dibujo técnicotécnico ii - grefu. n+guía.pdf · pdf filecon este...
TRANSCRIPT
Ø
Ø
Ø
Ø
DIBUJO
GEOM
ÉTRIC
ODE
SCRIP
TIVA
NORM
ALIZAC
IÓN
DIBUJODIBUJOTÉCNICOTÉCNICO II
EDITORIAL DONOSTIARRA
!"#$%&'())*+%,-
GUÍA PRÁCTICA PARA EL ALUMNOSOLUCIONARIO
JOAQUÍN GONZALO GONZALO
EDITORIAL DONOSTIARRAPokopandegi, nº 4 - Pabellón Igaralde - Barrio Igara
Apartado 671 - Teléfonos 943 215 737 - 213 011 - Fax 943 219 52120018 - SAN SEBASTIÁN
!"#$%&'()*")&
!"#$%&'()*")&
+,-#./012234.56+,-#./012234.56
7$89-:;<)'")9:9;9-=>-9>$?*&
7$89-:;<)'")9:9;9-=>-9>$?*&
Texto adaptado a los currículos de Bachillerato, modalidades:Texto adaptado a los currículos de Bachillerato, modalidades:Texto adaptado a los currículos de Bachillerato, modalidades:Texto adaptado a los currículos de Bachillerato, modalidades:Texto adaptado a los currículos de Bachillerato, modalidades:
Tecnología, Artes y Ciencias de la Naturaleza y SaludTecnología, Artes y Ciencias de la Naturaleza y SaludTecnología, Artes y Ciencias de la Naturaleza y SaludTecnología, Artes y Ciencias de la Naturaleza y SaludTecnología, Artes y Ciencias de la Naturaleza y Salud
Texto adaptado a los currículos de Bachillerato, modalidades:Texto adaptado a los currículos de Bachillerato, modalidades:Texto adaptado a los currículos de Bachillerato, modalidades:Texto adaptado a los currículos de Bachillerato, modalidades:Texto adaptado a los currículos de Bachillerato, modalidades:
Tecnología, Artes y Ciencias de la Naturaleza y SaludTecnología, Artes y Ciencias de la Naturaleza y SaludTecnología, Artes y Ciencias de la Naturaleza y SaludTecnología, Artes y Ciencias de la Naturaleza y SaludTecnología, Artes y Ciencias de la Naturaleza y Salud
@&>$)"&*9;"&@&>$)"&*9;"&
Con este solucionario de la GUÍA PRÁCTICA PARA EL ALUMNO deDIBUJO TÉCNICO I de 1º de Bachillerato, tratamos de ahorrarle trabajoal profesor a la hora de corregir las láminas de la misma que sus alumnosrealicen.
Si exceptuamos los ejercicios de acotación, que se pueden resolvercon diferentes criterios, el resto de los ejercicios propuestos en las treintaláminas de la GUÍA PRÁCTICA PARA EL ALUMNO tienen un únicoresultado, si consideramos que éste debe quedar dentro del espaciodesignado al efecto. La corrección de este tipo de ejercicios se facilitaconsiderablemente si se dispone de la solución o plantilla, sobre todocuando no es una sola lámina a calificar, sino las correspondientes atodos los alumnos que forman el grupo.
Proporcionando este solucionario de la GUÍA PRÁCTICA PARA ELALUMNO a los profesores que la adopten como material de trabajopara sus alumnos, pretendemos facilitarles la calificación de los mismosevitándoles dedicar un tiempo importante a resolver todos los ejercicios.
El autor
!"#$#%&!"#$#%&!"#$#%&!"#$#%&!"#$#%&'''''()*%()*%()*%()*%()*%!"#$#%&!"#$#%&!"#$#%&!"#$#%&!"#$#%&'''''()*%()*%()*%()*%()*%
o
o
o
o
A Bs
A
B
1234567
A
P s
37 30’o
67 30’
75
67 30’
135
P
A
Q
r
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 2
Lámina Nº 1 TRAZADOS FUNDAMENTALES
!"#$#"%&#%'()*#+"*$%)(&%,(-'(.+/%01010101012!"#$#"%&#%3("3(.)*45&#"%#%&#%,('*""(4+#%,,,,,%(.%,5%(6+"('/%00000,*.%3"/&/.-#"%7,+#2
8(+("'*.#"%(&%4(.+"/%)(&%#"4/%)#)/2%9/%,(%3("'*+(%(&%+#.+(/28*:*)*"%-";<*4#'(.+(%(&% ,(-'(.+/% 0101010101%(.%,*(+(%3#"+(,*-5#&(,2
=+*&*$#.)/%>.*4#'(.+(%"(-&#%?%4/'3;,@%+"#$#"%#%&#%"(4+#%"""""&#%3("3(.)*45&#"%3/"%(&%35.+/%AAAAA%?%&#%3#"#&(&#%3/"%(&%35.+/%BBBBB2
C/.,+"5*"%(&%;.-5&/%)(%DEDEDEDEDE/////%DFG%DFG%DFG%DFG%DFG%5./%)(%45?/,%&#)/,%(,%&#,('*""(4+#%,,,,,%?%(&%:7"+*4(%,5%(6+"('/%000002%!"#$#"%3/"%(&%35.+/AAAAA%&#%"(4+#%H5(%</"'#%4/.%,,,,,%(&%;.-5&/%3/,*+*:/%)(%IEIEIEIEIE/////%DFG%DFG%DFG%DFG%DFG2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 4
Lámina Nº 2 TRIÁNGULOS
A
B
60
42
a = 70
a = 78
c = 62
52
B
A
c
C
B
C
h
A
6045
o
o
m
h
m
B
C A
b
C
b
A
a C
8(+("'*.#"%(&%35.+/%H5(%,(%J#&&#%#%IF%''IF%''IF%''IF%''IF%''%)(&%35.+/%00000%?#% KL%''KL%''KL%''KL%''KL%''%)(&% 111112
8*M5N#"%(&%+"*;.-5&/%45?/,%)#+/,%,/.O%(&%&#)/%#####%)#)/%?%&/,;.-5&/,%1%P%IF1%P%IF1%P%IF1%P%IF1%P%IF/////%?%C%P%KQC%P%KQC%P%KQC%P%KQC%P%KQ/////2%!"#$#"%&#%#&+5"#%)(&%&#)/%444442
C/.,+"5*"%(&%+"*;.-5&/%45?/,%)#+/,%,/.O%(&%&#)/%)#)/%44444@%(&&#)/%#%P%EF%''#%P%EF%''#%P%EF%''#%P%EF%''#%P%EF%''%?%(&%;.-5&/%1%P%EQ1%P%EQ1%P%EQ1%P%EQ1%P%EQ/////2%!"#$#"%&#%'()*#.#)(&%&#)/%MMMMM2 C/.,+"5*"%5.%+"*;.-5&/%(H5*&;+("/%45?#%#&+5"#%'*)(%QL%''QL%''QL%''QL%''QL%''2
8*M5N#"%(&%+"*;.-5&/%"(4+;.-5&/@%4/.%;.-5&/%"(4+/%(.%00000@%)(&H5(%,(%4/./4(%(&%4#+(+/%MMMMM%)#)/%?%H5(%&#%J*3/+(.5,#%'*)(ER%''ER%''ER%''ER%''ER%''2%!"#$#"%&#%#&+5"#%)(%7,+#2
C/.,+"5*"%(&%+"*;.-5&/%"(4+;.-5&/@%4/.%;.-5&/%"(4+/%(.%00000@%45?/,)#+/,%,/.O%(&%4#+(+/% MMMMM%)#)/%?%(&%/+"/%4#+(+/% 4%P%IL%''4%P%IL%''4%P%IL%''4%P%IL%''4%P%IL%''2!"#$#"%&#%'()*#.#%)(&%&#)/%444442
SSSSS SSSSS
SSSSS
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 4
Lámina Nº 3 TRIÁNGULOS Y ÁNGULOS DE LA CIRCUNFERENCIA
B
B
c
A A
h
M
A
A
A
rr
r
a52 30’
75
120
45
60
!
