48-175 descriptive geometry
TRANSCRIPT
![Page 1: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/1.jpg)
48-175 Descriptive Geometry
Spatial Relations on Lines
1
![Page 2: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/2.jpg)
Lines parallel to a plane
A line is parallel to a plane if it has no common point with the plane.
To test whether a given line and plane are parallel:
simply, construct an edge view of the plane and project the line into the same view; if the line appears in point view or parallel to the edge view, then it cannot meet the plane in a point, and is therefore parallel to the plane
This fact can be used to construct a plane parallel to a given line or a line parallel to a given plane.
![Page 3: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/3.jpg)
2
1
M
B
C
A
O
O
C
A
B
1 3
Line through O parallel to theedge view of plane ABC
2
1
M
O
B
A
C
B
C
A
O
O
C
A
B
1 3
Two possible lines parallel toplane ABC through point O
Line through O parallel to theedge view of plane ABC
2
1
M
O
B
A
C
B
C
A
O
O
C
A
B
How do we locatepoints M and N?
1 3
Two possible lines parallel toplane ABC through point O
Line through O parallel to theedge view of plane ABC
2
1
M
N
M
O
B
A
C
B
C
A
O
O
C
A
B
M
N
How do we locatepoints M and N?
1 3
Two possible lines parallel toplane ABC through point O
Line through O parallel to theedge view of plane ABC
2
1
M
N
N
M
O
B
A
C
B
C
A
O
O
C
A
B
M
N
line parallel through a point parallel to a plane
![Page 4: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/4.jpg)
parallel planes
How do we determine if two planes are parallel ?
2
1
D
E
E
F
F
B
C
A
D
C
A
B
by constructing an auxiliary view that shows
one plane in edge view; if the other plane is
also seen in edge view then the two planes
are parallel
![Page 5: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/5.jpg)
parallel planes
Constructing an auxiliary view that shows one plane in edge view; if the other plane is also seen in edge view then the two planes are parallel
1 3
2
1
D
E
E
F
F
C
B
B
C
A
D
C
A
B
E
parallel edge viewsindicate parallel planes
1 3
2
1
D
D
E
E
F
F
F
C
A
B
B
C
A
D
C
A
B
E
![Page 6: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/6.jpg)
line perpendicular to plane (normal)
A line is perpendicular to a plane if every line in the plane that passes through the point of intersection of the given line and the plane makes a right angle with the given line Line AB is perpendicular to
the plane
Lines LM, NO, PQ alllie in the plane
B
A
P
Q
L M
N
O
![Page 7: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/7.jpg)
perpendicular line to plane (normal)
p
90º90º
32
2
1
p is a planeLine AB is a normal to itLines LM, NO and PQ lie in the plane
A
BM,NL,O
B M,QL,P
P QA,B
L
MN
O
A
![Page 8: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/8.jpg)
direction of the normal to a plane
normal is perpendicularto the edge view of plane
2
1
direction of thenormal in view #2
TL
normal is perpendicularto the edge view of plane
1 3
2
1
direction of thenormal in view #1
90º
direction of thenormal in view #2
TL
normal is perpendicularto the edge view of plane
1 3
2
1
direction of thenormal in view #1
90º
direction of thenormal in view #2
![Page 9: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/9.jpg)
direction of the normal to a plane
direction of thenormal in view #2
direction of thenormal in view #1
2
1
TL
direction of thenormal in view #2
90º
direction of thenormal in view #1
1
2
TL
TL
2
1
direction of thenormal in view #2
direction of thenormal in view #1
90º
90º
Two-view method to find direction (bearing)
![Page 10: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/10.jpg)
quiz: perpendicular to the plane at point P
1
2
B
A
C
P
A
C
B
1
2
P
B
A
C
P
A
C
B
1
