chapter 2 using drawing tools & applied geometry
DESCRIPTION
Chapter 2 Using Drawing Tools & Applied Geometry. Using of Tools. Applied Geometry. TOPICS. Preparation of Tools. Preparation of Tools. Fastening Paper to Drafting Board. 1. Place the paper close to the table’s left edge. 2. Move the paper until its lower edge place about - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/1.jpg)
Chapter 2
Using Drawing Tools& Applied Geometry
![Page 2: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/2.jpg)
TOPICS
Preparation of Tools.
Using of Tools
Applied Geometry
![Page 3: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/3.jpg)
Preparation of Tools
![Page 4: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/4.jpg)
Fastening Paper to Drafting Board1. Place the paper close to the table’s left edge.
2. Move the paper until its lower edge place about
the top edge of T-square.
![Page 5: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/5.jpg)
3. Align the top edge of the paper with T-square blade.
4. Attach the paper’s corners with tape.
Fastening Paper to Drafting Board
![Page 6: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/6.jpg)
5. Move T-square down to smooth the paper.
6. Attach the remaining paper’s corners with tape.
Fastening Paper to Drafting Board
![Page 7: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/7.jpg)
1. Remove the wood with penknife while expose a
lead about 8-10 mm.
2. Polish the lead into a conical shape with a sandpaper.
3. Clean the lead with tissue paper.
Sharpening the Pencil
![Page 8: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/8.jpg)
Preparing the Compass
2. Adjust the needle and the lead so that the tip of
the needle extends slightly more than the lead.
1. Sharpen the lead with a sandpaper.
needle lead
![Page 9: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/9.jpg)
Using the Tools
![Page 10: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/10.jpg)
Straight line
Arc, Circle4. Circle template
1. T-square
2. Triangles
3. Compass
Tools Shape to be drawn
Function of the Tools
![Page 11: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/11.jpg)
Using the Compass
1. Locate the center of the circle by two intersecting lines.
2. Adjust the distance between needle and lead to a distance
equal to radius of the circle.
3. Set the needle point at center.
![Page 12: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/12.jpg)
4. Start circle.Start circle. Apply enough pressure to the needle,
holding compass handle between thumb and index fingers.
5. Complete circleComplete circle. Revolve handle clockwise.
Using the Compass
![Page 13: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/13.jpg)
Using a Circle Template
1. Draw two perpendicular lines that pass through center of
a circle to be drawn.
Construction line
Object line
2. Place the template till all marking coincide with center lines.
3. Tracing the circle. (Hold the pencil normal to the paper.)
GivenCenter of a circle to be drawn
![Page 14: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/14.jpg)
Draw a Horizontal Line
1. Press the T-square head against the left edge of the table.
2. Smooth the blade to the right.
![Page 15: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/15.jpg)
Draw a Horizontal Line3. Lean the pencil at an angle about 60o with the paper in the
direction of the line and slightly “toed in”.
4. Draw the line from left to right while rotating the pencil slowly.
![Page 16: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/16.jpg)
Draw a Vertical Line1. Set T-square as before. Place any triangle on T-square edge.
2. Slide your left hand to hold both T-square and triangle in
position.
![Page 17: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/17.jpg)
Draw a Vertical Line3. Lean the pencil to the triangle.
4. Draw the line upward while rotating the pencil slowly.
![Page 18: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/18.jpg)
Draw a line at 45o with horizontal
2. Draw the line in the direction as shown below.
1. Place 45o triangle on the T-square edge and press them
firmly against the paper.
![Page 19: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/19.jpg)
1. Place 30o-60o triangle on the T-square edge and press
them firmly against the paper.
2. Draw the line in the direction as shown below.
Draw a line at angle 30o and 60o
![Page 20: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/20.jpg)
0 deg.
15 deg.
30 deg.
45 deg.
60 deg.
75 deg.
90 deg.
= 30 + 45 deg
Alreadydemonstrated.
= 30 + 45 deg
Alreadydemonstrated.
Draw the lines at 15o increment
![Page 21: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/21.jpg)
A
B
Draw the line passing throughtwo given points
1. Place the pencil tip at one of the points.
2. Place the triangle against the pencil tip.
A
B
Given
3. Swing the triangle around the pencil tip
until its edge align with the second point.
4. Draw a line.
![Page 22: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/22.jpg)
Applied Geometry
![Page 23: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/23.jpg)
To Bisect a Line
1. Swing two arcs of any radius greater than half-length of
the line with the centers at the ends of the line.
2. Join the intersection points of the arcs with a line.
(not to scale)
A
B
r1
Given
A
B
r1
3. Locate the midpoint.
![Page 24: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/24.jpg)
To Bisect an Angle
2. Swing the arcs of any radius from the intersection
points between the previous arc and the lines.
