```Randy H. Shih
Jack Zecher
PUBLICATIONS
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Lesson 1
Geometric Construction Basics
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Introduction
Learning to use a CAD system is similar to learning a new language. We need to begin
with the basic alphabets and learn how to use them correctly and effectively through
practice. This will require learning some new concepts and skills as well as learning a
different vocabulary. All CAD systems create designs using basic geometric entities.
Many of the constructions used in technical designs are based upon two-dimensional
planar geometry. The method and number of operations that are required to accomplish
the construction are different from one system to another.
In order to become effective in using a CAD system, we must learn to create geometric
entities quickly and accurately. In learning to use a CAD system, Lines and Circles are
the first two, and perhaps the most important two, geometric entities that we need to
master the skills in creating and modifying. Straight lines and circles are used in almost
all of the technical designs. In examining the different types of planar geometric entities,
we can see that triangles and polygons are planar figures bounded by straight lines.
Ellipses and Splines can be constructed by connecting arcs with different radii. As we
gain some experience in creating lines and circles, the similar procedures can be applied
to create other geometric entities. In this lesson, we will examine the different ways of
creating lines and circles in AutoCAD® LT 2000.
1. Select the AutoCAD® LT 2000 option on the program menu or select the
AutoCAD® LT 2000 icon on the desktop. Once the program is loaded into
memory, the AutoCAD® LT 2000 Drawing Screen and the Startup dialog
box will appear on the screen.
2. In the Startup dialog
box, select the Start
from Scratch icon
with a single click of
the left-mousebutton.
Start from scratch
3. In the Default
Settings section, Pick
English (Feet and
Inches) as the
drawing units.
English
OK
4. Pick OK in the
Startup dialog box to
accept the selected
settings.
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Using the LINE command
1. Move the graphics cursor to the first
icon in the Draw toolbar. This icon is
the LINE icon. A Help-tip box appears
next to the cursor and a brief
description of the icon is displayed at
the bottom of the AutoCAD Drawing
Screen: "Creates Straight line
segments: LINE."
Draw
Toolbar
Coordinates of the location of
the graphics cursor.
2. Select the icon by clicking once with
the left-mouse-button; this will
activate the LINE command. In the
command prompt area, near the bottom
of the AutoCAD Drawing Screen, the
message "_line Specify first point:" is
identify the starting location of a
straight line.
3. Move the graphics cursor inside the Graphics window and watch the display of
the coordinates of the graphics cursor at the bottom of the AutoCAD LT Drawing
Screen. The three numbers represent the location of the cursor in the X and Y
directions. We can treat the Graphics window as if it is a piece of paper and we
are using the graphics cursor as if it is a pencil with which to draw.
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4. We will create a freehand sketch of a fivepoint star using the LINE command. Create
the sketch near the center of the Drawing
window. Do not be overly concerned with
the size or the accuracy of your freehand
sketch. This exercise is to give you a feel for
the AutoCAD® LT 2000 user interface.
5. Start at a location about one-third from the
bottom of the Graphics window, then leftclick once to position the starting point of
our first line. This will be point 1 of our
sketch. Next move the cursor upward and
toward the right side of point 1. Notice the
rubber-band line that follows the graphics
cursor in the Graphics window. Left-click
again and we have created our first line of
the sketch.
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6. Move the cursor to the left of point 2 and create a horizontal line about the
same length as the first line on the screen.
7. Repeat step 5 and complete the freehand sketch by adding three more lines
(from point 3 to point 4, then connect to point 5 and back to point 1).
8. Notice that the LINE command remains
activated even after we connected the last
segment of the line to the starting point (point
1) of our sketch. Inside the Graphics window,
click once with the right-mouse-button and a
popup menu appears on the screen.
9. Select Enter with the left-mouse-button to end
the LINE command. (This is equivalent to
hitting the [Enter] key on the keyboard. The
right-mouse-click brings up more options and
we should get used to using the option menu.)
10. Move the cursor near point 2 and point 3, and
estimate the length of the horizontal line by
watching the displayed coordinates for each
point at the bottom of the screen.
Visual reference
The method we just used to create the freehand sketch is known as the interactive
method, where we use the cursor to specify locations on the screen. This method is
perhaps the fastest way to specify locations on the screen. However, it is rather difficult
to try to create a line of a specific length by watching the displayed coordinates. It would
be helpful to know what one-inch or one-meter looks like on the screen while we are
creating entities. AutoCAD LT 2000 provides us with many tools to aid the construction
of our designs. We will use the GRID and SNAP options to get a visual reference as to
the size of objects and learn to restrict the movement of the cursor to a set increment on
the screen.
