13-12-05 Phan IV (hinh chieu truc do den het hinh cat).pdf

7/21/2019 13-12-05 Phan IV (hinh chieu truc do den het hinh cat).pdf

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GIAO TRNH VE KY THUAT- HNH HOC HOA HNH

Chng

HNH CHIEU TRUC O

4.1. Khai Niem.

1. Cac nguyen tac

Hnh chieu truc o (HCT) hay

thng goi la hnh khong gian la loaihnh bieu dien noi, de nhn, c xaydng tren c s cac phep chieu songsong, do o no co ay u tnh chat cuaphep chieu song song.

- Hai ng thang song songnhau th hnh chieu truc o cung songsong nhau.

-Hai ng thang cat nhau th

hnh chieu truc o cung cat nhau. Hnh 4.1

- Hnh chieu truc o bao toan ty so n cua 3 iem thang hang.

- Hnh chieu truc o thng c ve canh hnh chieu thang goc cua no egiup ngi oc ban ve de hnh dung vat the.

- Phng phap chieu truc o nh sau:

+ Gan vao vat the he truc toa o thang goc, roi chieu song song theo hngchieu s ca he truc va vat the len mot MPHC truc o.

+ Trong HCT tnh song song cua cac oan thang c bao toan cac oanthang OA, OB, OC thuoc 3 truc toa o chieu thanh OA, OB, OC

Cac ty so:' ' ' ' ' 'O A O B O C

p ; q ; rOA OB OC

= = = Goi la cac he so bien dang theo truc.

Tuy theo goc tao bi hng chieu s vi MPHC truc o, ngi ta phan ra cacloai HCT:

-

Hng chieu s khong vuong goc vi MPHC truc o th HCT thu c lahng chieu truc o xien.

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1 2 3 4

2Hnh chieu truc o vuong

goc can

p = r = 1

q = 0.5

3Hnh chieu truc o xien

goc ng eu

cho phep lay gocnghieng cua truc y,la

300hoac 600

p = q = r =1


goc bang eu

cho phep lay gocnghieng cua truc y,la

45

0

hoac 60

0

p = q = r =1


gocng can

cho phep lay goc

nghieng cua truc y,

la300hoac 600

p = r = 1

q = 0.5

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Chu y:Trong HCT xien goc cung nh trong HCT nh trac thang goc trucOy co the nghieng trai hoac sang phai.

- Trong HCT thang goc ang trac he so bien dang theo cac truc la 0,82nhng e tien cho viec ve ngi ta lay theo qui c p = q= r = 1.

Nh vay hnh ve c phong to len 1,22 lan.

- Trong HCT thang goc nh trac cac he so bien dang theo truc 0x va Ozbang 0,47 theo Oy la 0,94, nhng theo qui c ngi ta ve p = r = 1 va q = 0,5 nhvay hnh ve c phong to len la 1,06 lan.

3. Lu y khi dng HCT

- Hnh chieu truc o co the ve theo ty le khac vi ty le ve hnh chieuvuong goc.

-Tren hnh chieu truc o khong can ve cac net khuat cua khoi.

( bai tap trong nha trng cac net khuat c the hien bang net manh, me the hien cac bc thc hien).

- Hnh chieu truc o co the to bong am nhat e de nhn (Hnh 4.2)

Hnh 4.2

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Khi chon hnh chieu truc o lu y:

Thng chon loai hnh chieu truc o vuong goc eu v loai nay cho hnh bieudien can oi (chu y vi khoi vuong khong nen chon loai nay v no lam mot so bemat cua vat the b suy bien).

- Loai khoi vuong nen chon hnh chieu truc o nh trac.

- Loai khoi co ng tron song song vi MPHC P1nen chon loai hnh chieuHCT can, v loai nay khong lam bien dang khi hnh bieu dien song song viMPHC P1nen de ve.

- Hnh chieu truc o xien goc bang eu thng s dung cho ve tong mat bangkhu xay dng ( Hnh 4.3)

Hnh 4.3

4.2 Cac Bc Dng Hnh Chieu Truc o T Hnh Chieu Thang Goc

1. Cac bc dng hnh chieu truc o

Bc 1:Chon loai hnh chieu truc o hp ly , sao cho hnh bieu dien noi, denhn, ep va khong b bien dang.

