No.5,192,078还描述了一种二十面体表面凹坑图案,其中将每个二十面体三角形分成六个直角三角形。将与模型分割线相交的凹坑除去而用不与分割线相交的半圆或其它在空气动力学上等效的凹坑来代之。这种图案可以获得空气动力学上的对称性,但不能得到几何学上的对称性。
美国专利No.5,249,804描述了另一种二十面体表面凹坑图案,其中将二十面体的三角形分成六个直角三角形。其分割线一般为锯齿形并且来回穿过球上平分球体的圆。
已经发现,通过利用以最短线展开的二十面体来构成形成球面二十面体的重复部件能够达到较高的重复性水平。通过形成被和高尔夫球具有相同直径的球体相外接的正二十面体可以使二十面体以最短线展开。球体与二十面体的每个顶点相交。将由三角形每个边上的平分线交叉而在二十面体每个三角面上形成的点投影到球面上获得最短线汇聚点。利用该最短线汇聚点,通过汇聚点和三角面上每个顶点之间的连接线段可以在每个三角面上构成一个直角正四面体。每个正四面体的基面是由二十面体的三角面构成的,而四面体的其它三个面在汇聚点处相汇合。20个四面体的三个表面提供了60个重复的球面三角形,其比标准二十面体图案的可重复性高出三倍。将表面凹坑设计成使60个三角形中的每一个上都具有相同的或基本相同的凹坑图案。
下面将结合附图中所示的说明性实施例对本发明进行解释,其中:
图1是二十面体中一个三角面的顶视平面图;
图2是二十面体的表面侧视图,其带有用虚线表示的外接球面;
图3是二十面体中一个三角面的顶视平面图,其表示各边平分线相交的情况;
图4是与图2相似的侧视图,其表示平分线的交点投影到球面上所确定的最短线汇聚点;
图5是在二十面体的三角面顶部构成的正四面体的顶视平面图;
图6是图5所示四面体的侧视图;
图7是二十面体的透视图;
图8是以最短线展开的二十面体的透视图;
图9是以最短线展开的二十面体中一个四面体的顶视图,其适用于具有392个表面凹坑的表面凹坑图案;
图10是以最短线展开的二十面体中一个四面体的顶视图,其适用于具有452个表面凹坑的表面凹坑图案;
图11是以最短线展开的二十面体中一个四面体的顶视图,其适用于具有492个表面凹坑的表面凹坑图案;
图12是以最短线展开的二十面体中一个四面体的顶视图,其适用于具有500个表面凹坑的表面凹坑图案;
图13是以最短线展开的二十面体中一个四面体的顶视图,其适用于具有512个表面凹坑的表面凹坑图案;
图14是高尔夫球的极线图,其包含具有320个表面凹坑的以最短线展开的二十面体表面凹坑图案;
图15表示图14的高尔夫球,其中该高尔夫球上的一个大圆呈竖向延伸状态;
图16是图14的高尔夫球视图,其中该高尔夫球上的一个大圆是横向延伸的;
图17表示图16的高尔夫球,但两者的位置略有不同;
图18是高尔夫球的极线图,其包含具有432个表面凹坑的最短线二十面体表面凹坑图案;
图19表示图18的高尔夫球,其中该高尔夫球上的一个大圆呈竖向延伸状态;
图20是图18中的高尔夫球视图,其中该高尔夫球上的一个大圆是横向延伸的;
图21表示图20中的高尔夫球,但两者的位置略有不同;
图22是高尔夫球的极线图,其包含具有500个表面凹坑的最短线二十面体表面凹坑图案;
图23表示图22中的高尔夫球,其中该高尔夫球上的一个大圆是竖向延伸的;
图24是图22的高尔夫球视图,其中该高尔夫球上的一个大圆是横向延伸的;和
图25表示图24中的高尔夫球,但两者位置略有不同。
图1和图2说明已有技术中将正二十面体的一个三角面投影到球面上以形成球面二十面体三角形的方法。图1是一个平面二十面体三角形30的顶视平面图,该三角形30带有三条边31和三个顶点32。图2是平面二十面体三角形的侧面正视图。与二十面体外接的球面33和三个顶点32相交。平面三角形30在球面上的投影构成球面三角形。
图3和图4说明形成最短线二十面体的方法。平面二十面体的三角形35具有三条边36和三个顶点37。将每条边用垂直于该边的线38进行平分。平分线在点39处相交。图4表示点39投影到与二十面体外接的球面40上以确定最短线汇聚点41。
图5和图6说明通过利用最短线汇聚点41来建立直角正四面体。三条线段42将最短线汇聚点41与每个顶点37相连形成三个三角面43,这些三角面在最短线汇聚点41处相汇合。四面体的基面是二十面体三角形35的表面。
图7表示带有20个平面三角面46的正二十面体45。图8表示一种最短线二十面体47,其在每个二十面体三角形46的顶部设有三个三角面48。每个三角面48都是一个精确的重复部件,而且在最短线二十面体上有60个这样的重复部件。