c = 62
o
o
o
o
o
28
C
A c B
8*M5N#"%5.%+"*;.-5&/%"(4+;.-5&/%45?#%J*3/+(.5,#%(,%(&,(-'(.+/%#####%)#)/%?%&#%#&+5"#%)(%7,+#%'*)(%J%P%LR%''J%P%LR%''J%P%LR%''J%P%LR%''J%P%LR%''2T8/,%,/&54*/.(,U2
C/.,+"5*"%(&%+"*;.-5&/%"(4+;.-5&/@%4/.%;.-5&/%"(4+/%(.%00000@)(&%H5(%,(%4/./4(%(&%4#+(+/%44444%)#)/%?%C%P%QLC%P%QLC%P%QLC%P%QLC%P%QL/////%DFG%DFG%DFG%DFG%DFG%(&%;.-5&//35(,+/%#%7,+(2
C/.,+"5*"%(&%+"*;.-5&/%*,V,4(&(,%)(&%H5(%,(%4/./4(%5./%)(%&/,&#)/,%*-5#&(,%4%4%4%4%4%)#)/%?%5./%)(%&/,%;.-5&/,%*-5#&(,%C%P%EQC%P%EQC%P%EQC%P%EQC%P%EQ/////2
8*M5N#"%(&%+"*;.-5&/%*,V,4(&(,%4/./4*(.)/%5./%)(%&/,%&#)/,*-5#&(,%4%P%IL%''4%P%IL%''4%P%IL%''4%P%IL%''4%P%IL%''%?%&#%#&+5"#%)(&%&#)/%)(,*-5#&%J%J%J%J%J%)#)#2
8*M5N#"%&/,%;.-5&/,%H5(%,(%3*)(.@%"(*/.#)/,%4/.%&#,%4*"45.<("(.4*#,%)#)#,@%,#M*(.)/%H5(%(.%+/)/,%(&&/,%(&%35.+/%00000(,%(&%:7"+*4(%?%H5(%5./%)(%&/,%&#)/,%+*(.(%4/'/%,/3/"+(%&#%"(4+#%"%"%"%"%"%)#)#2
SSSSS
SSSSS
W.-5&/%*.,4"*+/%)(%KQ/ W.-5&/%,('**.,4"*+/%)(%IF/ W.-5&/%4*"45.,4"*+/
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 5
Lámina Nº 4 CUADRILÁTEROS
A
d d105
a = 40
a = 40
o
A
D
B
D
d
A
C
D
C
B
D
h =
38
A B
d = 60d = 60
b’ CC
D
A
d =
49
d = 72
2
1
B
h
Ah
= 35
b = 40
aB
CD
B
C
C/.,+"5*"%(&%45#)"#)/%5.#%)(%45?#,%)*#-/.#&(,%(,%(&,(-'(.+/%)))))2
8*M5N#"%(&%"(4+;.-5&/%4/./4*)/%(&%;.-5&/%H5(%</"'#.%&#,)*#-/.#&(,%!%P%XFQ%P%XFQ%P%XFQ%P%XFQ%P%XFQ/////%%%%%?%,#M*(.)/%H5(%5.#%)(%7,+#,%(,%(&,(-'(.+/%)))))2
8*M5N#"%(&%"/'M/%45?/,%)#+/,%,/.O%&#%)*#-/.#&%)))))%)#)#%?H5(%(&%&#)/%'*)(%#%P%KF%''#%P%KF%''#%P%KF%''#%P%KF%''#%P%KF%''2
C/.,+"5*"%(&%"/'M/*)(%45?/,%)#+/,%,/.O%(&%&#)/%#%#%#%#%#%)#)/@%(&&#)/% M%P%KF%''M%P%KF%''M%P%KF%''M%P%KF%''M%P%KF%''%?%&#%#&+5"#% J%P%DQ%''J%P%DQ%''J%P%DQ%''J%P%DQ%''J%P%DQ%''2
C/.,+"5*"%(&%+"#3(4*/%*,V,4(&(,%)(&%H5(%,(%4/./4(%&#%M#,(%'(./"MGMGMGMGMG%)#)#@%&#%#&+5"#%J%P%DR%''J%P%DR%''J%P%DR%''J%P%DR%''J%P%DR%''%?%&#%)*#-/.#&%)%P%IF%'')%P%IF%'')%P%IF%'')%P%IF%'')%P%IF%''2
8*M5N#"%(&%+"#3(4*/%"(4+;.-5&/%45?#%#&+5"#%(,%(&%,(-'(.+/%JJJJJ)#)/%?%,#M*(.)/%H5(%,5,%)*#-/.#&(,%'*)(.%)))))
XXXXX%P%EL%''%P%EL%''%P%EL%''%P%EL%''%P%EL%''%?
)))))LLLLL% P% KY% ''% P% KY% ''% P% KY% ''% P% KY% ''% P% KY% ''2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 5
Lámina Nº 5 POLÍGONOS REGULARES
OO
A
O
1
2
3
4
5
6
7
8
9 A
A B
26
B
8*M5N#"%5.%)/)(4;-/./%"(-5&#"%T3/&Z-/./%)(%)/4(%&#)/,U*.,4"*+/%(.%&#%4*"45.<("(.4*#%)#)#2
8*M5N#"@%5+*&*$#.)/%(&%'7+/)/%3#"+*45&#"@%(&%3(.+;-/./"(-5&#"%*.,4"*+/%(.%&#%4*"45.<("(.4*#%)#)#@%,*(.)/%(&%35.+/00000%5./%)(%,5,%:7"+*4(,2
C/.,+"5*"%3/"%(&%'7+/)/%-(.("#&@%5.%(.(;-/./%"(-5&#"*.,4"*+/%(.%&#%4*"45.<("(.4*#%)#)#2
C/.,+"5*"%(&%3(.+;-/./%"(-5&#"%5./%)(%45?/,%&#)/,%(,%(&,(-'(.+/%0101010101%)#)/2
8*M5N#"%(&%/4+V-/./%"(-5&#"%5./%)(%45?/,%&#)/,%(,%(&%,(-'(.+/01%01%01%01%01%)#)/2 C/.,+"5*"%5.%J(3+;-/./%"(-5&#"%45?/%&#)/%'*)(%LI%''LI%''LI%''LI%''LI%''2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 5
Lámina Nº 6 DIVISIÓN DE LA CIRCUNFERENCIA
R
O
4831
148
28
110
!/'#.)/%4/'/%M#,(%&#%4*"45.<("(.4*#%)(%4(.+"/%[[[[[@%)*M5N#"%&#%"5()#%)(%+"*.H5(+(%"(3"(,(.+#)#%#%'(./"%(,4#
8*M5N#"%#%(,4#&#%XOXXOXXOXXOXXOX%&#%"5()#%)(%4#)(.#%"(3"(,(.+#)#2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 6
Lámina Nº 7 PROPORCIONALIDAD Y SEMEJANZA
a
a a
a
a
a
D
D’
OC’
B’A’
F’
E’
C
BA
B’
A’
F
E
b
b
x
a
bb
b b
c
c
x
x
a a
a
c b
x
b b
x
x x
b
= =
=
B
O
A
C#&45&#"%-";<*4#'(.+(%(&%,(-'(.+/%45#"+/%3"/3/"4*/.#&%#&/,%,(-'(.+/,%#####@%MMMMM%?%444442
\#&&#"%-";<*4#'(.+(%(&%,(-'(.+/%+("4("/%3"/3/"4*/.#&%#&/,%,(-'(.+/,%#####%?%MMMMM2
[M+(.("%-";<*4#'(.+(%(&%,(-'(.+/%'()*/%3"/3/"4*/.#&%#&/,%,(-'(.+/,%#%#%#%#%#%?%MMMMM2
C/.,+"5*"%(&%3/&Z-/./%,('(N#.+(%#&%01C8]^01C8]^01C8]^01C8]^01C8]^%)#)/@%,*(.)/&#%"#$V.%)(%,('(N#.$#%XODXODXODXODXOD2
8*M5N#"%&#%N#""#%,('(N#.+(%#%&#%)#)#%,#M*(.)/%H5(%(&%,(-'(.+/%0101010101%,(%+"#.,</"'#";%(.%(&%00000G1G1G1G1G1GGGGG2%8(+("'*.#"%3"(:*#'(.+(&#%"#$V.%)(%,('(N#.$#2
*
_0`a9%P%222222222222222222222222 : 1
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 6
Lámina Nº 8 IGUALDAD, EQUIVALENCIA Y SIMETRÍAS
A
E
DG
F
e
A
A
A’
G
F’
E’
D’
C’
F’
E’
C’
O
B’
D’
B’
GA
F
E
DC
B
B
C
D
A’
E
FB
C
B
8*M
5N#
"%&#
%<*-
5"#
%*-
5#
&%#
%&#
% 01
C8
]^
b0
1C
8]
^b
01
C8
]^
b0
1C
8]
^b
01
C8
]^
b%4
/&4;
.)