2
P
B
A
C
P
A
C
B
1
2
P
B
A
C
P
A
C
B
![Page 11: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/11.jpg)
shortest distance from a point and a plane
Observer's line of sight – plane ABC is seen as an edgeand true length of OP appears
Shortest line (OP) frompoint O to plane ABC
Lines AD and EFlie in the plane ABC
P
A
C
B
O
D
E
F
![Page 12: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/12.jpg)
2
1
C
A
A
C
Edge view of plane ABC
True length of the shortestline from M to the plane
2
1
13
P
M
C
B
MC
A
B
M
A
C
Bh
h
Edge view of plane ABC
True length of the shortestline from M to the plane
P is located by using thetransfer distance from view #3or by tracing a line on theplane through P
2
1
13
P lies on the perpendicular from Mto the true length line in view #1
P
P
P
M
C
A
B
MC
A
B
M
A
C
Bh
h
Edge view of plane ABC
True length of the shortestline from M to the plane
P is located by using thetransfer distance from view #3or by tracing a line on theplane through P
2
1
13
P lies on the perpendicular from Mto the true length line in view #1
P
P
P
M
C
A
B
MC
A
B
M
A
C
B
![Page 13: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/13.jpg)
perpendicular planes
this requires finding edge views of the plane and seeing if they are perpendicular to each other – which we will consider it later when we
consider lines of intersection
how do we determine if a plane is perpendicular to a given plane ?
![Page 14: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/14.jpg)
revisiting an old problem – shortest distance to a line
![Page 15: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/15.jpg)
constructing shortest distance to a line (line method)
As line AB is in true length, the constructedperpendicular from X to AB produces point Y
True length of theshortest distance
1
2
A
X
A
BX
TL
As line AB is in true length, the constructedperpendicular from X to AB produces point Y
True length of theshortest distance
31
1
2
X
A
B
A
X
A
BX
TL
4 3
As line AB is in true length, the constructedperpendicular from X to AB produces point Y
Point view of line AB
True length of theshortest distance
31
1
2
X
AB,Y
X
A
B
A
X
A
BX
TL
Project back from view #1 to get Y
Project back from view #3 to get Y
4 3
As line AB is in true length, the constructedperpendicular from X to AB produces point Y
Point view of line AB
True length of theshortest distance
31
1
2
Y
Y
Y
X
AB,Y
X
A
B
A
X
A
BX
![Page 16: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/16.jpg)
constructing shortest distance to a line (plane method)
ABX defines a plane
X Y is the shortestdistance from X to AB
1
2
A
B
X
A
BX
ABX defines a plane
X Y is the shortestdistance from X to AB
Edge view of ABX
31
1
2
A
X
B
A
B
X
A
BX
ABX defines a plane
X Y is the shortestdistance from X to AB
43
Edge view of ABX True shape of ABX3
1
1
2
A
XX
B
A
B
X
A
BX
ABX defines a plane
X Y is the shortestdistance from X to AB
Project back from view #4 to get Y
43
Project back from view #1 to get Y
Edge view of ABX True shape of ABX3
1
1
2
A
XX
B
A
B
X
A
BX
![Page 17: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/17.jpg)
shortest distance between skew lines
A
B
D
C
Line XY is the shortest distancebetween skew lines AB and CDas it is perpendicular to both lines
90°
90°X
Y
![Page 18: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/18.jpg)
shortest distance between skew lines
2
1
A
B
C
D
B
A
D
C
![Page 19: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/19.jpg)
shortest distance between skew lines (line method)
90°
90°
Common perpendicular XYbetween skew lines AB andCD in view #1
AB is in true length in view #3
Common perpendicular XY betweenskew lines AB and CD in view #2
True length of shortest lineXY is seen in view #4
4 3
3
1
2
1
X
Y
X