图9说明如何能用最短线二十面体来布置具有392个表面凹坑的对称表面凹坑图案。最短线二十面体的每一个四面体都包含三个三角形面50。每个三角形包括一条基线51和一对在最短线汇聚点处相交的边线52。实心凹坑53与边52相交,而基线51则穿过空白凹坑54。带阴影线的凹坑55与基线或边线均不相交。每个三角形50包含三个完整的凹坑,六个1/2凹坑、一个在最短线汇聚点处的1/3凹坑、和两个在基线与各边相交处的1/10凹坑。60个三角形的凹坑总数是392。将三角面50上的凹坑投影到与最短线二十面体外接的球面上以确定凹坑在球面上的位置。
如果需要的话,可以按照美国专利No.4,560,168来设置凹坑以便形成六个不与凹坑相交的大圆。可以用其中的一个大圆作为模型分割线。三条基线51构成一个二十面体的三角形,而连接二十面体三角形各边中点的线段56在其投影到球面上时构成大圆的线段。在球体上总共有六个这样的大圆。可以将凹坑设计成使之不与大圆线段相交。如果需要的话,可以允许与不构成模型分割线的大圆上有一些轻微的相交。
图10表示具有452个凹坑的凹坑图案。每个三角形50包含三个完整的凹坑,八个1/2凹坑,一个1/3坑,和两个1/10凹坑。
图11表示具有492个凹坑的凹坑图案。每个三角形50包含三个完整的凹坑,十个1/2坑,和两个1/10凹坑。
图12表示具有500个凹坑的凹坑图案。每个三角形50包含三个完整的凹坑,十个1/2凹坑,和一个1/3凹坑。
图13表示具有512个凹坑的凹坑图案。每个三角形50包含三个完整的凹坑,十个1/2坑,一个1/3凹坑,和两个1/10凹坑。
图14是带有320个凹坑的高尔夫球58的球形图。实线代表穿过球面二十面体三角形各边中点的六个大圆。大圆构成了十二个五边形59和二十个小三角形60,有时也称之为二十-十二面体。每个五边形的中心是五个二十面体三角形相遇的极点或顶点。虚线61是一个四面体的基线,而虚线62构成四面体上三个三角面的边。每个三角形包含一个完整的凹坑,八个1/2凹坑,和一个1/3凹坑。
图14是高尔夫球58的极线图。图15是将球转动使一个大圆竖向延伸的辅助视图。
图16和17是高尔球58的变换图,其中一个大圆构成平分该球体的图。
图18表示具有432个凹坑的高尔夫球64。每个由虚线61和62构成的三角形包含三个完整的凹坑,八个1/2凹坑,和两个1/10凹坑。
图19-21是高尔夫球64的变换图。
图22表示具有500个凹坑的高尔夫球65。其凹坑图案与图12中所示的图案相同。
图23-25是高尔夫球65的变换图。
可以设计带有更多或更少凹坑的其它凹坑图案。通常,使凹坑覆盖大约65-85%的球表面,而且凹坑的间隔应基本均匀且无重叠。可以使用不同尺寸的凹坑来获取最佳的飞行特性,而且凹坑截面的几何形状可以是球形、截锥形、六角形、或其它形状,或是它们的任意结合。凹坑的弦或直径通常在约0.075-0.200英寸的范围。
尽管在以上说明书中,为了说明的目的而对本发明的具体实施例进行了详细描述,但是很明显,对熟悉本领域的人员来说,可以在不脱离本发明构思和范围的情况下对本文给出的很多细节作出很大的改进。
Claims (8)
1、一种在高尔夫球上布置表面凹坑图案的方法,包括以下步骤:
a)建立一个带有二十个二十面体三角形的二十面体,这些二十面体三角形被一个和高尔夫球具有相同直径的球面相外接,从而使二十面体的每个顶点与球面相交,
b)确定二十面体三角形上由平分二十面体三角形各边的线相交而形成的点,
c)将所说的点投影到球面上以确定二十面体三角形的最短线汇聚点,
d)用线段将最短线汇聚点与二十面体三角形的每个顶点相连使该线段和二十面体三角形的各边构成一个直角正四面体,该四面体的基面由二十面体三角形构成,而三个三角面在最短线汇聚点处汇合,
e)对每个二十面体三角形重复步骤b-d以形成具有60个所说三角面的以最短线展开的二十面体,
f)在所说60个三角面的每一个上布置基本上相同的表面凹坑图案,和
g)将所说60个三角面上的凹坑图案投影到球面上。
2、根据权利要求1所述的方法还包括以下步骤:
用连接线将每个二十面体三角形各边的中点相连,将连接线投影到球面上从而使每条连接线构成球面大圆上的一条线段,并布置表面凹坑使之均基本上不与大圆的线段相交。
3、根据权利要求1所述的方法,其中60个三角面中的每一个都包含一个完整的凹坑,八个1/2坑,和一个1/3凹坑。
4、根据权利要求1所述的方法,其中60个三角面中的每一个都包含有三个完整的凹坑,六个1/2坑,一个1/3凹坑,和两个1/10凹坑。
5、根据权利要求1所述的方法,其中60个三角面中的每一个都包含有三个完整的凹坑,八个1/2凹坑,和两个1/10凹坑。
6、根据权利要求1所述的方法,其中60个三角面中的每一个都包含有三个完整的凹坑,八个1/2坑,一个1/3凹坑,和两个1/10凹坑。
7、根据权利要求1所述的方法,其中60个三角面中的每一个都包含有三个完整的凹坑,十个1/2坑,和一个1/3凹坑。