3. Draw the line.
1. Swing an arc of any radius whose centers at the vertex.
(not to scale)
r1
Given
A
B
C
A
B
C
r2
r2
![Page 25: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/25.jpg)
To draw the line parallel to a given lineand passes through a given point
Given
+C
![Page 26: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/26.jpg)
To draw the line parallel to a given lineand passes through a given point
Given
+C
Repeat
![Page 27: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/27.jpg)
To draw the line parallel to a given linewith a specified distance
Given distance = r
r
![Page 28: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/28.jpg)
r
To draw the line parallel to a given linewith a specified distance
Repeat
Given distance = r
![Page 29: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/29.jpg)
To draw the line perpendicular to a given line at a given point
+C
Revolve method
![Page 30: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/30.jpg)
+C
To draw the line perpendicular to a given line at a given point
Repeat
Revolve method
![Page 31: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/31.jpg)
To draw the line perpendicular to a given line at a given point
+C
Adjacent-sides method
![Page 32: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/32.jpg)
+C
To draw the line perpendicular to a given line at a given point
Adjacent-sides method
Repeat
![Page 33: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/33.jpg)
To draw the line perpendicular to a given line at a given point
Using Compass
+C
![Page 34: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/34.jpg)
To draw the line perpendicular to a given line at a given point
Using Compass
r1
r2
+C
r2
r2 > r1
A
B
D
Repeat
![Page 35: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/35.jpg)
Adjacent-sides method
To draw the line perpendicular to a given line from a point not on the line
+C
![Page 36: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/36.jpg)
+C
To draw the line perpendicular to a given line from a point not on the line
Adjacent-sides method
Repeat
![Page 37: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/37.jpg)
Using compass+ C
To draw the line perpendicular to a given line from a point not on the line
![Page 38: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/38.jpg)
Using compass
r2
+ Cr2
r1
Note:You can also use revolve method. How ? Try by yourself !!!
To draw the line perpendicular to a given line from a point not on the line
B
A
D
Repeat
![Page 39: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/39.jpg)
+C
To draw a line making 15o with a given line and pass through a given point.
Given
![Page 40: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/40.jpg)
+C
To draw a line making 15o with a given line and pass through a given point.
Given
![Page 41: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/41.jpg)
To draw a line making 30o with a given line and pass through a given point.
+C
Given
![Page 42: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/42.jpg)
To draw a line making 75o with a given line and pass through a given point.
+C
Given
![Page 43: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/43.jpg)
FILLET AND ROUND
Sharp corner
Fillet
Round
Round
![Page 44: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/44.jpg)
FILLET AND ROUND
To draw the arc, we must find the location of the center of that arc.
How do we find the center of the arc?
![Page 45: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/45.jpg)
To draw an arc of given radius tangent to two perpendicular lines
Given arc radius r
r
r
![Page 46: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/46.jpg)
To draw an arc of given radius tangent to two perpendicular lines
Given arc radius rcenter of the arc
Starting point
Ending point
![Page 47: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/47.jpg)
To draw an arc of given radius tangent to two lines
Given arc radius r
++
rr
![Page 48: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/48.jpg)
To draw an arc of given radius tangent to two lines
Given arc radius r
T.P.1T.P.2
![Page 49: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/49.jpg)
C
To draw a line tangent to a circle at a point on the circle
Given
![Page 50: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/50.jpg)
To draw a line tangent to a circle from a point outside the circle
Given
C
mark a tangent point
![Page 51: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/51.jpg)
When circle tangent to other circle
C1
C2
Tangent point
R1
R2
R1 + R2
The center of two circles and tangent point lie on the same straight line !!!
![Page 52: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/52.jpg)
To draw a circle tangent to two circles I
+C2
Given
+C1
C+
Example
![Page 53: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/53.jpg)
+C1
Given Two circles and the radius of the third circle = R
To draw a circle tangent to two circles I
+C2
![Page 54: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/54.jpg)
+ +C1
C2
R + R1
Given Two circles and the radius of the third circle = R
R + R2
R1
R2
C
center of the arc
To draw a circle tangent to two circles I
R
Repeat
![Page 55: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/55.jpg)
C2
R2
When circle tangent to other circle
C1
Tangent point
R1
The center of two circles and tangent point must lie on the same straight line !!!
R2 R1
![Page 56: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/56.jpg)
Given
+C1
+C2
C+
To draw a circle tangent to two circles II
Example
![Page 57: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/57.jpg)
+ +C1
C2
To draw a circle tangent to two circles II
Given Two circles and the radius of the third circle = R
![Page 58: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/58.jpg)
+ +C1
C2
R – R2
To draw a circle tangent to two circles II
Given Two circles and the radius of the third circle = R
R – R1
R1
R2
C
R
Repeat
![Page 59: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/59.jpg)
+C1+C2
To draw a circle tangent to two circles III
Given Two circles and the radius of the third circle = R
R + R2
R – R1
R1
R2
C
![Page 60: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/60.jpg)
To draw an approximate ellipse
Given Major and minor axes
![Page 61: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/61.jpg)
To draw an approximate ellipse
Given Major and minor axes
Repeat
![Page 62: Chapter 2 Using Drawing Tools & Applied Geometry](https://reader036.vdocuments.mx/reader036/viewer/2022082203/56815a9c550346895dc81df5/html5/thumbnails/62.jpg)
How to Keep Your Drawing Clean
Do Don’t