The Status Bar area is located at the bottom of the AutoCAD LT Drawing Screen. The
words SNAP, GRID, ORTHO, POLAR, OSNAP, LWT and MODEL appearing to the
right of the coordinates are buttons that we can left-click to turn these special options ON
and OFF. When the corresponding button is highlighted, the specific option is turned on.
These buttons act as toggle switches; each click of the button will toggle the option on or
off. Using the buttons is a quick and easy way to make changes to these Drawing Aid
options. We can toggle the options on and off in the middle of another command.
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Option Buttons
GRID ON
1. Left-click the GRID button in the Status Bar to turn ON the GRID option.
(Notice in the command prompt area, the message “<Grid on>” is also
displayed.)
2. Move the cursor inside the Graphics window, and estimate the distance in
between the grid points by watching the coordinates display at the bottom of the
screen.
GRID turned ON
The GRID option creates a pattern of dots that extends over an area on the screen.
Using the grid is similar to placing a sheet of grid paper under a drawing. The grid
helps you align objects and visualize the distance between them. The grid is not
displayed in the plotted drawing. The default grid spacing, which means the distance
in between two dots on the screen, is 0.5 inches. We can see that the sketched
horizontal line in the above sketch is about 2.5 inches long.
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SNAP ON
1. Left-click the SNAP button in the Status Bar to turn ON the SNAP option.
2. Move the cursor inside the graphics window, and move the cursor diagonally
on the screen. Observe the movement of the cursor and watch the coordinates
display at the bottom of the screen.
The SNAP option controls an invisible rectangular grid that restricts cursor movement to
specified intervals. When SNAP mode is on, the screen cursor and all input coordinates
are snapped to the nearest point on the grid. The default snap interval is 0.5 inches, and
aligned to the grid points on the screen.
3. Click on the LINE icon in the Draw toolbar. In the
command prompt area, the message “_line Specify first
point:” is displayed.
4. Create another sketch of the star with the GRID and SNAP
options switched on.
5. Use the right-mouse-button and select Enter in the
popup menu to end the LINE command if you haven’t
done so.
6. In the command prompt area, notice that “Command:” is displayed. This
indicates that AutoCAD LT is waiting for us to activate the next desired
command.
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Using the ERASER
One of the advantages of using a CAD system is the ability to remove entities without
leaving any marks. We will erase two of the lines using the ERASE command.
1. Pick Erase in the Modify toolbar. (The icon is the first
icon in the Modify toolbar. The icon is a picture of an
eraser at the end of a pencil.) The message “Select
objects” is displayed in the command prompt area and
AutoCAD awaits us to select the objects to erase.
2. Left-click the SNAP button on the Status Bar to turn
off the SNAP option so that we can more easily move
the cursor on top of objects. We can toggle the Status
Bar options on and off in the middle of another
command.
3. Select any two lines on the screen, and right-mouseclick once to accept the selections. The selected two
lines are erased.
Repeat the last command
1. Inside the Graphics window, click once with the
right-mouse-button to bring up the popup option
2. Pick Repeat Erase, with the left-mouse-button, in
the popup menu to repeat the last command. Notice
the other options available in the popup menu.
AutoCAD LT 2000 offers many options to accomplish the same task. Throughout this
text, we will emphasize the use of the new AutoCAD Heads-up DesignTM interface,
which means focus on the screen, not on the keyboard.
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3. Move the cursor to a location that is above and toward the left side of the
entities on the screen. Left-mouse-click once to start a corner of a rubberband window.
First corner
Second corner
4. Move the cursor toward the right and below the entities, then left-mouse-click
to enclose all the entities inside the selection window. Notice all entities that
are inside the window are selected.
5. Inside the Graphics window, right-mouse-click to proceed with erasing the
selected entities.
On your own, create a sketch of your choice using the LINE command. Experiment
with using the different commands we have discussed so far, such as switching the
GRID and SNAP options on and off in the middle of a command.
Do not be in a hurry to rush through the tutorials. Build up your CAD skills by
familiarizing yourself with the commands and options demonstrated, along with the
concepts discussed in the lessons. Feel free to repeat, at any time, any of the lessons.
