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BAI GIANG VE KY THUAT Trang 1
CHNG ICAC TIEU CHUAN TRNH BAY BAN VE
BAI 1 PHNG TIEN TRNH BAY BAN VE
I. VAT LIEU VE VA DUNG CU VE Vat lieu vela phng tien thc hien ban ve di dang tieu hao : Giay, but ch, gom,
Dung cu ve : la phng tien thc hien ban ve di dang tai s dung : thc
ke, eke, compa, rap ve vong tron,
II. CACH S DUNG CAC DUNG CU VE1. Van ve
Dung e thay the cho ban ve
chuyen dung. Khi s dung nen chon
mat that phang va canh trai that
thang. Giay c co nh ben goc trai
pha di cua van ve.
2. Thc TThc T c ket hp vi van ve e
dng cac ng bang. au thc T luon
ap sat vao van ve.
3. EkeDung e ket hp vi thc T e
dng cac ng thang ng hay cac
ng xien 30o, 45o, 60o.
4. Compa va rap vong tronCompa : dung e ve cac cung tron hay vong tron co ban knh ln.
Rap vong tron : dung e ve cac cung tron hay vong tron co ban knh nho.
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BAI GIANG VE KY THUAT Trang 2
5. Gom (tay)Dung e tay, xoa cac vet d, cac net ve sai, tha tren ban ve. Trc khi dung
phai lau sach au gom.
6. But chNen chon but ch theo ky hieu cua ngoi ch. But ch mem (ky hieu B) dung e
ve cac netam, viet ch va so. But ch cng (ky hieu HB) dung e ve cac net manh.
Khi ve mui but ch phai ta vao canh tren cua thc va c xoay luc ve.
Nen dung but ch kim.
BAI 2 TIEU CHUAN TRNH BAY BAN VE
I. ng net (Theo TCVN 0008 1993 qui nh)
e bieu dien vat the, tren ban ve ky thuat dung cac loai net ve co hnh dang va
kch thc khac nhau. Cac loai net ve c qui nh theo TCVN.
Ten goi Hnh dang ng dung c ban
Net lien am
Be rong s
- Khung ban ve, khung ten.
- Canh thay, ng bao thay.
- ng nh ren thay, ng ren thay.
Net lien manh
Be rong s/3
- ng dong, ng dan, ng kch thc.
- ng gach gach tren mat.
- ng bao mat cat chap
- ng tam ngan.- ng than mui ten ch hng.
Net t
Be rong s/2
- Canh khuat, ng bao khuat.
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BAI GIANG VE KY THUAT Trang 4
e n gian, ta dung ba kho ch sau :
Kho ch to (h7): ghi ta ban ve.
Kho trung bnh (h5): ghi ten hnh bieu dien, hng chieu, vet mat phang cat
Kho ch nho (h3.5): ghi so kch thc, yeu cau ky thuat, noi dung khung ten
va bang ke.
III.KHO GIAY (TCVN 2 74 qui nh)Kho giay la kch thc qui nh cua ban ve.
Theo TCVN kho giay c ky hieu bang 2 so lien
nhau.
Ky hieu theo TC ISO Ky hieu TCVN Kch thc
Kho giay 44 A0 1189 841
Kho giay 24 A1 594 841
Kho giay 22 A2 594 420
Kho giay 12 A3 297 420
Kho giay 11 A4 297 210
IV. KHUNG BAN VE VA KHUNG TEN
( TCVN 3821 83 qui nh)
Khung ban ve va khung ten ke bang net
lien am. Khung ban ve ke cach mep ngoaicua kho giay la 5mm. Trng hp muon ong
thanh tap th pha ben trai ke cach mep kho
giay la 25 mm. Khung ten at pha di goc
ben phai cua ban ve.
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BAI GIANG VE KY THUAT Trang 5
Khung ban ve mau :
Trng Trung hoc KT - CN - NLp : THSCCK05A (6) (7)
(3)
(4)(2)Kiem tra
(1)Ngi ve
Ty le
(5)
- O
- 1 : Ho va ten ngi ve
- O2 : Ngi kiem tra ky ten- O3 : Ngay ve
- O4 : Ngay kiem tra
- O5 : Ten bai tap, ten chi tiet
- O6 : Ky hieu vat lieu
- O7 : Ky hieu bai tap
IV. TY LE (TCVN 3 74 qui nh)Ty le la ty so gia kch thc o c tren ban ve va kch thc tng ng o
c tren vat that. TCVN qui nh cac loai ty le sau :
Ty le nguyen hnh 1 : 1
Ty le phong to 2 : 1 2.5 : 1 4 : 1 5 : 1 10 : 1
Ty le thu nho 1 : 2 1 : 2.5 1 : 4 1 : 5 1 : 10
Chu y : Ty le cua ban ve ghi trong khung ten. Ty le cua hnh bieu dien ghi ben canh.
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BAI GIANG VE KY THUAT Trang 6
BAI 3 GHI KCH THC
Kch thc ghi tren ban ve dung e cho biet o ln cua vat the. Theo TCVN5705 1993 qui nh.
I. QUI NH CHUNG Con so kch thc khong phu thuoc vao ty le ban ve va mc o chnh xac
cua ban ve.
n v kch thc dai la (mm) nhng khong ghi n v sau con so kch
thc.
n v : o, phut, giay phai ghi sau con so kch thc.
V DU :
II. CAC THANH PHAN CUA KCH THC1. ng dong
Ke bang net lien manh, vuong goc vi oan can ghi kch thc (trng hp
ac biet cho phep ke xien). ng dong vt qua ng ghi kch thc 3 5mm. Co
the dung ng tam keo dai lam ng dong.
2. ng kch thc
Ke bang net lien manh, song song vi oan can ghi kch thc, ng kch
thc cach oan can ghi kch thc t 5 10mm. Khong dung ng truc, ng
tam lam ng kch thc.
3. Mui tenMui ten at hai au ng kch thc, cham vao ng dong.
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BAI GIANG VE KY THUAT Trang 7
Goc mui ten khoang 30o.
o ln cua mui ten ty le thuan vi be
rong cua net lien am. Neu ng
kch thc qua ngan th cho phep
thay mui ten bang net gach xien hay
dau cham.