Hnh 4.4

Bc 2:Gan vao vat the he truc toa o vuonggoc khi ve hnh chieu truc o cua khoi. Thng chongoc toa o goc phai pha sau khoi vat the. Cung cothe chon truc Oz trung vi truc oi xng cua vat the.Viec qui nh chieu cua cac truc tren hnh chieu truco rat quan trong. Khi can the hien ro chi tiet nao tau tien tam quan sat cho mat phang cha chi tiet o.V du muon the hien mat ay ta chon chieu truc nh

hnh ve 4.4

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e chon hng nhn thuan li trong giai oan nay ta ve phac mot vai kieu truco khac nhau, sau o chon hng nao thch hp nhat (Hnh 4.5)

Hnh 4.5

Bc 3:- Dng hnh chieu truc o cua hnh chieu bang sau o dng cao o cac iem

(theo truc Oz) hoac dng hnh chieu truc o cua hnh chieu ng sau o dng o sau(theo truc Oy) cua cac iem (oi vi hnh chieu truc o xien goc thng ve hnhchieu truc o cua hnh chieu ng trc v loai nay hnh chieu ng khong b biendang con cac loai khac thng s dung hnh chieu bang lam mat xuat phat).

- Khi dng hnh chieu truc o thng dng cac bo phan ln trc sau o mive cac bo phan nho, khi cac bo phan co cho vat, cho ln phai dng hnh khoi tong

quat (hnh ch nhat ngoai tiep) roi i sau vao chi tiet. Vi vat the phc tap co nhieulo uc khoet can da vao toa o cac iem ac biet e xac nh cac giao tuyen, trongqua trnh ve da vao ng sinh, cac tiet dien ong dang

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- Sau khi xac nh c hnh chieu truc o cua cac iem ta noi chung lai theoung s lien he cua cac iem hnh chieu vuong goc.

Hnh 4.6

Bc 4:To am cac net the hien vat the co the s dung am nhat anh bonge hnh ve noi, de quan sat hn

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2. Mot So Qui nh Trong Hnh Chieu Truc o

Hnh 4.7

- e the hien cac phan khuat ben trong cua khoi ngi ta dng hnh chieutruc o cat bo hoac vat the. Mat phang cat nay tren hnh chieu truc o thnglay trung vi cac mat phang oi xng cua vat the.

- Co hai cach dng hnh cat tren hnh chieu truc o, co the ve toan bo hnhchieu truc o sau o cat bo i hoac hoac ve hnh chieu truc o khi a bcat bo.

- Cac net gach tren hnh cat cua hnh chieu truc o khong ve nghieng 45sovi ng bang cua ban ve ma phai ke song song vi hnh chieu truc o cua ngcheo hnh vuong nam tren cac mat phang toa o tng ng va co cac canh songsong vi Ox, Oy, Oz.

- Tren ban ve ben canh hnh chieu truc o phai ve s o he truc va he sobien dang.

Ta nghien cu cach dng hnh chieu truc o t cac yeu to c ban.

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4.3 Dng Hnh Chieu Truc o Cua iem, oan, Hnh Phang T Hnh ChieuThang Goc:

Trong phng phap HCT cac ieu kien tng quan nh iem thuoc ngthang, hai ng thang cat nhau, hai ng thang song song ve c ban c baotoan tng t nh trong hnh chieu thang goc.

1. Dng hnh chieu truc o iem:

V du:Cho hnh chieu vuong goc cua iem A (2, 4, 3) dng hnh chieu truc ocua iem A.

- Phng phap toa o e chuyen t o thc 1 iem sang hnh chieu truc o.

Hnh 4.8

- Theo ba toa o thang goc cua A la XA,YA,ZAva cac he so bien dang theo batruc toa o la : p = q = r =1 (Hoac p = r = 1 ; q = 0,5).

- Suy ra ba toa o truc o tng ng cua A la:

( Hoac X

' ' 'A A A A AX X ; Y Y ; Z Z= = = A

A= XA; YA= 0,5.YA; ZA= ZA)

-

Tren truc Ox at OAX= XA. Qua AXke ng song song vi Oy vaat tren o oan AxA2= YA.

- Qua A2 ke ng thang song song vi OZ va at tren o oanA2A = ZA.

- iem A la hnh chieu truc cua A phai dng.