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Designs and drawings created in a CAD system are
usually defined and stored using sets of points in
what is called world space. In most CAD systems,
the world space is defined using the threedimensional Cartesian coordinate system. Three
mutually perpendicular axes, usually referred to as
the X, Y, and Z axes, define this system. The
intersection of the three coordinate axes forms a point
called the origin. Any point in world space can then
be defined as the distance from the origin in the X, Y
and Z directions. In most CAD systems, the direction
of the arrows shown on the axes identify the positive
sides of the coordinates.
A CAD file, which is the electronic version of the design, contains data that describe the
entities created in the CAD system. Information such as the coordinate values in world
space for all endpoints, center points, etc., along with the descriptions of the types of
entities are all stored in the file. Knowing that AutoCAD stores designs by keeping
coordinate data helps us understand the inputs required to create entities.
WCS icon
The icon near the bottom left corner of the default AutoCAD Graphics Window shows
the positive X-direction and positive Y-direction of the coordinate system that is active.
The letter W appearing in the icon indicates that the world coordinate system (WCS) is
active. The world coordinate system is a coordinate system used by AutoCAD as the
basis for defining all objects and other coordinate systems. We can think of the origin of
the world coordinate system as a fixed point being used as a reference for all
measurements. The default orientation of the Z-axis can be considered as positive values
in front of the monitor and negative values inside the monitor.
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Cartesian and Polar Coordinate Systems
In a two-dimensional space, a point can be represented using different coordinate
systems. The point can be located, using Cartesian coordinate system, as X and Y units
away from the origin. The same point can also be located using the polar coordinate
system, as r and units away from the origin.
For planar geometry, the polar coordinate system is very useful for certain applications.
In the polar coordinate system, points are defined in terms of a radial distance, r, from the
origin and an angle between the direction of r and the positive X axis. The default
system for measuring angles in AutoCAD LT 2000 defines positive angular values as
counter-clockwise from the positive X-axis.
Absolute and Relative Coordinates
AutoCAD LT 2000 also allows us to use absolute and
relative coordinates to quickly construct objects.
Absolute coordinate values are measured from the
current coordinate system's origin point. Relative
coordinate values are specified in relation to previous
coordinates.
The coordinate display area can also be used as a
toggle switch, each left-mouse-click will toggle the
coordinate display on or off.
In AutoCAD LT 2000, the absolute coordinates and the Relative coordinates can be used
in conjunction to the Cartesian and Polar coordinate systems. By default, AutoCAD
expects us to enter values in Absolute Cartesian coordinates, distances measured from
the current coordinate system's origin point. We can switch to using the Relative
coordinates by using the @ symbol. The @ symbol is used as the Relative coordinates
specifier, which means that we can specify the position of a point in relation to the
previous point.
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Defining Positions
In AutoCAD, there are five methods to specify the locations of points when we create
planar geometric entities.
Interactive method: Use the cursor to select on the screen.
Absolute Coordinates (Format: X,Y): Type the X and Y coordinates to locate the
point on the current coordinate system relative to the origin.
Relative rectangular coordinates (Format: @X,Y): Type the X and Y coordinates
relative to the last point.
Relative polar coordinates (Format: @Distance<angle): Type a distance and angle
relative to the last point.
Direct Distance Entry Technique: Specify a second point by first moving the cursor
to indicate direction and then entering a distance.
The Guide Plate
We will next create a mechanical design using the different coordinate entry methods.
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Use the ERASE command and erase all entities on the screen before proceeding to the
next section.
The rule for creating CAD designs and drawings is that they should be created Full Size
using real-world units. The CAD database contains all the definitions of the geometric
entities and the design is considered as a virtual, full-sized object. Only when a printer or
plotter transfers the CAD design to paper is the design scaled to fit on a sheet. The
tedious task of determining a scale factor so that the design will fit on a sheet of paper is
taken care of by the CAD systems. This allows the designers and CAD operators to
concentrate their attentions on the more important issues – the design.
1. Select the LINE command icon in the Draw toolbar. In the
command prompt area, near the bottom of the AutoCAD
Graphics window, the message "_line Specify first point:" is
displayed. AutoCAD expects us to identify the starting
location of a straight line.
2. In the command prompt area, we will locate the starting
point of our design at the origin of the world coordinate
system.
Command: _line Specify first point: 0,0 [Enter]
(Type 0,0 in the command prompt area and press the
[Enter] key once.)
3. We will create a horizontal line by entering the absolute coordinates of the
second point.