/&#%
)(%
'/)
/%H
5(%
(&%,
(-'
(.+/
% 0000 0G1G1G1G1 G1
GGGG G/4
53
(%&#
%3/,
*4*V
.%)
#)#2
8(+
("'
*.#"
%(&%+
"*;.
-5&/
%(H5
*:#&
(.+(
%#&%3
(.+;
-/.
/%0
1C
8]
01
C8
]0
1C
8]
01
C8
]0
1C
8]
%)(%
'/)
/%H5
(%(&
%:7"
+*4(
% 0000 0%,
(#5.
/%)(
%&/,%
)(&%+
"*;.
-5&/
%?%H
5(%&/
,%/+
"/,%
)/,%
,(%J
#&&(
.%,
/M"(
%&#%"(
4+#%
H5(%
4/.
+*(.
(%#&
%&#)/
% C8
C8
C8
C8
C8
2
]&%3
5.
+/% 0000 0
GGGG G%(,%
(&%,
*'7+
"*4/
%)(%
0000 0%(
.%5
.#%
,*'
(+"Z
#%4(
.+"
#&2%\
#&&#
"%(&%4
(.+"
/%)
(%,*
'(+
"Z#%
?)
*M5
N#"%
&#%<*
-5
"#%,
*'7+
"*4#
%)(%
&#% 0
1C
8]
^0
1C
8]
^0
1C
8]
^0
1C
8]
^0
1C
8]
^%)
#)#2
]&%,
(-'
(.+/
% 01
01
01
01
01
%(,%
(&%&#
)/%*.
<("*
/"%)
(%5
.%3
(.+;
-/.
/%"(
-5&#
"2%8
*M5
N#"%(
,(%3
/&Z-
/./%
?%,5
4/""
(,3/
.)*
(.+(
%,*'
7+"*
4/%+/
'#.
)/%&#
%"(4+
#%(((( (%
4/'
/%(N
(%)(
%,*'
(+"Z
#2*
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 7
Lámina Nº 9 TRASLACIÓN Y GIRO
Vd
V’
D
EE
’
F’
G’
A’
B’
C’
D’
F
G
E
F AA
’120
o
"
B
F’
E’D’
C’
B’
C
D
AB
C
rs
N’
M’
N’’
M’’
N
F
E
D
C
!
BA
A’
B’
O
C’
D’
E’
F’
M
8#)
/%(&
%:(4
+/"%
)(%
+"#,
*
V.% c
cG
cc
Gc
cG
cc
Gc
cG%?
%&#%<*
-5
"#% 0
1C
8]
^b
01
C8
]^
b0
1C
8]
^b
01
C8
]^
b0
1C
8]
^b
@%)(+
("'
*.#"
%&#%+
"#.
,</"
'#)
#)
(%7,
+#2
8#)
#,%&#
,%"(
4+#,
% """" "%?%
,,,, ,%?%
(&%,
(-'
(.+/
% d9
d9
d9
d9
d9
@%)(+
("'
*.#"
%(&%,
(-'
(.+/
%H5
(@%4
/.%&#
%'*,
'#
&/.
-*+5
)%?%
)*"(
44*V
.%H
5(%
(&%)
#)/@
%+(.
-#%&/
,%(6
+"('
/,%,
/M"(
%&#,%
"(4+
#,% """" "%
?%,,,, ,2
8#
)/%
(&%3
/&Z-
/./%
01
C8
]^
01
C8
]^
01
C8
]^
01
C8
]^
01
C8
]^
@%)
*M5
N#"%
&#%<
*-5
"#%H
5(%
"(,5
&+#%
#&%#
3&*
4#"&
(%5
.%-
*"/%
(.%(
&,(
.+*
)/%
)(%
&#,%
#-5
N#,%
)(&
%"(&
/N%)
(%XL
FXL
FXL
FXL
FXL
F//// / %?%4
(.+"
/%(&
%35
.+/
% 0000 02
"*
]&%,
(-'
(.+/
% 01
01
01
01
01
%,(%
+"#.
,</"
'#%
'()
*#.
+(%5
.%-
*"/%
(.%(
&% 0000 0G1G1G1G1 G1
GGGG G2%C
#&45
&#"%(
&%4(.
+"/%
?%(&
;.-
5&/
%)(%
)*4
J/%
-*"
/2%8
(+("
'*.
#"%&#
%<*-
5"#
%+"#
.,<
/"'
#)#%
H5
(%"(
,5&+
#%#&
%#3
&*4#"
%#&
3/&
Z-/.
/%0
1C
8]
^0
1C
8]
^0
1C
8]
^0
1C
8]
^0
1C
8]
^%&#
%"/+#
4*V.
%)(<
*.*)
#2
**
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 7
Lámina Nº 10 HOMOTECIA
O
D
B
a
b
P’
A’
r’
r
A
B
B’
P
A
E
D’
C’
B’
A’
E’
1
2
3
4
5
C
O
A
D’
C’
B’
A’
E’
E
D
O
CO
O
C
21
2
1
C
B
8#)
/,%(
&%3(.
+;-
/./%
01
C8
]0
1C
8]
01
C8
]0
1C
8]
01
C8
]%?
%(&%3
5.
+/% [[[[ [
@%4/.
,+"5
*"%#
&%<*-
5"#
%J/'
/+7+
*4#%
)(%
&#%)
#)#%
(.5
.#%
J/'
/+(4
*#%)
(%4(
.+"
/%[[[[ [
%?%"
#$V.
% DeQ
DeQ
DeQ
DeQ
DeQ2
8*M
5N#"
%&#,%
<*-5"
#,%J
/'/+
7+*4
#,%)
(%&#
%4*"
45.
<("(
.4*
#%)(
%4(.
+"/%
[[[[ [%4
/""(
,3/.
)*(.