Hnh 4.8 ve hnh chieu truc o cua A theo hai loai: HCT vuong goc eu vaHCT xien goc ng can.

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2. Dng hnh chieu truc o cua oan thang

e ve hnh chieu truc o cua oan thang ta lan lt ve hnh chieu truc ocua hai iem xac nh oan thang o.

V du:Dng hnh chieu truc o cua AB biet toa o:

A (Ax, Ay, Az) ; B (Bx, By, Bz)

Hnh 4.9

Cach dng:

- Dng hnh chieu truc o cua iem A t hai hnh chieu a cho; Dng hnhchieu truc o cua iem B (theo cach dng HCT cua iem nh a biet ). Noi A vaB ta co hnh chieu truc o cua oan AB.

- Khi cha biet toa o cu the cua cac iem ta s dung phng phap o t hnhchieu thang goc a cho. Chu y he so bien dang theo loai truc o a chon.

- Hnh 4.9 dng HCT cua AB theo hai loai (HCT vuong goc eu va xiengoc ng can).

3. Dng hnh chieu truc o cua hnh phang

e ve HCT cua a giac phang, ngi ta ve HCT cac nh cua no

Ta dng hnh chieu truc o cua cac iem thuoc nh cua hnh phang roi noi laitheo ung s lien he nh hnh chieu thang goc.

Khi hnh phang co hnh dang bat ky, ta cho hnh noi tiep hnh ch nhat hoacvuong dng hnh chieu truc o cua hnh phang ngoai tiep xac nh hnh chieu

truc o iem cua hnh noi tiep va noi lai theo s lien he nh hnh chieu thang goc.

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V du: Dng hnh chieu truc o cua hnh chieu ABCD biet hnh chieu vuonggoc cua no

Dng hnh chieu truc o cua tam giac MNQ t hnh chieu vuong goc a cho

ABCD // MPHC P1

MPHC P 2

Co BC MPHCP2 p = r = 1 ; q = 0.5

p = q = r = 1

Hnh 4.10a

Lan lt dng HCT cua cac iem A,B,C,D ta co A,B,C va D noiABC va D ta co hnh chieu truc o can dng.

Hnh 4.10b

MNQ bat ky co M thuoc MPHC P2, ta co hnh chieu truc o cua tam giac MNQnh hnh 4.10b

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Hnh chieu truc o cua hnh phang co v tr song song vi mot mat phang hnhchieu.

ABCD MPHC P1

// MPHC P2 p = r = 1 ; q = 0.5

p = q = r = 1

Hnh 4.11a

ABCD MPHC P1Co ABMPHC P2Va AOx

Hnh 4.11b

- Khi hnh phang la hnh tron ta cho no noi tiep hnh vuong va ve hnh chieutruc o theo phng phap tam iem.

+ Dng hnh chieu truc o cua hnh vuong, o la mot hnh bnh hanh

+ Dng lai hnh chieu truc o cua bon ng knh (ng cheo cuahnh vuong)

+ Ta co bon iem 1, 2, 3, 4. Va thuoc hnh vuong va thuoc hnh tron.

+

Bon iem con lai 5, 6, 7, 8 thuoc elp noi tiep hnh bnh hanh. Noi 8 iemta co hnh chieu truc o cua hnh tron.

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+ Hoac khi HCT cua ng tron la hnh elp. Ta dng hnh elp o theophng phap hai ng knh lien hp (chu y: hai ng knh lien hp cua elp lahnh chieu truc o cua hai ng knh vuong goc nhau cua ng tron).

Hnh 4.12 trnh bay cach ve HCTcua cac ng tron nam trong cac matphang hnh chieu theo hai dang vuong goceu va xien goc ng can.

Hnh 4.12

Hnh 4.13 ve hnh chieu truc ovuong goc eu cua hnh tron tam Inam trong mot mat phang chieu ng.

Ngoai tiep hnh tron nay bang

mot hnh vuong va ve hnh chieu truco vuong goc eu cua hnh vuongnay, o la mot hnh bnh hanh.

Ve elp noi tiep hnh bnh hanh(bang phng phap 8 iem), o lahnh chieu truc o cua hnh tron.

- Chu y: Khi hnh phang cohnh dang bat ky ta cho no noi hoac

ngoai tiep hnh a giac phang. Ve hnh chieu truc o cua hnh a giac nay va suy rahnh chieu truc o gan ung cua hnh phang can ve.

