| Learning Outcomes |
When you have completed this module, you will be able to:
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Geometry Lesson: Tangency
A point of tangency is the theoretical point where a line joins an arc, two arcs join each other, or two circles join each other making a smooth transition. A line is tangent to a circle or an arc when it passes touching only one point on the circle or arc. The tangent point is located where a line drawn perpendicular from the center of the circle or arc touches the line. Study Figure 12-1.
A fillet is a tangent arc. A tangent arc must be tangent at both ends where it connects to existing lines or arcs. Figure 12-2 shows five examples of fillets.
| AutoCAD Command: FILLET |
| The FILLET command is used to draw a tangent arc. It inserts an arc tangent to the two existing
drawing objects selected in the command. Shortcut: F |
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WORKALONG: Using the FILLET Command
Step 1
Start a new drawing using the template: 2D English.
Step 2
Save and name the drawing: AutoCAD 2D Workalong 12-1.
Step 3
Create layers: Object and Construction. Set layer: Object as the current layer.
Drawing Outside the Box |
Step 4
Using the LINE command and referring to the figures, draw the 6 lines to match the figure. (Figure Step 4A and 4B)
Step 5
Using the LINE command, draw the vertical line. (Figure Step 5A and 5B)
| AUTHOR’S COMMENTS: To draw this line, you must know its start point. Figure Step 5B shows how I solved the start point of the line. Since you don`t know the exact length of the line, guess at the length and try to draw it longer. I drew it 3.5 inches. Ensure you understand how I solved for the start point. |
Step 6
Using the LINE command, draw the inclined line. First you have to solve the angle. Guess at the length and try to make it longer. After you know the angle and the length, snap to end point of the existing to start the line. (Figure Step 6A and 6B)
| AUTHOR’S COMMENTS: Figure Step 6B shows the three steps I used to solve the angle of the line. Draw it longer than required since you don`t know its exact length. I drew it 2.0 inches long. |
Step 7
Using the principles you just learned, use the LINE command to draw the two lines on the left side of the object. (Figure Step 7)
Step 8
Enter the FILLET command, as shown below, and select the two vertical lines to insert the fillet (tangent arc). (Figure Step 8A, 8B, and 8C)
Command: FILLET
Current settings: Mode = NOTRIM, Radius = 0.5000
Select first object or [Undo/Polyline/Radius/Trim/Multiple]: T
Enter Trim mode option [Trim/No trim] : T
Select first object or [Undo/Polyline/Radius/Trim/Multiple]:
Command: (This commands simply sets the FILLET command to trim objects when filleted. You only have to do this the first time you use the FILLET command or if you re-set it to NOTRIM.)
Command: FILLET
Current settings: Mode = TRIM, Radius = 0.0000
Select first object or [Undo/Polyline/Radius/Trim/Multiple]: (Pick left vertical line)
Select first object or [Undo/Polyline/Radius/Trim/Multiple]: (Pick right vertical line)
Select second object or shift-select to apply corner:
Command:
| AUTHOR’S COMMENTS: When the lines selected in the FILLET command are parallel, AutoCAD will automatically calculate the radius of the arc for you, regardless of the current radius setting. Note how the radius is set to zero in this example. |
Step 9
Enter the FILLET command, as shown below, to insert a 0.5 radius fillet between the two lines. (Figure Step 9A. 9B, and 9C)
Command: FILLET
Current settings: Mode = TRIM, Radius = 0.0000
Select first object or [Undo/Polyline/Radius/Trim/Multiple]: R
Specify fillet radius <0.0000>: 0.5 (Set the radius for the fillet.)
Select first object or [Undo/Polyline/Radius/Trim/Multiple]: (Pick right vertical line)
Select second object or shift-select to apply corner: (Pick the horizontal line)
Command:
| AUTHOR’S COMMENTS: Since this fillet is inserted between lines that are not parallel, you must set the radius of the fillet. In this case, 0.5. |
Step 10
Using what you learned in Step 9, insert the 0.5 radius fillet on the other side to match the figure. (Figure Step 10)
Step 11
Using what you learned in Step 9 and 10, insert the two 0.75 radius fillets on top left and right corners. (Figure Step 11)
| AUTHOR’S COMMENTS: Ensure that you set the radius in the FILLET command to 0.75 before you select the lines to fillet. |
Step 12
Insert the four 1.0 radius fillets to match the figure. (Figure Step 12)
Step 13
Enter the CIRCLE command and draw 1.0 diameter circle by snapping to the center of the arc to locate the its center. The completed drawing should match the figure. (Figure Step 13A and 13B)
| AUTHOR’S COMMENTS: The circle and arc share the same center point. Ensure that AutoSnap is set to locate centers and Osnap is enabled. Use the CIRCLE command and snap to the center of the arc to locate the center of the circle. |
Step 14
Save and close the drawing.
