Surfaces II Lecture Series. Prof. G. Wang Department of Mechanical and Manufacturing Engineering University of Manitoba
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1 Srfces II 5.5 Lectre Seres rof. G. Wg Dertmet of Mechcl d Mfctrg Egeerg Uversty of Mtob
2 Tye of Srfces lr Srfce Bler Srfce Rled (lofted Srfce B-cbc srfce Bezer Srfce B-Sle Srfce
3 B-Cbc Srfce tch
4 B-Cbc Srfce tch ( ( ( ( [ ] j j j T z y x ( ( C A Cbc Sle A B-cbc Srfce tch
5 B-Cbc Srfce tch ( ( ( ( [ ] j j j T z y x ( [ ] UAW T T A M H BM H B ] [ ] [ ] [ ] [ M H
6 B-Cbc Srfce tch T A M H BM H B ] [ ] [ ] [ ] [ M H
7 Notes The srfce tch s determed by 4 bodres. Use to geerte the bodry (terctvely of the srfce. The for bodres re cbc sles. Chrcterstcs of the bcbc srfce tch re very smlr to those of the cbc sle mely lck of locl cotrol d the order of crve s fxed. Reqremet of tget d tst vectors s t dt does t ft very ell the desg evromet
8 Bezer Srfce tch Bezer srfces re formed by lottg fmles of Bezer crves. Chges of cotrol ots lter the globl she of the srfce tch. ( ( ( (
9 A Bezer Crve B Bezer Srfce tch ( B ( (! A Exmle (4 ots! (! ( 4
10 A Exmle 4 Bezer Srfce tch j 44 { } 4 j
11 4 Bezer Srfce tch j 44 ( * B ( ( j or ( ( ( 4
12 4 Bezer Srfce tch j For other three Bezer crves: j j * B ( ( j
13 Bezer Srfce tch j ( * B ( j j ( * B ( [( ( ( ] U j T [ M B j * B ][ ][ M B ] T W j ( ( (
14 Bezer Srfce tch 6 [ B ] M A geerl *m Bezer srfce: ( ( ( B B m j m j j ( ( ( ( ( ( j m j m j j m j m B B!!!!!!
15 A Exmle A Bezer srfce tch s secfed by e cotrol ots: ( T ; ( T ; ( T ( T ; ( T ; ( T ( T ; ( T ; ( T. lot the cotrol olygo d sketch the srfce tch of (.. Gve s the crve d s the crve derve the Bezer crve exresso for the to bodry crves q( d q(.. Derve the mthemtcl reresetto of the srfce tch (. 4. Clclte (.5.5
16 . Sketch Solto X( Y(
17 Solto. If defes the crve B ( B (! ( ( (!! ( ( ( ( ( ( [ ( ] If defes the crve smlrly ( ( ( [ ] T T
18 Solto ( ( ( ( [ ] ( ( ( * * B B j j j. Srfce tch ( ( ( ( ( ( ( ( ( ( ( ( (
19 Solto. Clclte (.5.5 ( ( ( ( ( ( ( ( ( ( ( ( ( (.5.5[.5] T.
20 B-Sle Srfce
21 B-Sle Srfce
22 B-Sle Srfce ( ( ( ] ( ( ( [ ( ( ( mx mx v N v N v N N N N v v v N N v m l l l m m m k k k m j l j k j Fetres: Locl cotrol d vrto of degree
23 Srfce Mltos Offset Bled Dsly Segmetto (dvso Trmmg Itersecto rojecto Trsformto
24 Alcto: Mchg Srfce Norml
25 Srfce Offset ( ' ( ' ( ' ( ( ; ' ( ( Geerte the offset srfce of crved srfce. ( ( ( d offset * Exected Srfce Rogh Mchg Srfce Fsh Mchg
26 Bledg Srfces A bledg srfce s srfce tht coects to djcet srfces or tches. The bledg srfce s slly creted th to gve tches.
27 Bledg Srfces A b-cbc bledg srfce c be redly geerted Ho bot Bezer or B-Sle bledg srfces?
28 Reve: le ( ( ( ( ( x c A y c B c D z z y y x x D Cz By Ax
29 Reve: Bler Srfce ( ( ( ( ( [] ( ( ( ( ] [ (
30 Reve: Rled (lofted Srfce ( ( ( ( ( ( ( ( or ( ( ( ( []
31 Reve: Bezer Srfce tch ( ( ( ( ( m j j B ( B j m( []
32 Qck Qestos. Wht re the fo reqred to defe lr bler lofted d Bezer srfce tch?. Wht re the dfferece betee bler srfce d rled srfce?. C e crese the order of b-cbc srfce tch by trodcg more ots? 4. Bezer srfce cotrst to Bezer crve c be loclly ted f rorte mthemtcl mlto s led. 5. Is the bledg srfce slly b-cbc srfce Bezer srfce or B-sle srfce? Why?
33 roblem ( % Hlf of smle rfol s costrcted by bledg to rllel cross sectos S S th dstce of 4 log X-xs s sho the fgre belo. Crve C s cbc B-sle crve defed by for ots [ - ] T [ -.5 ] T [ ] T d [ ] T. Crve C s costrcted by sclg C th resect to the org O by fctor of d trslted to the osto of S. Fd: The eqto of crve C The cotrol olygo for crve C The eqto of the er srfce of the rfol Z C O Y S 4 C X S
34 Smmry lr bler d rled srfces Cbc Bezer B-Sle Srfces -roertes smlr to corresodg crves -Crves re rdmetl for srfces -A exteso to to dmeso ( Srfce mlto (offset d bledg
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