+(,%
#%)/
,J
/'/+
(4*#
,O%&#
%3"*
'("
#%)
(%4(
.+"
/%CCCC C
XXXX X%?%"#
$V.
% LLLL L@%&
#%,(
-5
.)
#%)
(%4(
.+"
/%CCCC C
LLLL L%?%"#
$V.
% fLfLfLfL fL2
!"#
$#"%
&#%"
(4+#
%H5
(%3
#,#
%3/"
%(&%3
5.
+/% AAAA A
%)#)
/%?%
3/"
%(&%3
5.
+/%)
(%4/
.45
""(.
4*#%
)(%
&#,
"(4+
#,% #
%#
%#
%#
%#
%?% MMMM M
2%05
.H
5(%
(,+(
%35
.+/
%(,%
*.#4
4(,*
M&(
@%+/'
#)/%
4/'
/%4(
.+"
/%)
(%J
/'/+
(4*#
%,(
35
()(.
%/M
+(.
("%<*
-5
"#,%
J/'
/+7+
*4#,
%)(%
&#)
/,%3
#"#&
(&/,
2*\
#&&#
"%&#%
<*-
5"#
%J/'
/+7+
*4#%
H5
(%"(
,5&+
#%)
(%#3
&*4#
"%#&%3
(.+;
-/.
/%0
1C
8]
01
C8
]0
1C
8]
01
C8
]0
1C
8]
%&#%J
/'/+
(4*#
)(%
4(.
+"/%
[[[[ [%?
%"#
$V.
% fDeL
fDeL
fDeL
fDeL
fDeL
2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 8
Lámina Nº 11 TANGENCIAS
AB
MN
O
O
O
R + R
R + R
AB
O
O
O
R R
R
2
3
1
2
1
1
3
1
2
3
1
2
3
O
A#"+
*(.
)/%)
(&%&#
)/% 0
10
10
10
10
1%)
(&%4
5#)
"#)/
@%)*M
5N#
"%#%'
#?/"
%+#'
#g/%
&#%<*
-5"#
%H5
(%,(
%#4/
'3#
g#2
8*M
5N#
"@%#%
3#"+
*"%)
(%&#
%4*"
45.
<("(
.4*
#%)(
%4(.
+"/%
[[[[ [@%&
#%<*-
5"#
%,('
(N#.
+(%#
%&#%)
#)#2
*
8*M
5N#
"%&#,
%4*"
45.
<("(
.4*
#,%)
(%4(
.+"
/,% [[[[ [
XXXX X@% [[[[ [
LLLL L%?% [[[[ [
DDDD D%+#.
-(.
+(,%
(.+"
(%,Z
2%A#"
#%+(
.("
%5.
#3*
,+#%
)(&%3
"/4(
,/%#
%,(-
5*"%3
#"#%
"(,/
&:("
%(,+
(%(N
("4*
4*/@
%#.
#&*$
#"@%4
/.%#
?5)#
%)(%
&#%<*
-5"#
)(%
&#%)
("(4
J#@
%H5
7%3
#,#"
Z#%,
*%&/,
%"#)
*/,%
____ _XXXX X%
?%____ _
LLLL L%,(
%#-
"#.
)#"
#.%J
#,+#
%4/.
:("+
*",(
@"(
,3(4
+*:#
'(.
+(@%(
.% ____ _
XXXX X%h
%_%h
%_%h
%_%h
%_%h
%_DDDD D%
?%____ _
LLLL L%h
%_%h
%_%h
%_%h
%_%h
%_DDDD D2
**
8*M
5N#
"%&#
%<*-
5"#
%,('
(N#
.+(
%#%&#
%)#
)#
%,*(
.)
/%(&
%,(-
'(.
+/% d
9d
9d
9d
9d
9%5
./%
)(%
&/,%
&#)
/,%)
(&+"
*;.
-5&/
%(H5
*&;+(
"/2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 8
Lámina Nº 12 TANGENCIAS
104
14
A
F
D
AB
C
DE
F
C
B
E
P
P
42
1846
R50
45
90
8*M
5N#
"%&#%
4/""
(#%)
(%+"
#.,'
*,*V
.%(
.+"
(%&#
,%)
/,%3
/&(#
,%)
#)#,
28
*M5
N#"%
#%(,
4#&#
% XOL
XOL
XOL
XOL
XOL%
&#%<
*-5
"#%#
)N5
.+#
2%8
(N#"
%*.
)*4
#)#,
%&#,
%4/.
,+"5
44*/
.(,
%3#"
#)
(+("
'*.
#"%&/
,%3
5.
+/,%
)(%
+#.
-(.
4*#2
8*M
5N#
"%&#%
3*(
$#%4
5?/
%4"/
H5
*,%,
(%#4
/'3
#g#%
3#"
+*(.
)/%
)(%
&#%3
/,*4
*V.
%)(&
%35
.+/
% AAAA A%?
%*
"45
.<(
"(.
4*#%
)(%)
*;'
(+"/
%KI2
%8(N
#"%+/
)#,%
&#,%
4/.
,+"5
44*/
.(,
%H5
(%,(
%J#.
%.(4
(,*+
#)/
3#"#
%(&%+
"#$#
)/2
*8
(&*.
(#"%(
&%3("
<*&%,
('(N
#.+(
%#&%)
#)/@
%</"'
#)/%
3/"
%,(-
'(.
+/,%
?%#"
4/,%
)(%
4*"4
5.
<("(
.4*
#+#
.-
(.+(
,@%4
/./4
*(.
)/%
&/,%
35
.+/
,%0000 0
@%1111 1
@%CCCC C
@%8888 8
@%]]]] ]
%?% ^̂̂̂̂
%3/"
%&/,
%H5
(%3
#,#2
%8(N
#%&#
,%&Z.
(#,
#56*
&*#"(
,%H5
(%J
#?#.
%,*)
/%.
(4(,
#"*#
,2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 8
Lámina Nº 13 TANGENCIAS
ø210
240
45
11
ø50
R8
R6
25
18
ø54
ø36
R30
62
R18
8(&
*.(#
"%#%(
,4#&
#%LO
XLO
XLO
XLO
XLO
X%(&
%,/3
/"+(
%)(&
%,(&
&/%)
(%4#
54J
/%)(
%&#%<*
-5"#
%#)N
5.+#
%(.
%&#%3
/,*4
*V.
%H5(
)(+(
"'*.
#%(&
%(N(
%H5(
%,(%
#4/'
3#g#
2%9/%
M/""
#"%&/
,%+"
#$#)
/,%#
56*&*
#"(,
%(%*.
)*4#
"%&/,
%35.
+/,%
)(+#
.-(.
4*#2
%9/%
#4/+
#"2
8*M
5N#
"%#%(
,4#&
#%XO
LXO
LXO
LXO
LXO
L%&#
%:#,
*N#%)
(%:*
)"*/
%45
?/%4
"/H5
*,%#
4/+#
)/%,
(%#4
/'3#
g#%
(.%&#
%3/,
*4*V
.H5
(%)(
+("'
*.#%
(&%(
N(%#
)N5.
+/2%8
(N#"
%&#,%
&Z.(#
,%)(
%+"#$
#)/%
(%*.
)*4#
"%&/,
%35.