4. Con so kch thcCon so kch thc ghi pha tren, khoang gia ng kch thc. Chieu cao
cua con so kch thc khongbe hn 3,5mm.
a. oi vi con so kch thc o dai : cac ch so c xep thanh hang song
song vi ng kch thc. Hng cua con so kch thc phu thuoc vao phng cua
ng kch thc.
ng kch thc nam ngang : con so kch thc ghi pha tren.
ng kch thc thang ng hay nghieng sang ben phai : con so kch thc
nam ben trai.
ng kch thc nghieng trai : con so kch
thc ghi ben phai.
ng kch thc nam trong vung gach gach :
con so kch thc c dong ra ngoai va at tren gia
ngang.
b. oi vi con so kch thc goc : hng vet cuacon so kch thc tuy thuoc vao phng cua ng vuonggoc vi ng phan giac o .
III.MOT SO QUI NH KHI GHI CAC LOAI KCH THC1. Kch thc song song : khi co nhieu kch
thc song song nhau th ghi kch thc nho trc, ln
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BAI GIANG VE KY THUAT Trang 8
sau. Cac con so kch thc ghi so le nhau va khoang cach
eu nhau.
2. Ghi kch thc vong tron
3. Ghi kch thc cung tron
4. Ghi kch thc hnh vuong
IV. TRNH T THC HIEN BAN VE
1. Giai oan chuan b- Moi trng lam viec : sach, thoang mat, khong on.- Phng tien : ay u, hp ly.
2. Giai oan thc hien- Bo tr hnh ve tren giay
- Ve m
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BAI GIANG VE KY THUAT Trang 9
- Ve am
- Ghi kch thc, noi dung khung ten.
- Ghi kch thc, noi dung khung ten.
3. Giai oan hoan chnh
- Kiem tra va sa lai ban ve.
CHNG 2VE HNH HOC
BAI 1 DNG HNH HOC
I. CAC NG THANG1. Dng ng trung trcCho oan thang AB, yeu cau dng ng trung trc
cua AB.
- Ve ng tron (A, R > AB/2)
- Ve ng tron (B, R)
- Hai ng tron nay cat nhau tai hai iem C va D.
- CD chnh la ng trung truc cua AB.
2. Dng ng vuong goca. Qua iem D nam ngoai ng thang (a)- Ve [D, R > d(D/a)], ng tron nay cat (a) tai
hai iem A va B.
- Dng ng trung truc cua oan thang AB.
- Nh vay DC chnh la oan thang can dng.
b. Qua iem D nam tren ng thang (a)
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BAI GIANG VE KY THUAT Trang 10
- Dng (D, R), ng tron nay cat (a) tai hai iem
A va B.
- Dng ng trung trc cua oan AB.
- Nh vay, DC chnh la oan thang can dng.
c. Qua iem D nam au mut cua ng thang(a)
(Hoc sinh t dng)
3. Dng ng thang song song
Cho iem D nam ngoai ng thang (a).
Qua D hay dng ng thang song song vi (a).
II. VE CAC GOC
Goc phan giac Ve lai goc a cho Cac goc ac biet
III. O DOCo doc cua ng thang AB oi vi
ng thang AC la tg
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BAI GIANG VE KY THUAT Trang 11
Goi o doc la i :AC
BCtgi ==
V du : ve o doc i = 1 : 6 cua ng thang i qua iem B oi vi ng thang
AC cho trc
IV. O CONo con ty so gia hieu ng knh hai mat cat vuong goc cua mot hnh non tron
xoay vi khoang cach gia hai mat cat o : tgh
dDk 2=
=
V du : ve hnh con nh A truc AB co o con : k = 1 : 5
V. CHIA EU NG TRON1. Chia ng tron lam 3 phan bang nhauCho (O, R = 2d), chia ng tron nay lam ba phan
bang nhau.
- Dng hai ng knh AB va CD vuong goc nhau.
- Ve ng tron tam (C, R). ng tron nay cat (O,
R) tai hai iem E va F.
- Nh vay, ba phan bang nhau cua ng tron (O, R) la ba cung DE, EF va FD.
2. Chia ng tron lam 5 phan bang nhau- Xac nh trung iem M cua oan AO.
- Dng ng tron tam M ban knh R=MC, ng
tron nay cat ng knh AB tai N.
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BAI GIANG VE KY THUAT Trang 12
- CN chnh la canh cua hnh ngu giac noi tiep trong ng tron.
3. Chia ng tron lam 6 phan bang nhau(Hoc sinh t ve)
4. Chia ng tron lam 7, 9, 11, phan bang nhau- Dng (D, DC), ng tron nay cat AB keo dai tai E va F.
- Chia DC lam 7 oan thang bang nhau.
- Noi E va F vi cac iem chan.
- Cac ng thang nay keo dai cat ng tron tai cac iem G, H, I, K, L, M.
- Noi cac iem C, G, H, I, D, K, L, M lai ta co hnh can dng.
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BAI GIANG VE KY THUAT Trang 13
BAI 2 VE NOI TIEP
I. VE TIEP TUYEN VI NG TRON1. Qua iem A tren ng tron
- Xac nh O oi xng vi O qua A
- Dng ng trung trc cua oan OO.
- AA chnh la tiep tuyen can dng.
2. Qua iem A ngoai ng tron- Xac nh trung iem M cua oan OA.
- Dng ng tron tam M, ng knh
OA, ng tron nay cat (O, R) tai 2
iem B va C.
- AB va AC chnh la tiep tuyen can dng.
II. TIEP TUYEN CHUNG CUA HAI NG TRON1. Tiep tuyen chung ngoai
Cho (O1, r va O2, R).
Yeu cau dng tiep tuyen chung cua hai ng tron nay.
r
O2
B2
O1
B1
M
BR-r
A1
A2
A R
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BAI GIANG VE KY THUAT Trang 14
- Ve (O2, R-r).
- Dng tiep tuyen cua iem O1 oi vi (O2, R-r)
- O1A va O1B la hai tiep tuyen cua iem O1 oi vi (O2, R-r).
- O2A va O2B keo dai cat (O2, R) tai hai iem A1 va B1.
- Dng A1A2 song song vi O1A.
- Dng B1B2 song song vi O1A.