WORKALONG: Drawing Tangent Lines
Step 1
Start a new drawing using the template: 2D English.
Step 2
Save and name the drawing: AutoCAD 2D Workalong 12-2.
Step 3
Create the layers: Object and Construction. Set Layer: Construction as the current layer.
Step 4
Referring to the figures, draw the 2 radius circle with its center at 10,10. (Figure Step 4A and 4B)
Step 5
Using polar coordinates, enter the LINE command, two times, to draw two construction lines. Start each line starting at the center of the circle and ending at the center of the other two circles. (Figure Step 5)
Step 6
Draw circles locating their centers at the endpoints of the lines you drew in Step 5. (Figure Step 6)
Step 7
Enter the LINE command, as shown below, to draw a line tangent to the two circles. Enter the TAN object snap mode manually by typing it in on the keyboard. (Figure Step 7)
Command: LINE
Specify first point: TAN to P1
Specify next point or [Undo]: TAN to P2 Specify next point or [Undo]:
Command:
| AUTHOR’S COMMENTS: Notice how you have to enter TAN for both ends of the line. It is a very common error to forget to enter it at the second end. Do not use AutoSnap, enter them manually by typing TAN on the keyboard and then press Enter. Note the AutoSnap marker when AutoCAD is finding the tangent location on the circle. |
Step 8
Using what you learned in Step 7, enter the LINE command and draw a line tangent to the two circles as shown in the figure. (Figure Step 8)
Command: LINE
Specify first point: TAN to P3
Specify next point or [Undo]: TAN to P4
Specify next point or [Undo]:
Command:
| AUTHOR’S COMMENTS: Note the AutoSnap Marker icon that displays when you use the TAN object snap mode. |
Step 9
Using what you just learned, insert the two tangent lines as shown in the figure. (Figure Step 9)
Step 10
Using the FILLET command, insert a 3.0 radius fillet as shown in the figures. (Figure Step 10A , 10B, and 10C)
Step 11
Change the layer of the objects from layer: Construction to layer: Object to match the figure. (Figure Step 11)
Step 12
Freeze layer: Construction. (Figure Step 12)
Step 13
Insert a 2.0 radius fillet to complete the drawing. (Figure Step 13)
Step 14
Save and close the drawing.
WORKALONG: Drawing Construction Techniques
Step 1
Start a new drawing using the template: 2D English.
Step 2
Save and name the drawing: AutoCAD 2D Workalong 12-3.
Step 3
Create layers: Object and Construction. Set layer: Construction as the current layer.
Step 4
Referring to the figures, enter the LINE command and draw the lines shown in the figures in two steps. (Figure 4A, 4B, and 4C)
| AUTHOR’S COMMENTS: Draw the vertical line on the left side any length over 4 inches. The length is not important at this time. |
Step 5
Enter the LINE command, as shown below, to draw two lines. (Figure Step 5)
Command: L
Specify first point: (end) P1
Specify next point or [Undo]: @2<150
(Since you don’t know the length of the line, draw a line of any length at the correct angle.)
Specify next point or [Undo]:
Command: L
Specify first point: (end) P2
Specify next point or [Undo]: @3<210
(Draw any length line at the correct angle.)
Specify next point or [Undo]:
Command:
Step 6
Enter the FILLET as shown below. Set the radius to 0 to create perfect corners. (Figure Step 6A and 6B)
Command: FILLET
Current settings: Mode = TRIM, Radius = 0.3500
Select first object or [Undo/Polyline/Radius/Trim/Multiple]: R
Specify fillet radius <0.3500>: 0
(Set the radius to zero.)
Select first object or [Undo/Polyline/Radius/Trim/Multiple]: P3
Select second object or shift-select to apply corner: P4
Command: F
(F is the shortcut for the command FILLET.)