X
Y
Y
YD
C
AB, X
CD
AB
A
B
C
D
B
A
D
C
![Page 20: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/20.jpg)
shortest distance between skew lines (plane method)
2
1
A
B
C
D
B
A
D
C
HL2
1
Y
X
W
WX
A
B
C
B
A
D
C
![Page 21: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/21.jpg)
shortest distance between skew lines (plane method)
HL
43
Shortest distance RS between skew lines AB and CD
Plane CXYD seen inedge view in view #3
13
CXYD is a plane
XY is parallel to AB in view #1and passes through W
XY is parallel to AB in view #2and meets CD at WDY is parallel to folding line 1|2
2
1
S
R
S
RS
R
R,S
C
D
B
A D, Y
C,X
A
B
Y
X
W
WX
Y
A
B
C
D
B
A
D
C
![Page 22: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/22.jpg)
shortest horizontal distance between skew lines
parallel
Shortest horizontal distancebetween the two skew lines
Horizontal projection plane
XY
Y
X
![Page 23: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/23.jpg)
shortest horizontal distance between skew lines
1
2
B
A
D
C
A
B
D
C
![Page 24: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/24.jpg)
shortest horizontal distance between skew lines
HL
TL
View #3 is an elevation
XY is parallel to the edge view ofthe horizontal planeXY is also the true length of theshortest horizontal line
CD is parallel to the edgeview of plane ABLM inview #3
BL is intrue length
LM is parallel to CDin view #1
LM is parallel toCD in view #2
2
1
M
A
D
CB,L
L
M
L
MC
A
B
A
B
D
C
![Page 25: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/25.jpg)
shortest horizontal distance between skew lines
HL
TL
View #3 is an elevation
XY is parallel to the edge view ofthe horizontal planeXY is also the true length of theshortest horizontal line
3
CD is parallel to the edgeview of plane ABLM inview #3
4
1
3
BL is intrue length
LM is parallel to CDin view #1
LM is parallel toCD in view #2
2
1
M
X Y
Y
X
Y
X
X,Y
B
C
A
D
A
D
CB,L
L
M
L
MC
D
A
B
A
B
D
C
![Page 26: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/26.jpg)
shortest grade distance between skew lines
HL
TL
15°
View #3 is an elevation
XY is also the true length of the shortest upward 15° grade line
3
4
1
3
BL is intrue length
LM is parallel to CDin view #1
LM is parallel toCD in view #2
2
1
Y
X
Y
X
Y
X
X,Y
B
C
D
A
O4
M
A
D
CB,L
L
M
L
MC
D
A
B
A
B
D
C
N4
![Page 27: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/27.jpg)
which grade distance?
HL
TL
90°
20% grade
View #3 is an elevation
XY is also the true length of theshortest downward 20%grade line
3
4
1
3
BL is intrue length
LM is parallel to CDin view #1
LM is parallel toCD in view #2
2
1
XY
Y
X
Y
X
C
DB
A
M
A
D
CB,L
L
M
L
MC
D
A
B
A
B
D
C
![Page 28: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/28.jpg)
visibility
Observers line of sight in whichline AB is above line CD
D
CB
A
![Page 29: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/29.jpg)
quiz: find a point on a line equidistant to two points
l
l
f
t
A
B
B
A
l
l
l
f
t
B
A
A
B
B
A
l
l
TL
l
Project back from top view to get X
Project back from view #1 to get X
1t
f
t
X
X
X
midpoint
B
A
A
B
B
A
l
l
TL
l
1t
f
t
X
X
midpoint
B
A
A
B
B
A
![Page 30: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/30.jpg)
quiz: locating a line between two skew lines through a point
![Page 31: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/31.jpg)
quiz: construct a line at a certain grade
Lines AB and CD specify centerlines of two existing sewers as shown in the figure. The sewer pipes are to be connected by a
branch pipe having a downward grade of
2:7 from the higher to the lower pipe. Given that point C is 20' North of point A, the problem is to determine the true length and bearing of the branch pipe and show this pipe in all views. Line AC (in plan) measures 20'.