- A1A2 va B1B2 la tiep tuyen can dng
2. Tiep tuyen chung trong ( Hoc sinh t dng)
III. NOI HAI NG THANG BANG MOT CUNG TRON
IV. NOI NG THANG VI CUNG TRON BANG MOT CUNG TRON1. Tiep xuc ngoai
- Dng ng thang (d) song song va cach (d) mot khoang R.
- Dng ng tron (O, R + r), ng tron nay cat (d) tai O.
A1
B2
R
O1
A2
M
B1
B
O2
A
r
R+r
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BAI GIANG VE KY THUAT Trang 15
- OO cat (O, r) tai iem 2.
- O-1 vuong goc vi (d).
- Cung tron tam tai O ban knh
R can dng i qua hai iem 1 va
2.
2. Tiep xuc trong (hoc sinh t ve)
V. NOI HAI CUNG TRON BANG MOT CUNG TRON KHAC
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BAI GIANG VE KY THUAT Trang 16
1. Tiep xuc ngoai
- Ve ng tron (O, R + r).
- Ve ng tron (O, R +r).
- Hai ng tron nay cat nhau tai iem A.
- AO cat (O, r) tai B.
- AOcat (O, r) tai C.
- Cung tron (A, R) i qua hai iem B va C chnh la cung can dng.
2. Tiep xuc trong (Hoc sinh t ve)
3. Tiep xuc trong va ngoai (Hoc sinh t ve)
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BAI GIANG VE KY THUAT Trang 17
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BAI GIANG VE KY THUAT Trang 18
BAI 3
DNG MOT SO NG CONG THONG DUNG
I. HNH O VANCho trc o dai hai truc AB va CD.
- Dng cung tron (O, OA), cung tron nay cat
CD keo dai tai E.
- Dng cung tron (C, CE), cung tron nay cat
AC tai M.
- Dng ng trung trc cua oan AM, ng
trung trc nay cat AB tai O1 va cat CD tai O2.
- Ve cung tron (O1, O1A), dng lai tai ng trung trc cua oan AM.
- Ve cung tron (O2, O2C), dng lai tai ng trung trc cua oan AM.
- Cung AC chnh la hnh can dng.
- Cac phan con lai hoc sinh t ve.
(Lu y : cac tam con lai lay oi xng qua O)II. HNH ELP
Elip la quy tch cua nhng iem co tong
khoang cach en hai iem co nh F1, F2 bang
mot hang so ln hn khoang cach gia hai iem
co nh.
V elip bit hai trc AB v CD
V hai ng trn tm O, ng knh l AB v CD. Chia 2 ng trn ra lm 12 phn u nhau T cc im chia 1, 2, 3...v 1', 2', 3'... k cc ng thng song song vi
trc AB v CD.
Giao im ca cc ng 1 1', 2 2' l cc im ni thnh Elip.
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BAI GIANG VE KY THUAT Trang 19
V Elip khi bit 2 ng knh lin hp EF v GH* Phng php hai chm tia:
Qua E v F k MP v NQ // GH Qua G v H k PQ v MN // EF Chia cc on OH, PH, QH ra lm 3 phn bng nhau bi cc im 1, 2, 3 v
1',2', 3' (H l im chung 3 v 3' ca c 3 on ny) Ni E vi cc im 1', 2' thuc PH v vi 1, 2 thuc OH ; ni F vi cc im
1', 2' thuc HQ v 1, 2 thuc OH. Giao im ca 2 tia tng ng thuc 2 chm tia E v F xc nh cc im
thuc Elip.
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Phng php tm im
Qua A v B kng thng song song vi CD, qua C v D k hai ng
thng song song vi AB ta c hnh bnh hnh EFGH. Dng tam gic vung cn EIC (vung ti I). V cung trn tm C, bn knh CI ct ng thng EF ti K v L. Qua K v L v cc ng thng song song vi CD, cc ng thng ny
ct cc ng cho EG v HF ti 4 im 1,2, 3, 4 l nhng im thuc elipcn xc nh.
III. NG XOAN OC ARCHIMETng xoan oc Archimet la qui ao cua mot iem chuyen ong eu tren mot
ban knh quay khi ban knh nay quay eu quanh tam O.
o di cua iem tren ban knh quay nay
c mot vong goi la bc xoan.
Cac bc ve ng xoan oc Archimet
bc xoan a nh sau : Ve ng tron ban knh bang bc xoan
a va chia ng tron lam n phan bang nhau
Chia bc xoan a ra lam n phan bang nhau
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BAI GIANG VE KY THUAT Trang 21
at len cac ng chia tai cac iem 1, 2, 3, cac oan thang 01, 02, 03,
c cac iem M1, M2, M3, thuoc ng xoan oc Archimet.
IV. NG THAN KHAI CUA NG TRONng than khai cua ng tron la quy ao cua mot iem thuoc ng thang
khi ng thang nay lan khong trt tren mot ng tron co nh (ng tron c s)
Ve ng than khai khi biet ng tron c s ban knh R.
Chia ng tron c s lam n phan bang nhau (v du n = 12)
Ve tiep tuyen cua ng
tron tai cac iem chia eu ng
tron
Lan lt at cac tiep tuyen tai
cac iem 1, 2, 3, cac oan thang bang
1, 2, 3, lan12
2R
, ta c cac iem
M1, M2, M3, thuoc ng than khai
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BAI GIANG VE KY THUAT Trang 22
CHNG 3HNH CHIEU VUONG GOC
BAI 1 KHAI NIEM VE PHEP CHIEU
I. KHAI NIEM VE PHEP CHIEUTrong khong gian cho mat phang (P) va mot
iem S co nh ngoai mat phang (P). T mot iem
A bat ky trong khong gian dng ng thang SA.
ng thang nay cat (P) tai A. Ta noi rang a thc
hien phep chieu iem A len mat phang (P). S : tam chieu
A : vat chieu
(P) : mat phang hnh chieu
SA : tia chieu
A : hnh chieu cua A
II. PHAN LOAI PHEP CHIEU1. Phep chieu xuyen tamLa phep chieu ma cac tia chieu ong qui tai
mot iem S co nh. iem S goi la tam chieu.
A, B, C : goi la hnh chieu xuyen tam cua A,
B, C tren mat phang (P), tam chieu S.
2. Phep chieu song songPhep chieu song song la phep ma cac tia chieu song song vi mot ng
thang (a) co nh, ng thang nay goi la phng chieu.