Hnh 4.13

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4.3 Dng Hnh Chieu Truc o Cua Khoi Vat The T Hnh Chieu Thang Goc

Sau khi oc va nghien cu ky o thc vat the, hnh dung c khoi vat the tadng hnh chieu truc o cua cac iem thuoc nh khoi vat the. Sau o noi hnh chieutruc o cua cac iem e co hnh chieu truc o cua khoi.

V du 1:Dng hnh chieu truc o cua hinh khoi biet hai hnh chieu thang gocnh hnh ve.

Hnh 4.14

Giai:

- Bc 1: Chon he truc HCT vuong goc eu co he so bien dang p = q = r = 1va ba truc Ox, Oy, Ox, lap vi nhau mot goc 120. Dng hnh chieu th ba cua

vat the t hai hnh chieu a cho.- Bc 2: Di di he truc vuong goc cua khoi, chon iem O trung vi goc sau

ben phai cua khoi.

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- Bc 3:

+ Dng hnh chieu truc o cua hnh chieu bang khoi vat the (co the chondng hnh chieu truc o cua hnh chieu ng).

+

Dng o cao cac iem t chan HCT cua hnh chieu bang, ta co HCTcua cac iem thuoc nh khoi va noi cac HCT cua cac iem co lien he vi nhautheo ung hnh chieu vuong goc.

(chu y co hai ng cong la ng tron phai dung phng phap 8 iem exac nh, phan mat vat cho noi tiep khoi ch nhat).

- Bc 4: e giup hoc sinh theo doi cac bc dng HCT, nhng net phu trdng hnh e lai bang net lien manh, m nhng net thay bieu dien vat the cto am.

Cac b c dng c bieu dien tren hnh ve 4.14

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Chng 5

CAT VAT THE

5.1. Khai Niem

Cac hnh chieu vuong goc ch dien ta hnh dang ben ngoai cua khoi vat the.Vi vat the cau tao ben trong phc tap th so lng net t nhieu de lam roi ban vegay ra nham lan, e khac phuc van e nay va can xem xet cau tao ben trong vat the,ngi ta dung mot loai hnh bieu dien goi la hnh cat, mat cat.

Tng tng cat vat the bang mot mat phang, bo phan vat the gia ngi quansat va mat phang cat i, chieu phan vat the con lai len MPHC song song vi matphang cat. Hnh bieu dien thu c tren MPHC nay goi la hnh cat.

Hnh bieu dien gii han bi giao tuyen cua vat the vi mat phang cat goi lamat cat.

Nh vay tren hnh cat co ve ca mat cat va hnh chieu cua phan vat the nam

pha sau mat phang cat.

mp cat

Hnh cat 1-1

Hnh 5.1

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- Tren hnh cat cho phep khong ve mot so ng khuat, neu nhng ng naykhong can thiet va ch lam roi hnh bieu dien (chu y bai tap khi ang hoc trong nhatrng khong c t y bo cac net khuat, neu co).

- Neu mat phang cat i doc theo truc hoac chieu dai cua cac chi tiet nh gan

chu lc, thanh chong, inh tan th quy c khong ve gach gach tren cac chi tietnay.

5.2. Xay Dng Hnh Cat Mat Cat Hnh Cat

1. Cac Bc Dng Mat Cat Hnh Cat.

Bc 1:Ve o thc cua vat the. oc va hnh dung c hnhkhoi khong giancua vat the

Bc 2: Xac nh v tr cua mat phang cat (xac nh v tr tren hai hnh chieu a

cho bang cach noi hai v tr vet cat vao nhau va keo dai len 2 hnh chieu, ch sdung cho mat phang cat thong thng).

Bc 3 :Tm giao tuyen gia mat phang cat va vat the

- Ta luon a co mot hoac hai hnh chieu cua giao tuyen, tm hnh chieu conlai bang phng phap dong.

- Tm o cao cua giao tuyen hnh chieu ng, hnh chieu canh.

- Tm o rong, o sau hnh chieu bang, hnh chieu canh.

Bc 4:Xoa bo nhng net nam pha trc mat phang cat (neu co) va them vaonhng net mi xuat hien (nh net khuat tr thanh net thay).

ban ve ky thuat xay dng ng bao quanh tiet dien b cat c ve bang netam phan pha trong tiet dien b cat ve cac net gach gach theo quy nh phankhai niem .