+/,%
)(%+#
.-(
.4*
#29
/%#4
/+#"
2
Nom
bre:
J. GONZALO GONZALO
Fecha:
NO
TA:
TEM
A 8
Lámina N
º 14TA
NG
EN
CIA
S
130
R118
12
60 o
34
Pun
to d
e ta
ngen
cia
4
9
14
R40
R15 R
10
210
76
ø102
R112
R25
20
ø72
76
8(&*.(#"%#%(,4#&#% XOLXOLXOLXOLXOL%(&%N#""V.%H5(%,(%#4/'3#g#2%8(N#"%+"#$#)#,%+/)#,%&#,%&Z.(#,.(4(,#"*#,%3#"#%&#%"(,/&54*V.%)(%&#,%+#.-(.4*#,2%9/%#4/+#"2
* 8(&*.(#"%#%(,4#&#%XOXXOXXOXXOXXOX%(&%+*"#)/"%)(%&#%<*-5"#%#)N5.+#2%9/%M/""#"%.*.-5.#%)(%&#,%&Z.(#,.(4(,#"*#,%3#"#%&#%"(,/&54*V.%)(%&#,%+#.-(.4*#,2%9/%#4/+#"2
* *
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 9
Lámina Nº 15 CURVAS TÉCNICAS
14048
109
B
C
C
D
D
A
Ovo
ide
R13
R8
8(&
*.(#
"%#%(
,4#&
#%XO
XXO
XXO
XXO
XXO
X%&#
%454
J#"#
%45?
/%4"
/H5*
,%#4
/+#)
/%,(
%#4/
'3#
g#2%9
/%M/
""#"
%.*.
-5.#
)(%&#
,%&Z.
(#,%
.(4
(,#"
*#,%
3#"#
%&#%"(
,/&5
4*V.
%)(%
&#,%
+#.
-(.
4*#,
2%9/%
#4/+
#"2
**
C/.
,+"5
*"%5
.%V
:#&/
%)(%
45#+
"/%4
(.+"
/,%4
5?/
,%(N
(,%,
/.%&/
,%,(
-'(.
+/,%
01
01
01
01
01
%?% C
8C
8C
8C
8C
82
C/.
,+"5
*"%(
&%/:/
*)(%
45?/
%(N(
%'(.
/"%(
,%(&
%,(-
'(.
+/% C
8C
8C
8C
8C
82
Nom
bre:
J. GONZALO GONZALO
Fecha:
NO
TA:
TEM
A 10
Lámina N
º 16C
UR
VAS
CÓ
NIC
AS
F
F1
123
45
67
89
1011
2345
P
L
N
K
e
d
AF
P
F’B
A
C
D
1 2 3
F’B
a’
a
A O
C
D
M
i/,%35.+/,%̂̂̂̂̂ %?%̂ G^G^G^G^G%,/.%&/,%</4/,%)(%5.#%(&*3,(%?%AAAAA%5.%35.+/%)(%&#%45":#2%8(+("'*.#"%&/,(N(,%)(%&#%(&*3,(%?%+"#$#"&#%3/"%(&%'7+/)/%M#,#)/%(.%&#%)(<*.*4*V.2 !"#$#"%&#%(&*3,(%)(%&#%H5(%,(%4/./4(%&#%3#"(N#%)(%)*;'(+"/,%4/.N5-#)/,%jijijijiji%?%d9d9d9d9d92
]&%,(-'(.+/%C8C8C8C8C8%(,%(&%(N(%*'#-*.#"*/%)(%5.#%J*37"M/&#%?%&/,%35.+/,%^̂̂̂̂%?%^G^G^G^G^G%,5,%</4/,28(+("'*.#"%(&%(N(%"(#&%?%&#,%#,Z.+/+#,%)(%&#%45":#%?%+"#$#"&#%3/"%(&%'7+/)/%H5(%,(%M#,#%(.%&#)(<*.*4*V.2
8(%5.#%3#";M/&#%,(%4/./4(%(&%(N(%(((((@%&#%)*"(4+"*$%)))))%?%(&%35.+/%AAAAA%)(%&#%45":#2%C#&45&#"%(&%</4/)(%&#%3#";M/&#%?%+"#$#"&#%3/"%(&%'7+/)/%M#,#)/%(.%&#%)(<*.*4*V.2
F’F
F 1
BA
12
34
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 10
Lámina Nº 17 CURVAS CÓNICAS
21133
3
3 5064
99
1
1
2
2
3
3
4
4
ø40
F
F 1
F’B
A
dire
ctriz
ø15
ø12ø7s1
5
20
ø30
50
39
21
ø85
ø12 ø2
4
ø41
30O
3
R7
8(&
*.(#
"%#%(
,4#&
#%LO
XLO
XLO
XLO
XLO
X%&#
%3*(
$#%)
(%#N
()"(
$%45
?/%4
"/H5
*,%#
4/+#
)/%,
(%#)
N5.+
#2%]
.%&#
%3#"
;M/&
#@&#
%)*,
+#.4
*#%)
(%&#
%)*"
(4+"
*$@%H
5(%(
,%+#
.-(.
+(%#
%&#%(
,<("
#%)(
%&#%4
#M($
#@%#
&%</4
/%̂̂̂̂̂XXXX X%(
,%L@
Q%'
'L@
Q%'
'L@
Q%'
'L@
Q%'
'L@
Q%'
'2
*8
(&*.
(#"%#
%(,4
#&#%
XOX
XOX
XOX
XOX
XOX%
(&%3
/'/%
45?/
%4"/
H5*,
%#4/
+#)/
%,(%
#4/'
3#g
#2%A
#"#%
+"#$
#"%&#
%(&*3
,(%(
&#&
5'.
/%35
()(%
/3+#
"%3/"
%(&%'
7+/)
/%H5
(%)(
,((2
%9/%
#4/+
#"2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 12
Lámina Nº 18 SISTEMA DIÉDRICO
A’’’
C’’’
C’
B’B
B’’’
B’’
D’’’
A
D
C
A’’
D’’
P.V.
C’’
D’
1 D
C’
A’’
H’
H’’
F ’F’’
G’’
G’
E’’
E’
e’’ e’
d’’
c’’
b’’
a’’
d’c’
b’
a’
A’
B’
B’’
"
D’’ D’
C’’
3 D
2 D
4 D
er
er
o
o
A’
P.P.
P.H.
Dis
tanc
ia a
lpl
ano
de p
erfil
Ale
jam
ient
o
Cot
a
E 3 5 2
G 6 2 -1
F 7 -3 5
H 9 -4 -3
_(3
"(,(
.+#"
%3/"
%,5,
%3"/
?(44
*/.(
,%J/
"*$/
.+#&
?%:(
"+*4
#&%&/
,%35
.+/
,%)#
)/,%
(.%(
&%(,3
#4*/
2_
(3"(
,(.
+#"%3
/"%,
5,%
3"/?
(44*
/.(,
%J/"
*$/.
+#&%?
%:("
+*4#
&%&/,
%35
.+/
,%45
?#,%
4//"
)(.
#)#,
%,(
#4/'
3#g
#.2
_(3
"(,(
.+#
"%3/"
%,5
%3"/
?(44
*V.
%J/"
*$/.
+#&%?
%:("
+*4#
&%4#)
#%5
.#%
)(%&#
,%"(
4+#,
%H5
(%,(
%*.)*
4#2
#O%[
M&*4
5#MO
%A#"
#&(&
#%#%
&#%i
2!2
4O%\
/"*$
/.+#
&)O
%̂"/
.+#
&(O
%A("
3(.