Qua iem A dng ng thang song song vi (a). ng thang nay cat (P) tai
A. A goi la hnh chieu song song cua A tren (P) theo phng chieu (a).
P
A'
A
S
C
B'
P C'
A'
B A
S
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BAI GIANG VE KY THUAT Trang 23
Phep chieu song song c chia lam hai loai :
Phep chieu xien : la phep chieu ma phng chieu nghieng so vi mat
phang hnh chieu.
Phep chieu vuong goc : La phep chieu ma phng chieu vuong goc vi
mat phang hnh chieu.
Cac tnh chat cua phep chieu song song :
Hnh chieu cua ng thang song song van la
cac ng thang song song : AB // CD AB // CD
Ty so cua cac oan thang song song van
c gi nguyen khi chieu :
''
''//
DC
BA
CD
ABCDAB =
Ty so n cua 3 iem thang hang cung c gi nguyen.
( ) ( )'''''
''EBA
EB
EA
BE
AEABE ===
III. PHNG PHAP VE CAC HNH CHIEU VUONG GOCTa thay rang, mot iem A trong khong gian th co mot hnh chieu duy nhat tren
mat phang hnh chieu la A. Nhng ngc lai, t mot hnh chieu A ta lai co the xac
nh c vo so cac iem khac nhau A, B, C, tren cung mot hnh chieu. Suy ra,
biet mot hnh chieu cua vat the tren mot mat phang hnh chieu th ta cha the hnh
PA'
A(a)
PHEP CHIEU VUONG GOC PHEP CHIEU XIEN
PA'
(a)
A
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BAI GIANG VE KY THUAT Trang 24
dung c vat the o trong khong gian. Do vay, e tranh nham lan can phai co hai
hnh chieu tr len.
Phng phap ve hnh chieu vuong goc cua vat the :
Chieu vuong goc vat the len cac mat phang hnh chieu vuong goc nhau tng oi
mot. Sau o xoay cac mat phang hnh chieu trung nhau thanh mot mat phang (xoay
theo qui c). Mat nay chnh la mat phang ban ve. Luc nay tren mat phang cua ban
ve se co nhieu hnh chieu vuong goc cua vat the. Nghien cu cac hnh ve nay ta se
hnh dung ra hnh dang cua vat the trong khong gian
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BAI GIANG VE KY THUAT Trang 25
BAI 2
HNH CHIEU CUA IEM OAN THANG HNH PHANG
I. HNH CHIEU CUA IEM1. Hnh chieu cua iem tren hai mat phang
Trong khong gian cho iem A tuy y va hai mat phang (P1), (P2) vuong goc nhau
theo giao tuyen x.
T A dng ng thang vuong goc vi (P1) va (P2), ta co A1 va A2 tren hai mat
phang (P1) va (P2).
A1 : hnh chieu ng cua A
A2 : hnh chieu bang cua A
A1A2 : ng dong
P1 : mat phang hnh chieu ng
P2 : mat phang hnh chieu bang
AA1 = A2Ax : o xa cua A
AA2 = A1Ax : o cao cua A
Quay (P2) quanh x mot goc 90o theo chieu nh hnh ve, ta co P2 P1. Khi o
A1A2 Ax. A1A2 con goi la o thc cua A tren hai mat phang.
A
A1
AX
A2
Ox
P2
P1 P1
P2
A1
AX
A2
x
A2
AX
A1
x
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BAI GIANG VE KY THUAT Trang 26
2. Hnh chieu cua iem tren ba mat phangTrong khong gian cho iem A va 3 mat phang P1, P2, P3 vuong goc nhau theo
giao tuyen Ox, Oy, Oz
A3 : hnh chieu canh
AA3 = AzAy : o xa hnh chieu canh
Quay mat phang P3 va P2 trung vi mat phang P1, ta co o thc cua iem tren ba
mat phang.
II. HNH CHIEU CUA OAN THANG
oan thang c xac nh bi hai iem bat ky.
1. o thc cua oan thang
2. o thc cua oan thang v tr ac bietng thang song song vi MPHC nao th hnh chieu cua ng thang tren mat
phang o la chnh no.
A
A1
AX
A2
Ox
P2
P1 P1
P2
A1
AX
A2
xA3
AZ
Ay
z
y
O
Ay
AZ A3
z
y
AX
A2 y Ay
O
A3AZ
z
A1
x
P3
P3
A
A1
AX
A2
Ox
P2
P1
A3
AZ
Ay
z
y
AX
A2 Ay
O
A3AZA1
x
P3
BX
B1
B B3
By
B2
BZB1
ByB2
B3BZz
yBX
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2.1. ng thang song song vi MPHC
2.1.1. ng mat : ng thang song song vi MPHC
2.1.2. ng bang : ng thang song song vi MPHCB
Nhan xet : Hnh chieu ng song song vi truc x
2.1.3. ng canh : ng thang song song vi MPHCC
P1 z
x
P2 y
P3
Ox
z
y
yAB
B1
A1
A2 B2
B3
A3
B1
A1
A2 B2
B3
A3
P1 z
x
P2 y
P3O x
z
y
yAB
B1A1
A2 B2
B3
A3
B1A1
A2
B2
B3 A3
P1z
x
P2 y
P3
O x
z
y
yA
B
B1
A1
A2B2
B3
A3
B1
A1
A2
B2
B3
A3
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2.2.ng thang vuong goc vi MPHCng thang vuong goc vi MPHC nao th hnh chieu cua no tren mat phang o
la mot iem.
2.2.1. ng thang tia chieu ng : AB MPHC
2.2.2. ng thang tia chieu bang : AB MPHC
2.2.3. ng thang tia chieu canh : AB MPHCC
P1z
P3
yP2
xO
z
xyB
A A3
B3A2
B2
A1 B1A1 B1
A2
B2
A3 B3
O
z
x
P1
A2 B2
B1
B
A1
A
P3
O
A3B3
A3
A2 B2
B1
x
A1
O
z
y
yP2 y
B3
P1
x
P2 yP3
O
y
xy
z
O
A1 B1
A B
A2 B2
A3B
3
A1 B1
A2 B2
A3 B3
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BAI GIANG VE KY THUAT Trang 29
III. HNH CHIEU CUA MAT PHANG
1. Cach xac nh mat phang trong khong gianQua 3 iem khong
thang hang
Mot iem nam
ngoai mat phang
Hai ng thang
cat nhau
Hai ng thang
song song
2. o thc cua mat phangTrong khong gian cho 3 iem phan biet A, B, C va ba mat phang P1, P2, P3
vuong goc nhau theo giao tuyen Ox, Oy, Oz.