Current settings: Mode = TRIM, Radius = 0.0000
Select first object or [Undo/Polyline/Radius/Trim/Multiple]: P5
Select second object or shift-select to apply corner: P6
Command:
| AUTHOR’S COMMENTS: By setting the fillet radius to zero, the FILLET command will trim the lines to create perfect corners. |
Step 7
Change the layer of the necessary lines to reside on layer: Object. Freeze layer: Construction. (Figure Step 7)
Step 8
Save and close the drawing.
| USER TIP: To insert an arc at the end of two parallel lines, use the FILLET command.Regardless of what radius is currently set in the FILLET command, AutoCAD will draw a tangent arc using the one-half distance between the lines as the radius. The lines do not have to be the same length. |
| Command: FILLET
Current settings: Mode = TRIM, Radius = 0.0 (Notice how the radius is set to zero. It can be any size.) Select first object or [Polyline/Radius/Trim]: P1 (The first line you pick will retain it’s original length and the second one will be trimmed or extended.) Select second object: P2 Command |
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| USER TIP: By setting the radius of the FILLET command to zero, the FILLET command will square the lines to make a perfect corner. The lines can be too short or too long or a combination of the two as shown in the figure on the right. |
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Key Principles
| Key Principles in Module 12 |
| Point of tangency is the theoretical point where a line joins an arc, two arcs join each other, or two circles join each other making a smooth transition. A fillet is a tangent arc. To construct a fillet, use the FILLET command. The rule of thumb to follow is ‘ If the arc you are drawing is tangent to both objects it is connecting to, use the FILLET command. If the arc is tangent to one or neither of the objects, use the ARC command ‘. Use the LINE command and the TAN object snap mode to draw lines tangent to two circles or arcs. Make sure that you apply it to both ends of the line. By setting the radius of the FILLET command to zero, the FILLET command will square two lines to make a perfect corner. |
Lab Exercise 12-1
Time allowed: 30 minutes.
| Drawing Name | Template | Units |
| AutoCAD 2D Lab 12-1 | 2D English | Inches |
| Layering Scheme |
| Layer Name | Objects on Layer | Color |
| Construction | Construction objects | 253 |
| Object | Lines, circle and arcs | Red |
Step 1
Draw the object shown in the figures using the layering scheme. (Figure Step 1A and 1B)
| AUTHOR’S COMMENTS: Do not delete the construction lines. |
Step 2
Set the insertion units and check your drawing with the key.
Step 3
Turn layer: Key off and freeze layer: Construction.
Step 4
Save and close the drawing.
| AUTHOR’S CONSTRUCTION TECHNIQUES: The following steps are the construction technique suggested by the author to help you learn how to construct objects using AutoCAD. It is only the suggested method and if you can complete the drawing accurately using a different construction technique, that is what is important. You may want to compare your construction technique with the authors. |
| AUTHOR’S CONSTRUCTION HINTS: Do your best to complete the lab exercise drawing without using the following hint. If you get stuck and cannot complete it on your own, use the following hint to help you. |
Hint 1
The dashed line shown in the dimensioned drawing indicates that the lines should be constructed tangent to the small circle from the circles on either end of the object. After the lines are inserted tangent to both circles, you can then insert the fillet. (Figure Hint 1)
Lab Exercise 12-2
Time allowed: 30 minutes.
| Drawing Name | Template | Units |
| AutoCAD 2D Lab 12-2 | 2D Metric | Millimeters |
| Layering Scheme |
| Layer Name | Objects on Layer | Color |
| Construction | Construction objects | 253 |
| Object | Lines, circle and arcs | Red |
Step 1
Draw the object shown in the dimensioned drawing using the layering scheme. (Figure Step 1A and 1B)
| AUTHOR’S COMMENTS: Do not delete the construction lines. |
Step 2
Set the insertion units and check your drawing with the key.
Step 3
Turn layer: Key off and freeze layer: Construction.
Step 4
Save and close the drawing.
| AUTHOR’S CONSTRUCTION TECHNIQUES: The following steps are the construction technique suggested by the author to help you learn how to construct objects using AutoCAD. It is only the suggested method and if you can complete the drawing accurately using a different construction technique, that is what is important. You may want to compare your construction technique with the authors. |
| AUTHOR’S CONSTRUCTION HINTS: Do your best to complete the lab exercise drawing without using the following hints. If you get stuck and cannot complete it on your own, use the following hints to help you. |
Hint 1
Draw a construction line from the midpoint of the line across the bottom of the slot 95 units in the positive Y direction. Draw a circle with its center at the end of the line. (Figure Hint 1)
Hint 2
Since you don’t know the exact length of the lines shown in the figure, draw them any length but in the correct direction. When you insert the fillets, the line will automatically be trimmed. (Figure Hint 2)