)*45
&#"%#
&%A2c
2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 12
Lámina Nº 19 SISTEMA DIÉDRICO
A’’
Q’’
E’’
F’
N’
N’’
s’
s ’’
H’’
V’
N’
N’’
H’’
r’’
V’’
V’
r’
M’
t’’
H’’ H
’
V’’
V’
t’
M’’
H’
V’’ V
’
B’’’
B’’
P’’
A’’ A’
H’
V’’ P’
B’
P’’’
15
s’’’
H’’’
A’’’
V’’’
h’’ h’
M’
M’’
1 D
1 D
2 D
2 D
4 D
erer
oo
o
"
"
"
"
! !2 1
B’’ B’
A’
Q’
E’
3 D
4 D
ero
Dis
tanc
ia a
lpl
ano
de p
erfil
Ale
jam
ient
o
Cot
a
A 28 12 -8
B 28 32 22
i/,
%35
.+/
,%0
T00
T00
T00
T00
T0GfGfGfGf Gf
0000 0GGUGGUGG
UGGU GG
U%?% 1
T11
T11
T11
T11
T1Gf
1Gf
1Gf
1Gf
1Gf
1GGUGGUGG
UGGU GG
U%3("
+(.
(4(.
%#%&#
%"(4
+#% """" "2
%_(3
"(,(
.+#
"&#@
%)*<
("(.
4*#.
)/
3#"
+(,%
:*,*
M&(
,%?%
/45
&+#,
@%)(+
("'
*.#"
%&#,%
3"/
?(44
*/.
(,%)
(%,5
,%+"
#$#,
@%)*(
)"/
,%3
/"%&/
,H
5(%
3#,
#%?%
&/,%
35
.+/
,%)
/.)
(%4/
"+#%
#%&/
,%3
&#.
/,%M
*,(4
+/"(
,2
8(%
5.
#%"(
4+#%
J/"
*$/.
+#&% JJJJ J
%,(%
4/.
/4(.
%&#,%
)/,%
3"/?
(44*
/.(,
%)(%
5.
/%)(
%,5
,%35
.+/
,%]
T]Gf
]GGU
]T]
Gf]
GGU]
T]Gf
]GGU
]T]
Gf]
GGU]
T]Gf
]GGU
?%&#
%J/"
*$/.
+#&%̂
G^
G^G
^G ^G%)
(%/+
"/2%_
(3"(
,(.+
#"&#
@%)*<(
"(.4
*#.)
/%3#
"+(,
%:*,
*M&(
,%?%
/45&
+#,@
%)(+
("'
*.#"
&/,%
)*()
"/,%
3/"%&
/,%H
5(%
3#,#
%?%&/
,%35
.+/
,%)/
.)(
%4/"
+#%#
%&/,%
3&#.
/,%M
*,(4
+/"(
,2
i#%
"(4+
#%++++ +%
3#,
#%3
/"%&/
,%)
*()
"/,%
*.)
*4#)
/,%?
%4/.
+*(.
(%#&
%35
.+/
% BTB
GfB
GGUB
TBGf
BGGU
BTB
GfB
GGUB
TBGf
BGGU
BTB
GfB
GGU2%_
(3"(
,(.
+#"&
#*.
)*4#
.)/
%3#"
+(,%
:*,*
M&(,
%?%/
45&+
#,2
i/,%
35.+
/,% 0000 0
%?% 1111 1
@%45?
#,%4
//")
(.#)
#,%(
.%'
''
''
''
''
'%,
(%(6
3"(,
#.%(
.%(&
%45#
)"/%
#)N5
.+/@
%3("
+(.(
4(.
#%5.
#%"(
4#+% ,,,, ,
2%\#&
&#"%&
#,%3
"/?(
44*/
.(,%
)(%&#
,%+"
#$#,
%)(%
7,+#
%?%&#
,%3"
/?(4
4*/.
(,%)
(%5.
%35.
+/AAAA A
%)(%
)*4
J#%
"(4+
#%45
?#%4
/+#%
(,% X
Q%'
'XQ
%''
XQ%'
'XQ
%''
XQ%'
'2%]
&%3&#
./%!
TTTT T!XXXX Xffff f!
LLLL LU%U%U%U% U%"
(3"(
,(.
+#%(
&%3&#
./%
)(%
3("
<*&2
*
a’
a’’
"
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 12
Lámina Nº 20 SISTEMA DIÉDRICO
A’’
A’
B’B’’
r’’
#
#
!
!
#
#
!
!
1
1
1
s
l
ll
l
s
r
s
rr
r
s
1
2
2
2
2
B’
l’’
l’
A’
E’
D’
C’
r ’
C’’
r’’
C’’
D’’
E’’
A’’
B’’
P’P’’
f’
f’’
25 10
r’
s’’
V’’
H’H’’
V’
V’’
V’
V’’
H’
H’
H’’
V’
H’’
s’
M’
M’’
C’
8(+
("'
*.#"
%&#,%
+"#$
#,%)
(&%3
&#.
/%)
(<*.
*)/%
3/"
%&/,%
35
.+/
,%0
T00
T00
T00
T00
T0GfGfGfGf Gf
0000 0GGUGGUGGUGGU GGU
@% 1T1
1T1
1T1
1T1
1T1
Gf1
Gf1
Gf1
Gf1
Gf1
GGUGGUGGUGGU GGU%?
% CTC
CTC
CTC
CTC
CTC
GfGfGfGf GfCCCC C
GGUGGUGGUGGU GGU2
\#&
&#"%
&#,%
+"#$
#,%)
(&%3
&#.
/%#
%)(<
*.*.
*)/%
3/"
%5.
#%)
(%,5
,%&Z
.(#
,%)
(%'
;6*'
#%3
(.)
*(.
+(&T
&Gf&GG
U&T
&Gf&GG
U&T
&Gf&GG
U&T
&Gf&GG
U&T
&Gf&GG
U2%C
/.%#
?5)
#%)
(%&#
%<"/.
+#&%4
/""(
,3/.
)*(
.+(
@%J#&
&#"%&
#,%3
"/?(
44*/
.(,
%)(&
%35
.+/
% AAAA A@
3("
+(.
(4*(
.+(
%#&%3
&#.
/%#
@%45
?/%#
&(N#
'*(
.+/
%(,%
XF%'
'XF
%''
XF%'
'XF
%''
XF%'
'%?
%,5
%4/+
#% L
Q%'
'LQ
%''
LQ%'
'LQ
%''
LQ%'
'2
\#&
&#"%&
#,%+"
#$#,
%)(&
%3&#
./%!
%H5
(%4/
.+*
(.(%
#%&#
%"(4+
#%"T
""T
""T
""T
""T
" Gf"Gf"Gf"
Gf" Gf" G
GUGGUGGUGGU GGU%?
%(,%
3("3
(.)*
45&#
"%#&%3
&#.
/\\\\ \
2%8(+
("'
*.#"
%&#%&Z
.(#%
)(%'
;6*'
#%*.
4&*.
#4*V
.%)(
&%3&#
./%!
%H5(
%4/.
+*(.
(%#&
%35.
+/% dddd d
%)/.
)(&#
%"(4
+#% """" "
%4/"
+#%#
&%XXXX X("("("(" ("
% M*,
(4+/
"M
*,(4
+/"
M*,
(4+/
"M
*,(4
+/"
M*,
(4+/
"28
*M5N
#"%&#
%3"/
?(44
*V.%
:("+
*4#&
%)(&
%3(.
+;-/
./% 0
1C
8]
01
C8
]0
1C
8]
01
C8
]0
1C
8]
%4/.
+(.*
)/%(
.%(&
%3&#
./%#
TTTT T#XXXX Xffff f#
LLLL LUUUU U%4/
./4*
)#,5
%3"/
?(44
*V.
%J/"
*$/.
+#&% 0000 0
G1G1G1G1 G1GCGCGCGC GC
G8G8G8G8 G8G]
GG]
GG]
GG]
GG]
G2
*
R
R’’
I’
I’’i’’
i’
i
i ’’’
I
I
I’’’
I’’’
R
R’
R
R’’’
R’
R’’’
R’’’
R’’
R’’
R’
r’’
r’’’
2
22
1
2
11
3
21
2
3
1
3
2
1
1
3
"
""
"
"
"
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 14
Lámina Nº 21 SISTEMA AXONOMÉTRICO
#
#
!