A1BZ
A1
AXxO
A2P2
B2
BXA
B
AZ
y
ByAy
B3
A3P3
A2
B2
AXx
BX
P1B1
z zB1
AZA3
ByAy
O y
BZ B3
C1
C3C
C1
C2C2
C3CZ
Cy
3. o thc cua mat phang nhng v tr ac biet3.1.Mat phang vuong goc vi MPHCMat phang vuong goc vi mat phang hnh chieu th hnh chieu cua no suy bien
thanh mot oan thang.
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3.1.1.Mat phang chieu ng
- A, B, C thuoc mat phang (Q).
- (Q) (P1).
- Chieu A, B, C len (P1), (P2), (P3).
3.1.2.Mat phang chieu bang
3.1.3.Mat phang chieu canh
P1
x
P2 yP3
Ox
y
z
O
A1
B1
A2B2
A2
B2C2
A
B
C
C2
A3
B3
C1 C3
Q
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3.2.Mat phang song song vi MPHCMat phang song song vi MPHC nao th hnh chieu cua no tren mat phang
o la chnh no.
3.2.1. Mat phang bang : mat phang song song vi MPHCB
3.2.2. Mat phang ng (Mat phang mat) : mat phang song song vi MPHC
3.2.3. Mat phang canh : Mat phang song song vi MPHCC
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BAI 3 HNH CHIEU CUA CAC KHOI HNH HOC
I. KHOI A DIENKhoi a dien la khoi hnh hoc c gii han bang cac a giac phang. Cac a giac
phang c goi la cac mat cua khoi a dien, cac nh va cac canh c goi la nh
va canh cua khoi a dien.
Cac a dien thng gap : khoi lang tru, khoi thap, khoi thap cut.
3. Khoi lang tru : la khoi a dien co cac canh ben song song
Khoi lang tru ng : canh ben
vuong goc vi MPHC.
Khoi lang tru xien : canh ben
khong vuong goc vi MPHC
4. Khoi thap : la khoi a dien co cac canh ben ong qui.
Khoi thap ng : cac canh
ben bang nhau
Khoi thap xien : cac canh
ben khong bang nhau.
II. KHOI TRONLa khoi hnh hoc gii han bi mat tron xoay : khoi cau, khoi xuyen hay gii han
bi mot phan mat tron xoay va mat phang (mat tru, mat non, na cau, ). Mat tron
xoay tao bi mot ng thang bat ky quay quanh mot truc co nh. ng bat ky o
goi la ng sinh cua mat tron xoay. Truc co nh goi la truc quay cua mat tron
xoay.
KHOI LANG TRU XIENKHOI LANG TRU NG
KHOI LANG TRU XIENKHOI LANG TRU NG
S
O
BA
D C
S
A B
CD
O
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Mat tru tron xoay : ng sinh song song vi truc quay.
Mat non tron xoay : ng sinh cat truc quay
Neu ng sinh la na ng tron (hoac ng tron) quay quanh truc vi
ieu kien mat phang cha ng tron va truc i qua tam cua ng tron se
tao mat cau.
Neu truc quay thuoc mat phang cha ng tron nhng khong i qua tam
cua ng tron tao thanh mat xuyen.
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III. BIEU DIEN HNH CHIEU CUA CAC KHOI HNH HOC C BAN
Khi dng o thc cac khoi hnh hoc c ban theo cac v tr sau e
at cac khoi goc 1/8 th nhat.
Neu khoi hnh hoc co truc oi xng hay truc quay th nen at truc thang goc
hay song song vi mot MPHC.
1. Khoi hnh hop
2. Khoi lang tru ay tam giac
3. Khoi lang tru ay luc giac eu
4. Hnh chieu cua hnh chop ng4.1.Hnh chop ng ay vuong
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4.2. Hnh chieu cua chop xien
5. Hnh tru
6. Hnh non
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BAI GIANG VE KY THUAT Trang 36
7. Hnh cau
BAI 4 GIAO TREN BE MAT VI CAC KHOI HNH HOC
I. GIAO TUYEN CUA MAT PHANG VI KHOI A DIEN
1. Giao tuyen cua mat phang vi khoi a dienGiao tuyen cua mat phang vi khoi a dien la mot hnh a giac.
2. Giao tuyen cua matphang vi hnh tru
1.1. Mat phang vuong goc vi hnh tru : giao tuyen la mot ng tron
1.2. Mat phang nghieng vi truc cua hnh tru : Giao tuyen la mot hnh elp
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1.3. Mat phang song song vi truc cua
hnh tru : Giao
tuyen la hnh ch
nhat.
II. GIAO TUYEN CUA CAC KHOI HNH HOC
3. Giao tuyen cua cac khoi a dienKhoi a dien c gii han bi cac a giac
nen giao tuyen cua hai khoi a dien la ng
gay khuc khep kn.
4. Giao tuyen cua hai khoi truGiao tuyen cua hai khoi tron la mot
ng cong khong gian khep kn. Muon ve giao
tuyen cua khoi tron, ta tm mot so iem cua
giao tuyen roi noi lai.2.1. Giao tuyen cua hai hnh tru co truc vuong goc
Hai khoi tru co ng knh khac nhau Hai khoi tru co ng knh bang nhau
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5. Giao tuyen cua hnh tru vi hnh cau va hnh non vi hnh cau
III. GIAO TUYEN CUA KHOI A DIEN VI KHOI TRON
Giao tuyen cua khoi a dien vi khoi tron la giao tuyen cua cac mat a dien vi
cac mat cua khoi tron.
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BAI GIANG VE KY THUAT Trang 40
Neu hnh chieu th ba oi xng : chon truc oi xng lam truc.
Hnh chieu th ba khong oi xng : chon ng bao bien lam chuan.
Cac kch thc o c t hnh chieu bang a ra hnh chieu canh.
(Co the dung ng thang nghieng 45o lam ng phu tr e ve hnh chieu th ba).
