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Recursive Modelling of 3D Rectangular Braid

Recursive Modelling of 3D Rectangular Braid Roger Ng (Original article published in Vol.3 No.2 November 1999, page 16-26) ERRATA 1.2 Braiding machine Figure 1 Model of A Braiding Machine ,yc e ell Down Up 2 3 4 5 6 7 Down Up ,yc e Right 2 1 6 Right Left 3 8 7 Left ,yc e C I 3 Up Down 2 1 6 3 8 Up Down C,ycIe 4 Left 8 4 6 Left Right 3 5 1 Right Note: Numbers in bold face indicate yams in motion, while others are stationary during the cycle. 71 2.4 Properties of qx and qy 3. qy(x,y,c) = qy(X±2,y,c) Proof qy(x,y,c) = (-1) qy(X±1,y,c) = (_1)2 qy(X±2,y,c) Q.E.D. 6. x(x,y,c) = -qx(x,y±l,c) Proof V(y±l)V(y±l -(m+1» = V(y)V(y-(m+1» = 1, for interior y. Im({+c0+3) does not involves y. (-1) (_ly+l = (_l)(Y+l)+l, by rearrangement of terms. Q.E.D. 7. qx(x,y,c) = qx(x,y±2,c) Proof qx(x,y,c) = (-1) qx(x,y±l,c) = (_1)2 qx(x,y±2,c) Q.E.D. 5. DIRECT FORMULA Quarter Cycle Formula [2.9] c-1 c-1 p(xO,yO,cO;c) = q(xO,yO) + L qx(xi,yi,cO;c;) + L qy(xi,yi,cO;c;) i=O i=O c-1 3. p(xO,yO,cO;c+ 1) = q(xO,YO) + L qx(xi,yi,cO;c;) + i=O c-1 L qy(xi,yi,cO;c;) + qx(xc,yc,cO;c) + qy(xc,yc,cO;c) i=O c c = q(xO,YO) + L qx(xi,yi,cO;c;) + L http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research Journal of Textile and Apparel Emerald Publishing

Recursive Modelling of 3D Rectangular Braid

Ng, Roger
Research Journal of Textile and Apparel , Volume 4 (1): 2 – Feb 1, 2000
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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
1560-6074
DOI
10.1108/RJTA-04-01-2000-B008
Publisher site
See Article on Publisher Site

Abstract

Roger Ng (Original article published in Vol.3 No.2 November 1999, page 16-26) ERRATA 1.2 Braiding machine Figure 1 Model of A Braiding Machine ,yc e ell Down Up 2 3 4 5 6 7 Down Up ,yc e Right 2 1 6 Right Left 3 8 7 Left ,yc e C I 3 Up Down 2 1 6 3 8 Up Down C,ycIe 4 Left 8 4 6 Left Right 3 5 1 Right Note: Numbers in bold face indicate yams in motion, while others are stationary during the cycle. 71 2.4 Properties of qx and qy 3. qy(x,y,c) = qy(X±2,y,c) Proof qy(x,y,c) = (-1) qy(X±1,y,c) = (_1)2 qy(X±2,y,c) Q.E.D. 6. x(x,y,c) = -qx(x,y±l,c) Proof V(y±l)V(y±l -(m+1» = V(y)V(y-(m+1» = 1, for interior y. Im({+c0+3) does not involves y. (-1) (_ly+l = (_l)(Y+l)+l, by rearrangement of terms. Q.E.D. 7. qx(x,y,c) = qx(x,y±2,c) Proof qx(x,y,c) = (-1) qx(x,y±l,c) = (_1)2 qx(x,y±2,c) Q.E.D. 5. DIRECT FORMULA Quarter Cycle Formula [2.9] c-1 c-1 p(xO,yO,cO;c) = q(xO,yO) + L qx(xi,yi,cO;c;) + L qy(xi,yi,cO;c;) i=O i=O c-1 3. p(xO,yO,cO;c+ 1) = q(xO,YO) + L qx(xi,yi,cO;c;) + i=O c-1 L qy(xi,yi,cO;c;) + qx(xc,yc,cO;c) + qy(xc,yc,cO;c) i=O c c = q(xO,YO) + L qx(xi,yi,cO;c;) + L

Journal

Research Journal of Textile and Apparel – Emerald Publishing

Published: Feb 1, 2000

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