!
!
!
!
!
2
1
3
1
1
2
2
3
XX
X
YY
Y
ZZ
Z
O
O
C
B
A
C’
S
R’R
S R
S’
r’rs
s’
1
2
2
3 1
3
Q
P
B’
A’
O
r r’
C#&
45&#
"%&#,
%3"/
?(44
*/.
(,%)
*"(4
+#,%
)(%
&/,%
35
.+/
,%)
/.)
(%&#
%"(4+
#%"""" " f
"f"f"f" f"GGGG G%4
/"+#
%#%&/
,%3
&#.
/,)
(&%+
"*()
"/%T+
"#$#
,U%?
%)(+
("'
*.#"
%&#,%
/+"#
,%)
/,%3
"/?(
44*/
.(,
% """" "GGGGGGGG GG
%?% """" "
GGGGGGGGG
GGG GGG2
8*M
5N#
"%&#,
%+"#$
#,%!
XXXX X@%!
LLLL L%?%!
DDDD D%%%% %)
(&%3
&#.
/%!
%H5
(%4/
.+*
(.(%
#%&/
,%3
5.
+/,%
0000 0ffff f 0000 0
GGGG G@% 1111 1
f1f1f1f1 f1GGGG G%?
% CCCC Cffff f CCCC C
GGGG G2
\#&
&#"%
&#,%
45#+
"/,%
3"/
?(44
*/.
(,%)
(%&#
%"(4
+#%)
(%*.
+(",
(44*
V.@% **** *
@%)(%
&/,%
3&#
./,
%!%?
%#2%8
(&3"
*'("
/%,(
%4/.
/4(.
%,5
,%+"
#$#,
%!XXXX X%?
%!DDDD D%?
%)(&
%#%,
5%+"
#$#%!
LLLL L%?%H
5(%
(,%3
#"#&
(&/%
#&%3
&#.
/%k
[`
k[
`k
[`
k[
`k
[`
2
!"#$
#"%&#
,%&Z.
(#,%
:*,*
M&(,
%H5(
%"(,5
&+#.
%#&%(
<(4+
5#"%#
-5N(
"/,%
4*&Z.
)"*4
/,%)
(%LQ
%''
LQ%'
'LQ
%''
LQ%'
'LQ
%''
%)(%
)*;'
(+"/
4/.
%4(.
+"/,
%(.
%&/,%
35
.+/
,%AAAA A
%?% BBBB B
%3("
3(.
)*4
5&#
"(,%
#%&#
,%3
#"()
(,%)
(%&#
%3*(
$#2%9
/%+(
.("
%(.
45(.
+#%(
&%4/(
<*4*(
.+(%
)(%"(
)544
*V.2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 14
Lámina Nº 22 PERSPECTIVA ISOMÉTRICA
C
B
A
A’’ B’’C’’
A’
B’C’
"
B’’ C’’ A’’’ B’’’
C’
B’ A’
A’’ C’’’" "
A
C
B
8*M5N#"@%,*.%+(.("%(.%45(.+#%(&%4/(<*4*(.+()(%"()544*V.@%#%(,4#&#%LOXLOXLOXLOXLOX@%&#%3(",3(4+*:#*,/'7+"*4#%)(%&#%3*($#%)(<*.*)#%3/"%+"(,:*,+#,2%C/&/4#"&#%)(%'/)/%H5(%&/,%:7"+*4(,00000@% 11111%?% CCCCC%/453(.%&#,%3/,*4*/.(,%H5(%,(*.)*4#.2
8*M5N#"@%,*.%+(.("%(.%45(.+#%(&%4/(<*4*(.+()(%"()544*V.@%#%(,4#&#%LOXLOXLOXLOXLOX@%&#%3(",3(4+*:#*,/'7+"*4#%)(%&#%3*($#%#)N5.+#2%C/&/4#"&#)(%'/)/%H5(%&/,%:7"+*4(,%00000@%11111%?%CCCCC%/453(.&#,%3/,*4*/.(,%*.)*4#)#,2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 14
Lámina Nº 23 PERSPECTIVA ISOMÉTRICA
C
C
B
B
A
A
A’’’ B’’’B’’ C’’
C’
B’ A’
A’’ C’’’" "
B’’ C’’" A’’
A’
C’
B’
8*M5N#"@%,*.%+(.("%(.%45(.+#%(&%4/(<*4*(.+()(%"()544*V.@%#%(,4#&#%LOXLOXLOXLOXLOX@%&#%3(",3(4+*:#*,/'7+"*4#%)(%&#%3*($#%#)N5.+#2%C/&/4#"&#)(%'/)/%H5(%&/,%:7"+*4(,%00000@%11111%?%CCCCC%/453(.&#,%3/,*4*/.(,%*.)*4#)#,2
8*M5N#"@%,*.%+(.("%(.%45(.+#%(&%4/(<*4*(.+()(%"()544*V.@%#%(,4#&#%LOXLOXLOXLOXLOX@%&#%3(",3(4+*:#*,/'7+"*4#%)(%&#%3*($#%#)N5.+#2%C/&/4#"&#)(%'/)/%H5(%&/,%:7"+*4(,%00000@%11111%?%CCCCC%/453(.&#,%3/,*4*/.(,%H5(%,(%*.)*4#.2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 15
Lámina Nº 24 PERSPECTIVA CABALLERA
O
O
O
O
A
C B
C
A
B
C
$
$
X
X
X
X
Y
Y
YY
Z
Z
A
3830 30o o
Z
1
2
2
1
C
Z
C
D
B
E
A
E
E
D
C
H
A
B
G
F
F
G
H
AB
C
D
8#)/%(&%/4+V-/./%"(-5&#"%01C8]^b\01C8]^b\01C8]^b\01C8]^b\01C8]^b\%,*+5#)/%(.%(&%3&#./l[`l[`l[`l[`l[`@%"(3"(,(.+#"&/%#3/?#)/%(.%(&%3&#./%k[`k[`k[`k[`k[`2%]&%4/(<*4*(.+()(%"()544*V.%(,%$%P%F@Q%P%F@Q%P%F@Q%P%F@Q%P%F@Q2
8#)/,% &/,% (N(,% ?% (&% ;.-5&/% %@% )*M5N#"% &#% 3(",3(4+*:#4#M#&&("#%)(&%+"*;.-5&/%(H5*&;+("/%,*+5#)/%(.%(&%3&#./%lllll[[[[[kkkkk@4/&/4#)/%)(%'/)/%H5(%(&%&#)/%1C1C1C1C1C%,(#%3#"#&(&/%#&%(N(%lllll%?H5(%(&%:7"+*4(%';,%#&(N#)/%)(%7,+(%(N(%,(#%(&%35.+/%000002%i##&+5"#%)(&%+"*;.-5&/@%(.%:(")#)("#%'#-.*+5)@%(,%DR%''DR%''DR%''DR%''DR%''2
C/./4*)/,%&/,%(N(,%?%(&%4/(<*4*(.+(%)(%"()544*V.%$%P%LeD%P%LeD%P%LeD%P%LeD%P%LeD@"(3"(,(.+#"%(.%(&%3&#./%k[`k[`k[`k[`k[`%&#%3(",3(4+*:#%4#M#&&("#%)(&3(.+;-/./%"(-5&#"% 01C8]01C8]01C8]01C8]01C8]%45?#%'*+#)%,(%"(3"(,(.+##3/?#)#%(.%(&%3&#./%l[`l[`l[`l[`l[`2
8#)/,%&/,%(N(,%?%(&%;.-5&/%%@%)*M5N#"%&#%3(",3(4+*:#4#M#&&("#%)(%&#%4*"45.<("(.4*#@%,*+5#)#%(.%(&%3&#./%lllll[[[[[kkkkk@)(%4(.+"/%CCCCC%?%)*;'(+"/%QL%''QL%''QL%''QL%''QL%''2