CHNG IV HNH CHIEU TRUC O
BAI 1. KHAI NIEM VE HNH CHIEU TRUC O
1. Khai niemHnh chieu truc o : La hnh bieu dien
cua vat the c dng t mot he truc o.
He truc o : La hnh chieu cua mot he
gom 3 truc vuong goc xac nh 3 chieu kchthc, thc hien bi phep chieu song song va
c goi la phep chieu truc o.
Hnh chieu truc o c xac nh theo
phng chieu va he so bien dang cua cac truc.
2. Phan loai hnh chieu truc o.a. Phan loai hnh chieu truc o theo phng chieu : Hnh chieu truc o xien : Phng chieu v tr bat ky oi vi mat phang
hnh chieu.
Hnh chieu truc o vuong goc : Phng chieu vuong goc vi mat phang
hnh chieu.
Po
X'
Y'
Z'
Z
XYO
O'
A
AB
C
A'
B'
C'
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BAI GIANG VE KY THUAT Trang 42
BAI 2 CAC LOAI HNH CHIEU TRUC O
Co hai loai hnh chieu truc o tieu chuan va thng dung :
Hnh chieu truc o vuong goc eu.
Hnh chieu truc o xien ng can.
1. Hnh chieu truc o vuong goc eua. Khai niem :
Hnh chieu truc o vuong goc eu : La loai hnh chieu truc o co phng
chieu vuong goc vi mat phang hnh chieu.
b. Quy c :Tieu chuan nha nc quy nh v tr va he so bien dang cua he truc o vuong
goc eu nh sau :
Truc ng : (Oz)
Hai truc nghieng (Ox, Oy) mot goc 30o oi vi ng bang.
He so bien dang : Kx = p = 1 ; Ky = q = 1 ; Kz = r = 1
Chu y : Hnh phang nam trong hoac song song vi cac mat phang truc toa oeu ve bien dang tren hnh chieu truc o vuong goc eu.
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Cach ve hnh o van nh hnh ve :
Biet :
Truc ln cua hnh o van : 1,22d
Truc nho cua hnh ovan : 0.7d
2. Hnh chieu truc o xien ng canHnh chieu truc o xien ng can : La loai hnh chieu truc o co phng chieu
khong vuong goc vi mat phang hnh chieu (P).
Tieu chuan nha nc quy nh : V tr va he so bien dang cua he truc o xien
ng can nh sau :
Truc ng (Oz).
Truc ngang (Ox)
Truc nghieng (Oy) vi goc 45o oi vi ng bang.
Kx
= p = 1 ; Ky
= q = 0.5 ; Kz
= r = 1
Hnh phang nam trong hoac song song vi mat phang (Ox, Oz) se khong b
bien dang tren hnh chieu truc o xien ng can.
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BAI 3 CACH DNG HNH CHIEU TRUC O
1. Phng phap toa oPhng phap toa o : la phng phap c ban e dng hnh chieu truc o cua
vat the.
Tuy nhien, muon dng hnh chieu truc o cua vat the ta phai dng c hnh
chieu truc o cua mot iem.
Cach dng hnh chieu truc o cua mot iem nh sau :
Trc het ve v tr cac truc o cua he truc o va xac nh toa o vuong goc cua
iem A (XA, YA, ZA), sau o can c vao he so bien dang cua cac truc o ma xac nh
toa o truc o cua iem o vi :
XA = p3 XA ; YA = q3 YA ; Z = r3 ZA
Lan lt at cac toa o truc o len cac he truc o ta se xac nh c iem
A la hnh chieu truc o cua iem A.
2.ac iem ve cach dnga. Vat the co dang hnh hop : Ta ve hnh hop ngoai tiep cho vat the va chon 3
mat cua hnh hop lam 3 mat phang toa o.
b. Vat the co mat oi xng : Ta nen chon mat phang oi xng lam mat phangtoa o.
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BAI GIANG VE KY THUAT Trang 46
CHNG VHNH BIEU DIEN CUA VAT THE
BAI 1 HNH CHIEU
1. Khai niemHnh chieu : la hnh bieu dien cac phan
thay cua vat the oi vi ngi quan sat .
Cho phep the hien cac phan khuat cua vat
the bang net t e giam so lng ve hnh
bieu dien.
2. Phng phap bieu diene cu the hoa cach bieu dien, nha nc quy nh dung 6 mat cua hop lap
phng lam 6 mat phang chieu c ban. Hop lap phng nay goi la hop hnh
chieu. Cac mat (2), (3), (4) , (5), (6) co the m va trai phang ra trung vi mat (1) nh
hnh ve :
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3. Phan loaia. Hnh chieu c ban
Hnh chieu c ban la hnh chieu cua cac vat the tren cac mat phang hnh chieu
c ban cua hop hnh chieu.
Hnh chieu c ban co ten goi la :
Hnh chieu t trc (Hnh chieu ng hay hnh chieu chnh).
Hnh chieu t tren (Hnh chieu bang).
Hnh chieu t trai (Hnh chieu canh).
Hnh chieu t phai.
Hnh chieu t di.
Hnh chieu t sau.
Hnh chieu t trc con goi la hnh chieu
chnh, hnh chieu nay c chon sao cho phan
anh ac trng hnh dang cua vat the. Cac hnh
chieu khac phai ung v tr oi vi hnh chieu t
trcnhng neu cac hnh chieu nay khong ungv tr hoac b phan cach bi mot hnh bieu dien
khac th phai c ch danh bang ch hoa va ch
hng bang mui ten nh hnh ve tren.
b. Hnh chieu rieng phan- Hnh chieu rieng phan : La hnh
chieu mot phan cua vat the tren matphang hnh chieu song song vi mat
phang hnh chieu c ban.
- Hnh chieu rieng phan phai cch danh va ch hng neu khong ve
A
A
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BAI GIANG VE KY THUAT Trang 48
ung v tr chieu .
c. Hnh chieu phu- Hnh chieu phu la hnh chieu mot
phan cua vat the tren mat phang hnh
chieu khong song song vi mat phang hnh
chieu c ban.
- Hnh chieu phu nen at ung v tr chieu.Neu khong th phai ch danh va ch hng.
- e thuan tien cho viec bo tr tren banve, tieu chuan nha nc cho phep ve xoay
hnh ve v tr thch hp. Trong trng hp
nay hnh bieu dien phai c k hieu bang mui ten cong.