![Page 32: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/32.jpg)
20'
f
t
Y
X
Y
C
D
B
D
C
A
A
B
![Page 33: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/33.jpg)
20'
1t
XD
C
B,Y
A,X
Y
C
D
BA
TL = 30'-8"
bearing = S 51.5° E
21
2:7 grade
D
C
B
AD
C
B,Y
A,X
![Page 34: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/34.jpg)
20'
bearing = S 51.5° E
f
t
X
Y
Y
C
D
B
D
C
A
A
B
![Page 35: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/35.jpg)
quiz: construct a line at a certain grade
![Page 36: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/36.jpg)
quiz: shortest distance from X to nearest face
5'-0"4'-0"
3'-6"
1'-6"
1'-0"
45°
X
X
![Page 37: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/37.jpg)
a
f
t
X
X
![Page 38: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/38.jpg)
a
edge view of face a
t1
f
t
X1
X
X
![Page 39: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/39.jpg)
Y is not on face p∴ need to find point on face anearest Y in the same plane
Y is the foot of the perpendicularfrom X to the plane of face p
p
edge view of face p
t1
f
t
Y
Y
X
X
X
![Page 40: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/40.jpg)
p
Z is projected back from view #1
Z is projected back from view #2
true length of ABZ is perpendicular from XY to AB in view #2
2
1
t
1
f
t
Z
Z
Z
X,YA
Y
Y
B
A
X
X
X
AB
![Page 41: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/41.jpg)
= 2'-1"
true shortest distance betweenX and Z is given in view #3
3t
p
2
1
t1
f
t
Z
X
Z
Z
Z
X,YA
Y
Y
B
A
X
X
X
AB
![Page 42: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/42.jpg)
Problem
Three equal legs of a surveyor’s tripod are located in their relationship to the plumb line.Leg A bears N30°W and has a slope of 30°Leg B is 3’-3” due east of the plumb line and at the same elevation as the plumb lineLeg C bears S45°W and has a slope of 45°The plumb bob touches the bench mark at a vertical distance of 4’ below the top of the line
Determine TL of legs A, B and C ?
What is the angle B makes with plumb line?
Show legs in front and top views.
![Page 43: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/43.jpg)
Step 1
![Page 44: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/44.jpg)
Step 2
![Page 45: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/45.jpg)
![Page 46: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/46.jpg)
Problem
Two sewer lines AB and CB converge at manhole BA is 35’ north 10’ east of B and 30’ above BC is 20’ north 60’ west of B and 15’ above BA new line DB is located in the plane of ABC at a point 30’ due west of A
Using only two views locate D
What is the TL of each sewer line?
What is the angle of the plane ABC
![Page 47: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/47.jpg)
Step 1
![Page 48: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/48.jpg)
Step 2
![Page 49: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/49.jpg)
Step 3
![Page 50: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/50.jpg)
Problem AB is parallel to plane. Complete the view.
![Page 51: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/51.jpg)
Step
![Page 52: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/52.jpg)
Problem
Planes ABC and DEF
are parallel.
Complete the view
![Page 53: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/53.jpg)
Step
![Page 54: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/54.jpg)
What is the shortest length between non-
intersecting diagonals of adjacent faces of a cube?
![Page 55: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/55.jpg)
![Page 56: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/56.jpg)
Problem
Given two partial pipelines –
construct the shortest level pipeline to connect them.
These pipelines may be extended
![Page 57: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/57.jpg)
Step 1
![Page 58: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/58.jpg)
Step 2
![Page 59: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/59.jpg)
Step 3
![Page 60: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/60.jpg)
Problem involving perpendicular lines
Construct the pyramid with
base A(2, 2, 5), B(3.5, 1.5, 6), C(4.75, 2, 6) D(3.25, 2.5, 5)height 2.5
All measurements in inchesComplete top and front views with proper visibility ie., visible lines are
solid and not visible lines shown dashed.
![Page 61: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/61.jpg)
![Page 62: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/62.jpg)
![Page 63: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/63.jpg)
What is the clearance between a pipe and the ball?
![Page 64: 48-175 Descriptive Geometry](https://reader033.vdocuments.us/reader033/viewer/2022042107/6256db459515f00fda6a4754/html5/thumbnails/64.jpg)