Specify next point or [Undo]: 5.5,0 [Enter]
(0,0)
(5.5,0)
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The line we created is aligned to the bottom edge of the Drawing window. Let us
adjust the viewing of the line by using the PAN Realtime command.
4. Click on the PAN Realtime icon in the
standard toolbar area. The icon is the picture
of a hand with four arrows.
The PAN command enables us to move the
view to a different position. This function acts
as if you are using a video camera.
5. Move the cursor, which appears as a hand inside the graphics window, near
the center of the drawing window, then push down the left-mouse-button and
drag the display toward the right and top side until we can see the sketched
line. (Notice the scroll bars can also be used to adjust viewing of the display.)
6. Press the [Esc] key to exit the PAN command. Notice that AutoCAD goes
back to the LINE command.
7. We will create a vertical line by using the relative rectangular coordinates
entry method, relative to the last point we specified
Specify next point or [Close/Undo]: @0,2.5 [Enter]
8. We can mix any of the entry methods in positioning
the locations of the endpoints. Move the cursor to the
Status Bar area, and turn on the GRID and SNAP
options.
SNAP & GRID ON
9. Create the next line by picking the location, world coordinates (8,2.5), on the
screen.
10. We will next use the relative polar coordinates entry method, relative to the
last point we specified
Specify next point or [Close/Undo]: @3<90 [Enter]
(Distance is 3 inches and an angle of 90 degrees)
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Reference Coordinate System
aligned at the previous point
11. Using the relative rectangular
coordinates entry method to
create the next line, we can
imagine a reference coordinate
system aligned at the previous
point. Coordinates are measured
along the two reference axes.
Specify next point or [Close/Undo]:
@-1.5,1 [Enter]
(-1.5 and 1 inches are measured
relative to the reference point.)
12. Move the cursor directly to the left of the last point and use the direct distance
entry technique by entering 6.5 [Enter].
13. For the last segment of the sketch, we can use the CLOSE option
to connect back to the starting point. Inside the Graphics
window, right-mouse-click and a popup menu appears on the
screen.
14. Select Close with the left-mouse-button to connect back to the
starting point and end the LINE command.
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Creating Circles
to quickly activate the desired commands. Besides using the Draw toolbar, we can also
select the different Draw commands through the pull-down menus.
1. In the pull-down menus, select:
[Draw] => [Circle] => [Center, Diameter]
Notice the different options available under the circle submenu:
Center Point: Draws a circle based on a center point and a diameter or a radius.
3 Points: Draws a circle based on three points on the circumference.
2 Points: Draws a circle based on two endpoints of the diameter.
to two objects.
TTT—Tangent, Tangent, Tangent: Draws a circle tangent to three objects.
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2. In the command prompt area, the message “Specify center point for circle or
the location of a point or enter an option. We can use any of the four
coordinate entry methods to identify the desired location. We will enter the
world coordinates (3,3) of the center point for the first circle.
Specify center point for circle or [3P/2P/Ttr (tan tan radius)]: 3,3 [Enter]
3. In the command prompt area, the message “Specify diameter of circle:” is
displayed.
Specify diameter of circle: 2.5 [Enter]
4. Inside the Graphics window, right-mouse-click
to bring up the popup option menu.
5. Pick Repeat Center, Diameter with the leftmouse-button in the popup menu to repeat the
last command.
6. Using the relative rectangular coordinates entry
method, relative to the center-point coordinates
of the first circle, we specify the location as
(2.5,2).
Specify center point for circle or [3P/2P/Ttr (tan tan radius)]: @2.5,2 [Enter]
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7. In the command prompt area, the message “Specify Diameter of circle:
<2.50>” is displayed. The default option for the Circle command in
brackets.
Specify Diameter of circle<2.50>: 1.5 [Enter]
1. In the pull-down menus, select:
[File] >> [Save As]
2. In the Save Drawing As dialog box, select the folder in which you want to
store the CAD file and enter GuidePlate in the File name box.
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Select the folder to
store the file.
Enter GuidePlate
3. Pick SAVE in the Save Drawing As dialog box to accept the selections and
save the file.
To exit AutoCAD® LT 2000, select File then choose Exit from the pull-down menu
or type QUIT at the command prompt.
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Questions:
1. What is the first thing we should consider when starting a new model?
2. How do the GRID and SNAP options assist us in sketching?
3. List and describe the different coordinate entry methods available in AutoCAD LT?
4. List and describe two types of coordinate systems commonly used for planar
geometry.
5. Identify the following commands:
(a)
(b)
(c)
(d)