BAI 2 HNH CAT
oi vi nhng vat the co cau tao ben trong phc tap, neu ch dung hnh
chieu e bieu dien th hnh ve co nhieu ng khuat, nh the ban ve se khongro rang. e khac phuc ban ve ky thuat dung hnh cat va mat cat e bieu diencau tao ben trong cua vat the
1. Khai niemHnh cat : La hnh bieu dien phan con lai cua vat the sau khi a tng tng cat
i phan vat the gia mat phang cat va ngi quan sat.
2. Phng phap bieu dienVat the c cat bi mot hay nhieu mat phang goi la mat phang cat. Chieu phan
vat the nam gia mat phang cat va mat phang hnh chieu ta se co hnh cat. Do vay
hnh cat c xem la hnh chieu cua mot phan vat the ( gia mat phang cat va mat
phang hnh chieu) tren mat phang hnh chieu.
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Chu y :
Vat the c tng tng b cat e ve hnh cat nhng thc te khong b cat
nen cac hnh chieu khac phai c gi nguyen.
e phan biet hnh cat vi cac hnh chieu th hnh cat phai c ch danh bang
ch hoa va c k hieu vat lieu tren dien tch b cat, ong thi phai xac nh vet mat
phang cat bang net cat co ch danh va ch hng bang ch hoa tren hnh chieu.
ng gach gach (ng tuyen anh) : La nhng ng net lien manh dung
e k hieu vat lieu mat cat cua vat the, co khoang cach t 3 5mm vi o nghieng
45o oi vi ng bang, ng bao hay ng truc chnh cua hnh ve. Neu can co
the chon o nghieng 30o hoac 60o
1 2
3
P
A
A
A - A
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BAI GIANG VE KY THUAT Trang 50
ng gach gach phai thong nhat o nghieng va khoang cach tren cung
dien tch cat cua vat the.
ng gach gach phai khac o nghieng va khoang cach tren vung dien tch
cat cua hai vat the.
ng gach gach co the c gian lc theo chu vi ng bao neu dien
tch cat qua rong.
ng gach gach c thay bang boi en neu dien tch cat qua hep.
3. Phan loai hnh cata. Phan loai hnh cat theo v tr mat phang Hnh cat ng : Mat phang cat song song vi MPHC
Hnh cat bang : Mat phang cat song song vi MPHCB
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Hnh cat canh : Mat phang cat song song vi mat MPHCC.
Hnh cat nghieng : Mat phang chieu v tr bat ky. e tien bo tr hnh
tren ban ve, ta co the ve xoay hnh cat nghieng v tr thch hp va c ky hieu
bang mui ten cong tren hnh ve
Hnh cat ng, bang, canh, nhieng : La nhng hnh bieu dien c ve ung v
tr thay cho hnh chieu t trc, hnh chieu t tren (hoac hnh chieu t di), hnh
chieu t trai ( hoac hnh chieu t phai ), hnh chieu phu.
4. Phan loai hnh cat theo so lng mat phang cat Hnh cat n gian : La hnh cat ch co mot mat phang chieu. Hnh cat n
gian co dang la hnh cat doc hoac hnh cat ngang.
Hnh cat phc tap :
La do hai hay nhieu mat phang chieu. Hnh cat phc tap co dang la hnh cat
bac ( do ket hp bi 2 hay nhieu mat phang chieu ong qui ),
a. Hnh cat bac : Cac MPC song song nhau (dang bac thang)b. Hnh cat xoay : Cac MPC giao nhau hp thanh goc tu.
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BAI GIANG VE KY THUAT Trang 52
AA
A
A - A
A
A
A - A
5. Cac hnh cat ac biet Hnh cat rieng phan : Hnh cat rieng phan la
hnh cat mot phan nho cua vat the. Hnh cat nay at taingay v tr tng ng tren hnh chieu c ban . ng gach
gach c gii han bang net ln song. Khong can ch
danh va ch hng tren hnh cat.
Hnh chieu ket hp hnh cat : dung e dien ta hnh dang ben trong lan ben
ngoai cua vat tren mot hnh bieu dien. (Muc ch la giam bt so lng hnh bieu dien)
Neu hnh chieu va hnh cat co chung truc oi xng th ghep chung vi nhau,lay tam lam ng phan cach.
Net t (ng bao khuat) phan hnh chieu oi xng vi net am (ng bao
thay) phan hnh cat th boi i.
Neu net am trung vi ng tam th dung net ln song lam ng phan
cach (the hien net am).
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Neu hnh chieu va hnh cat khong co truc oi xng th dung net ln song lam
ng phan cach.
6. Nhng phan khong ve ky hieu vat lieu tren mat cata. Cac chi tiet nh : vt, bulong, inh tan, then, truc ac, qui c khong b cat
theo be doc. Cac vien bi cung qui c khong b cat.b. Mot so phan t cua chi tiet may nh : nan hoa cua vo lang, gan lc, rang
cua banh rang, qui c khong ky hieu vat lieu tren mat cat cua chung khi cat theo
be doc.
Bai 3 MAT CAT
Mat cat dung e the hien hnh dang va cau tao
phan t b cat ma tren cac hnh chieu kho the hien
c.
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1. Khai niemMat cat la hnh bieu dien nhan c tren MPC khi ta tng tng dung mat cat
nay cat vat the.
Hnh cat Mat cat
B
B
B - B
B
B
B - B
2. Phan loai2.1.Mat cat ri : dung e the hien nhng phan t co ng bao MC phc tap.Mat cat ri at ngoai hnh bieu dien tng ng (co the at gia hnh phan cat
la cua mot hnh bieu dien nao o). ng bao cua MC ri ve bang net lien am.
Mat cat ri c at doc theo ng keo dai cua net cat va at gan hnh bieu
dien tng ng ( cho phep at tuy y)..
2.2.Mat cat chapMat cat chap at ngay tren hnh bieu dien
tng ng. ng bao cua mat cat chap ve
bang net lien manh. Cac ng bao tai cho
at mat cat chap van gi nguyen.