V du 1:Cho 2 hnh chieu khoi vat the va v tr vet cat 1-1 hay dng hnh cat 1.1.

Giai:T 2 hnh chieu a cho, ta oc va hnh dung hnh khoi khong gian cuakhoi vat the (Ve phac hnh chieu truc o).

- Dng hnh chieu th 3.

- Dung net manh noi hai vet cat va dong thang len MPHC ng e xac nhv tr cua mat phang cat.

- Ta xac nh giao tuyen cua mat phang cat va khoi. Khi a biet hnh chieung va hnh chieu bang cua giao tuyen (v giao tuyen vuong goc vi MPHC P1 vaMPHC P2)

-Dong e tm hnh chieu canh cua giao tuyen (o cao dong t P1, o sau

dong t P2)

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- Xoa bo nhng net pha trc mat phang cat, them vao net mi xuat hien(net khuat thanh net thay); bao xung quanh tiet dien b cat thanh net am (mat cat)ke gach gach 450 phan mat cat, kiem tra cac net thay va khat pha sau mat phangcat (Hnh ve 5.3)

Hnh chieu canh

Hnh cat 1-1

Hnh 5.3

V du 2:Cho hai hnh chieu cua khoi vat the va mat cat A-A dng hnh cat,mat cat cua khoi.

Giai:

Bc 1:oc hai hnh chieu a cho va ve phac hnh khong gian cua khoi vehnh chieu canh cua khoi.

Bc 2:Xac nh giao tuyen mat phang cat va khoi: noi hai vet cat va keo dailen MPHC P1.

Bc 3:Tm giao tuyen ta a co hnh chieu ng va hnh chieu bang cuagiao tuyen (no trung vi hnh chieu cua mat phang cat v mat phang cat vuong gocvi P1va P2 dong tm hnh chieu canh cua giao tuyen .

Bc 4: Bo cac net pha trc mat phang cat, them vao nhng net mi(neu co), ve am mat cat ke ng gach gach 450trong tiet dien b cat.

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A

AMat cat

Hnh cat

Hnh 5.4

2. Phan Loai Hnh Cat

a.phan theo v tr cua mat phang cat:

Hnh cat ng: la hnh cat thu c khi dung mp cat song song vi MPHC P1

Hnh cat bang: la hnh cat thu c khi dung mp cat song song vi MPHC P2.Trong ban ve nha hnh cat bang cua ngoi nha, mp cat i ngang qua ca i, ca so vasong song vi san ,

nen nha hnh cat bang thng goi la Mat Bang cua ngoi nha.

Hnh cat canh: la hnh cat thu c khi dung mp cat song song vi MPHC P3.

Chu y:

Cac hnh cat ng (bang, canh) nen at gan v tr cua cac hnh chieu c bantng ng.

Hnh cat nghieng: la hnh cat thu c khi dung mp cat khong song song viMPHC c ban nao.

(Mat phang cat co v tr la cac mp chieu).

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1-1: Hnh cat ng 2-2: Hnh cat bang

3-3: Hnh cat canh

Hnh 5.5

b.Phan loai theo so lng mat phang cat:

- Hnh cat n gian: la hnh cat thu c khi dung mot mp cat, neu mp cat doctheo chieu dai hay chieu cao cua vat the th goi la hnh cat doc, neu mp cat vuonggoc vi chieu dai hay chieu cao cua vat the th goi la hnh cat ngang.

- Hnh cat phc tap: la hnh cat thu c khi dung hai mp cat tr len. No phanra hai loai: hnh cat bac: neu cac mp cat cung song song vi mot MPHC c ban.

(Neu ch dung mot mp cat ta ch the hien c mot lo rong do o ngi ta sdung hai mp cat lan lt i qua hai truc lo va cung song song vi MPHC P1. loai naydung nhieu trong ve xay dng e the hien cach bo tr cac phong, ca i, ca so)

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- Hnh cat xoay: la hnh cat thu c bang cach dung cac mat phang cat giaonhau di 1 goc nao o ( ) ngi ta tng tng xoay cac mat phangcat cho trung vi nhau thanh mot mat phang (Chieu xoay khong nhat thiet phaitrung vi hng nhn)

090 180< < 0

Hnh cat bac (A-A)

Hnh cat xoay (A-A)

Hnh 5.6

- Ngoai ra con co hnh cat toan phan lahnh cat the hien phan ln cau tao ben trong

cua vat the.