8、根据权利要求1所述的方法,其中60个三角面中的每一个都包含有三个完整的凹坑,十个1/2坑,一个1/3坑,和两个1/10凹坑。
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US5249804A (en) * | 1992-09-11 | 1993-10-05 | Karsten Manufacturing Corporation | Golf ball dimple pattern |
US5259624A (en) * | 1992-10-05 | 1993-11-09 | Geo Golf International Pte Ltd. | Golf ball with symmetrical dimple pattern |
US5308076A (en) * | 1993-01-19 | 1994-05-03 | Sun Donald J C | Golf ball with polar region uninterrupted dimples |
US5415410A (en) * | 1994-02-07 | 1995-05-16 | Acushnet Company | Three parting line quadrilateral golf ball dimple pattern |
-
1994
- 1994-09-06 US US08/301,245 patent/US5562552A/en not_active Expired - Fee Related
-
1995
- 1995-02-02 CA CA002141828A patent/CA2141828A1/en not_active Abandoned
- 1995-02-06 DE DE69509022T patent/DE69509022D1/de not_active Expired - Lifetime
- 1995-02-06 EP EP95101541A patent/EP0700695B1/en not_active Expired - Lifetime
- 1995-02-07 AU AU11577/95A patent/AU1157795A/en not_active Abandoned
- 1995-02-08 ZA ZA951007A patent/ZA951007B/xx unknown
- 1995-02-13 NZ NZ270487A patent/NZ270487A/en unknown
- 1995-02-15 KR KR1019950002753A patent/KR960010033A/ko not_active Application Discontinuation
- 1995-02-28 CN CN95102258A patent/CN1118704A/zh active Pending
- 1995-03-03 JP JP7044345A patent/JPH0871176A/ja not_active Withdrawn
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN103505850A (zh) * | 2012-07-02 | 2014-01-15 | 金武兄 | 高尔夫球的立方八面体凹痕结构 |
CN103933711B (zh) * | 2013-01-14 | 2017-04-12 | 阿库施耐特公司 | 多臂凹窝及包含该多臂凹窝的凹窝图案 |
Also Published As
Publication number | Publication date |
---|---|
JPH0871176A (ja) | 1996-03-19 |
EP0700695B1 (en) | 1999-04-14 |
ZA951007B (en) | 1995-10-20 |
AU1157795A (en) | 1996-03-21 |
NZ270487A (en) | 1995-10-26 |
KR960010033A (ko) | 1996-04-20 |
EP0700695A1 (en) | 1996-03-13 |
DE69509022D1 (de) | 1999-05-20 |
US5562552A (en) | 1996-10-08 |
CA2141828A1 (en) | 1996-03-07 |
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PB01 | Publication | ||
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