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3. Ky hieu va qui nh ve mat cata. Tren mat cat cung ghi ky hieu giong hnh cat (vet cat, ch hng bang mui ten
va ch danh bang ch hoa).
b. Neu mat phang cat la hnh oi xng ma truc oi xng trung vi vet mat cat
hay trung vi ng keo dai cua mat cat th khong can ghi chu.
c. Neu mat cat chap, mat cat ri khong phai la hnh oi xng th ch ve net cat va
mui ten ma khong can ch danh. (Nh mui ten, ta mi biet phan t nao pha trc).
Neu mat cat qua cac lo hoac phan lom dang tron xoay
th ng bao cua lo hay lom o c ve ay u tren mat
cat. Qui c nay giup ngi oc ban ve phan biet c
cac lo, cho lom tron xoay, ranh khong tron xoay.
d. Neu cac mat cat giong nhau ong thi de xac
nh v tr cac mat cat o hnh bieu dien th cho phep
ch ve net cat cua mot mat cat, ong thi ghi ro so
lng cua cac mat cat o.
B
B
B - B
C
C
C - C
B
B
B
B
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e. Cho phep ve xoay mat cat e tien bo tr tren ban ve. Trong trng hp nay
hnh ve phai c ky hieu bang mui ten cong.
BAI 4 HNH TRCH
1. Khai niemHnh trch : La loai hnh bieu dien thng c phong to trch t hnh bieu dien
chnh nham the hien ro ket cau qua nho cua vat the
2. Phng phap bieu diene ch dan phan c trch t hnh bieu dien chnh, tieu chuan nha nc qui nh
dung net lien manh khoanh vung c trch ( bang vong tron hoac elip) kem theo so
th t La ma tng ng va t le phong to.
3. Qui nh ve hnh trcha. Nen at hnh trch gan v tr khoanh vung trch.
b. Hnh trch bao gom ca nhng van e cha the hien tren hnh bieu dien chnh
va cung co the la loai hnh bieu dien khac vi hnh bieu dien chnh.
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BAI GIANG VE KY THUAT Trang 57
MUC LUC
CHNG 1 CAC TIEU CHUAN TRNH BAY BAN VEBAI 1 PHNG TIEN TRNH BAY BAN VE
I. Vat lieu ve va dung cu ve .............................................................................. 1II. Cach s dung cac dung cu ve ...................................................................... 1
BAI 2 TIEU CHUAN TRNH BAY BAN VEI. ng net .................................................................................................... 2II. Ch va so ..................................................................................................... 3III. Kho giay ....................................................................................................... 4IV. Khung ban ve va khung ten ......................................................................... 5V. Ty le ............................................................................................................ 5
BAI 3 CHI KCH THCI. Quy nh chung ............................................................................................ 6II. Cac thanh phan cua kch thc ................................................................... 6III. Mot so quy nh khi ghi kch thc ............................................................... 7IV. Trnh t thc hien ban ve ............................................................................. 8
CHNG 2 VE HNH HOCBAI 1 DNG HNH HOC
I. Dng cac ng thang ................................................................................. 9II. Ve cac goc .................................................................................................. 10
III. o doc ......................................................................................................... 11IV. o con ......................................................................................................... 11V. Chia ng tron thanh cac phan bang nhau ............................................... 11
BAI 2 VE NOI TIEPI. Ve tiep tuyen vi ng tron ....................................................................... 13II. Tiep tuyen chung cua hai ng tron .......................................................... 13III. Noi hai ng thang bang mot cung tron .................................................... 14IV. Noi ng thang vi cung tron bang mot cung tron .................................... 14
V. Noi hai cung tron bang mot cung tron khac ................................................ 15BAI 3 DNG MOT SO NG CONG THONG DUNG
I. Hnh ovan ..................................................................................................... 17II. Hnh elip ....................................................................................................... 17III. ng xoan oc archimet .............................................................................. 18
IV. ng than khai cua ng tron ................................................................. 18CHNG 3 HNH CHIEU VUONG GOCBAI 1 KHAI NIEM VE PHEP CHIEU
I. Khai niem ve phep chieu ............................................................................. 19II. Phan loai phep chieu ................................................................................... 19III. Phng phap ve cac hnh chieu vuong goc ................................................. 20
BAI 2 HNH CHIEU CUA IEM OAN THANG HNH PHANGI. Hnh chieu cua iem .................................................................................... 22
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II. Hnh chieu cua oan thang .......................................................................... 23III. Hnh chieu cua mat phang ........................................................................... 26
BAI 3 HNH CHIEU CUA CAC KHOI HNH HOCI. Khoi a dien ................................................................................................. 29II. Khoi tron ...................................................................................................... 29III. Bieu dien hnh chieu cac khoi hnh hoc c ban ............................................ 31
BAI 4 GIAO TUYEN TREN BE MAT VI CAC KHOI HNH HOCI. Giao tuyen cua mat phang vi khoi a dien ................................................ 33II. Giao tuyen cua cac khoi hnh hoc ............................................................... 34III. Giao tuyen cua khoi a dien vi khoi tron ................................................... 35
BAI 5 BIEU DIEN VAT THE1. Cach phan tch vat the thanh cac khoi hnh hoc c ban ............................. 352.. Cach ve hnh chieu th ba t hai hnh chieu a cho .................................. 36
CHNG IV HNH CHIEU TRUC OBAI 1 KHAI NIEM VE HNH CHIEU TRUC O
1. Khai niem ................................................................................................... 372.. Phan loai hnh chieu truc o ...................................................................... 37
BAI 2 CAC LOAI HNH CHIEU TRUC O1. Hnh chieu truc o vuong goc eu .............................................................. 382.. Hnh chieu truc o xien ng can ............................................................... 39
BAI 3 CACH DNG HNH CHIEU TRUC O1. Phng phap toa o .................................................................................... 402. ac iem ve cach dng .............................................................................. 40
CHNG V HNH BIEU DIEN CUA VAT THEBAI 1 HNH CHIEU
1. Khai niem .................................................................................................... 422.. Phng phap bieu dien ............................................................................... 423. Phan loai ..................................................................................................... 43
BAI 2 HNH CAT1. Khai niem .................................................................................................... 442.. Phng phap bieu dien .............................................................................. 443. Phan loai hnh cat ...................................................................................... 46
BAI 3 MAT CAT1. Khai niem ................................................................................................... 50
2.. Phan loai .................................................................................................... 503. Ky hieu va quy nh ve mat cat .................................................................. 50BAI 4 HNH TRCH
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