- Phng phap ket hp hnh cat vaHCT vat the (cat bo 1/4 hoac 1/8 cua vatthe e the hien c ben trong khoi ) chu yviec lam nay khong lien quan g ti cac hnhcat thc hien theo cac hng chieu thanggoc, ma o la hai viec cat rieng re.

Hnh 5.7

3. Mat Cat:

a. nh ngha: Mat cat la phan giao tuyen cua vat the vi mat phang cat.

b. Phan loai:

mat cat ri: la mat cat ve ngoai hnh chieu c ban, cho phep ve mat cat ritai cho cat la gia hai phan cua cung mot hnh chieu.

a) b) c)

A

A

A

A

Hnh 5.8

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mat cat chap:la mat cat ve ngay tren hnh chieu c ban tai v tr cat.

mat cat nghieng: la hnh ve thu c khi mp cat khong song song vi MPHCnao (mat phang cat vuong goc vi MPHC).

d) Mat cat chap

A-A

e) Mat cat nghieng

A

A

Hnh 5.9

c. Mot so qui c:

- ng bao cua mat cat ri ve bang net c ban, ng bao cua mat cat chapve bang net am.

- Cach ghi chu mat catgiong nh hnh cat: co anh dau vtr mp cat bang vet cat, co mui tench hng nhn, ghi ten v tr cat(tr trng hp khi mat cat la hnhoi xng va truc oi xng attrung vi v tr cua vet cat hoackhi mat cat la hnh oi xng attai cho cat la gia hai phan cuacung mot hnh chieu).

Tng ng

Tng ng

Hnh 5.10- Mat cat phai at theo

ung hng cua mui ten.

-

Tren ban ve xay dng cho phepghi v tr mp cat va hng nhn nh hnhve 5.10.

- Tren ban ve xay dng, oi vicac chi tiet ln cho phep ve chap tngbo phan nho va ch can gach gach phan sat ng bao cua mat cat. ngbao ve net am cho de nhn quy c

hng nhn t trai sang phai (hnh 5.11).

Hnh 5.11

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- Mat phang cat phai atvuong goc vi chieu dai va chieucao cua vat the. Co the xoay matcat i mot goc nao o cho de nhn,

khi o phai ve mui ten tren kyhieu e bieu th mat cat a cxoay (hnh 5.12).

Hnh 5.12

- Tren hnh 5.13a trnh bay cach the hien ban ve mat bang cua mot ngoi nha.

Hnh 5.13a

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- Tren hnh 5.13b trnh bay cach the hien ban ve mat cat cua mot ngoi nha.

Hnh 5.13b

- Tuy theo o phc tap cua vat the ma ngi ta s dung hnh cat hay mat catcho phu hp. Hien nay trong cac ban ve ky thuat ngi ta t phan biet hnh cat haymat cat ma eu goi chung la mat cat.

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4. Hnh ve tach (con goi la ve chi tiet):

hnh ve tach hay hnh trch la hnh bieu dien bo sung mot bo phan nao o khican bieu dien chi tiet hn ve hnh dang va kch thc cua no.

Hnh ve tach co the la hnh chieu hoac hnh cat va luon c ve phong to hnso vi hnh bieu dien co lien quan. Hnh 5.14 la v du cua hnh ve chi tiet matdan (v keo).

Tren hnh bieu dien chnh ngi ta khoanh tron bang net lien manh bo phancan ve tach va ghi ky hieu bang ch hoa hoac ch so.

Hnh ve tach thng c at gan hnh bieu dien chnh. Neu ve tren mot tgiay khac hoac at xa hnh bieu dien chnh th hnh ve tach c k hieu nh chdan 5.15.

Ch so ghi na tren vong tron la ky hieu bo phan ve tach, con so ghi nadi ch so th t t giay ve tren o co hnh ve tach tng ng.

hh= 4mm

CHI TIET A TL: ........

Hnh 5.14

Hnh 5.15

Documents

13-12-05 Phan IV (hinh chieu truc do den het hinh cat).pdf