*
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 15
Lámina Nº 25 PERSPECTIVA CABALLERA
O
O
O
O
O
O
X
X
X
X
X
Y
Y
Y
Y
Z
Z
Z
Z
Z
8*M5N#"%#%(,4#&#%LOXLOXLOXLOXLOX%&#%3(",3(4+*:#%4#M#&&("#%)(%&#%3*($#%"(3"(,(.+#)#%3/"%)/,%:*,+#,2%C/&/4#"&#%J#4*(.)/%4/*.4*)*"%4/.%&/,(N(,%)(&%,*,+('#%&#,%#"*,+#,%H5(%,(%*.)*4#.2%C/(<*4*(.+(%)(%"()544*V.%$%P%F@QP%F@QP%F@QP%F@QP%F@Q2
8*M5N#"%#%(,4#&#%LOXLOXLOXLOXLOX%&#%3(",3(4+*:#%4#M#&&("#%)(%&#%3*($#%"(3"(,(.+#)#%3/"%3&#.+#%?%#&$#)/2%C/&/4#"&#%J#4*(.)/%4/*.4*)*"4/.%&/,%(N(,%)(&%,*,+('#%&#,%#"*,+#,%H5(%,(%*.)*4#.2%C/(<*4*(.+(%)(%"()544*V.%$%P%F@QP%F@QP%F@QP%F@QP%F@Q2
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMA 15
Lámina Nº 26 PERSPECTIVA CABALLERA
O
O
O O
Z Z
Y
O
O
X
X
X
X
X Y
Z
Z
Y
Y
Z
8*M5N#"%#%(,4#&#%LOXLOXLOXLOXLOX%&#%3(",3(4+*:#%4#M#&&("#%)(%&#%3*($#%"(3"(,(.+#)#%(.%3&#.+#%?%#&$#)/2%C/&/4#"&#%J#4*(.)/%4/*.4*)*"%4/.&/,%(N(,%)(&%,*,+('#%&#,%#"*,+#,%*.)*4#)#,2%C/(<*4*(.+(%)(%"()544*V.%$%P%LeDP%LeDP%LeDP%LeDP%LeD2
8*M5N#"%#%(,4#&#%LOXLOXLOXLOXLOX%&#%3(",3(4+*:#%4#M#&&("#%)(%&#%3*($#%"(3"(,(.+#)#%(.%3&#.+#%?%:*,+#%&#+("#&2%C/&/4#"&#%J#4*(.)/4/*.4*)*"%4/.%&/,%(N(,%)(&%,*,+('#%&#,%#"*,+#,%*.)*4#)#,2%C/(<*4*(.+(%)(%"()544*V.%$%P%DeKP%DeKP%DeKP%DeKP%DeK2
*
30
48
18 12 6
30
12
18
24
48
36
18
30
18 12
36 6
30
24
18
18 126
1212
30
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMAS 16 Y 18
Lámina Nº 27 VISTAS DE PIEZAS Y ACOTACIÓN
ALZADO
ALZADO
8*M5N#"%&#,%+"(,%:*,+#,%)(%&#%3*($#%)#)#@%4/&/4;.)/&#,%(.%&#,%45#)"Z45&#,4/""(,3/.)*(.+(,2%A/,+("*/"'(.+(@%45#.)/%,(%J#?#%:*,+/%(&%!('#%XR@#4/+#"%&#%3*($#%(.%&#,%:*,+#,2
8*M5N#"%&#,%+"(,%:*,+#,%)(%&#%3*($#%)#)#@%4/&/4;.)/&#,%(.%&#,%45#)"Z45&#,4/""(,3/.)*(.+(,2%A/,+("*/"'(.+(@%45#.)/%,(%J#?#%:*,+/%(&%!('#%XR@#4/+#"%&#%3*($#%(.%&#,%:*,+#,2
12
30
186
36
186
30
30
12
6
66
12
36
6
12
18
48
18
618
12
6
24
18
48 12
30
6
6
24 24
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMAS 16 Y 18
Lámina Nº 28 VISTAS DE PIEZAS Y ACOTACIÓN
ALZADO
ALZADO
8*M5N#"%&#,%+"(,%:*,+#,%)(%&#%3*($#%)#)#@%4/&/4;.)/&#,%(.%&#,%45#)"Z45&#,4/""(,3/.)*(.+(,2%A/,+("*/"'(.+(@%45#.)/%,(%J#?#%:*,+/%(&%!('#%XR@#4/+#"%&#%3*($#%(.%&#,%:*,+#,2
8*M5N#"%&#,%+"(,%:*,+#,%)(%&#%3*($#%)#)#@%4/&/4;.)/&#,%(.%&#,%45#)"Z45&#,4/""(,3/.)*(.+(,2%A/,+("*/"'(.+(@%45#.)/%,(%J#?#%:*,+/%(&%!('#%XR@#4/+#"%&#%3*($#%(.%&#,%:*,+#,2
18
30 1818
6
6
6
6
6
48
18 24
18
12
30
18
48
6
12
18
12 24
12
12
12
18
30
6
6
306
6
12
18
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMAS 16 Y 18
Lámina Nº 29 VISTAS DE PIEZAS Y ACOTACIÓN
ALZADO
ALZADO
8*M5N#"%&#,%+"(,%:*,+#,%)(%&#%3*($#%)#)#@%4/&/4;.)/&#,%(.%&#,%45#)"Z45&#,4/""(,3/.)*(.+(,2%A/,+("*/"'(.+(@%45#.)/%,(%J#?#%:*,+/%(&%!('#%XR@#4/+#"%&#%3*($#%(.%&#,%:*,+#,2
8*M5N#"%&#,%+"(,%:*,+#,%)(%&#%3*($#%)#)#@%4/&/4;.)/&#,%(.%&#,%45#)"Z45&#,4/""(,3/.)*(.+(,2%A/,+("*/"'(.+(@%45#.)/%,(%J#?#%:*,+/%(&%!('#%XR@#4/+#"%&#%3*($#%(.%&#,%:*,+#,2
6
12 18
12
6
12
6
48
30
30
18
24
18
30
21 6
9
30
12
6
48
18
12
3
1212
30R6
6
Nombre:
J. G
ON
ZALO
GO
NZA
LO
Fecha:
NOTA:
TEMAS 16 Y 18
Lámina Nº 30 VISTAS DE PIEZAS Y ACOTACIÓN
ALZADO
ALZADO
6
12
12
18
* 8*M5N#"% &#,% +"(,% :*,+#,% )(% &#% 3*($#% )#)#@% 4/&/4;.)/&#,% (.% &#,45#)"Z45&#,%4/""(,3/.)*(.+(,2%A/,+("*/"'(.+(@%45#.)/%,(%J#?#%:*,+/(&%!('#%XR@%#4/+#"%&#%3*($#%(.%&#,%:*,+#,2
8*M5N#"%&#,%+"(,%:*,+#,%)(%&#%3*($#%)#)#@%4/&/4;.)/&#,%(.%&#,%45#)"Z45&#,4/""(,3/.)*(.+(,2%A/,+("*/"'(.+(@%45#.)/%,(%J#?#%:*,+/%(&%!('#%XR@#4/+#"%&#%3*($#%(.%&#,%:*,+#,2
*