- Objectives
- Objectives
- Overview
- Overview
- Coordinates for 3D Cad Modeling
- Coordinates for 3D Cad Modeling
- Geometric Entities
- Geometric Entities
- 4.1 Manually Bisecting a Line or Circular Arc
- 4.1 Manually Bisecting a Line or Circular Arc
- 4.2 Drawing Tangents to Two Circles
- 4.2 Drawing Tangents to Two Circles
- 4.3 Drawing an Arc Tangent to a Line or Arc and through a Point
- 4.3 Drawing an Arc Tangent to a Line or Arc and through a Point
- 4.4 Bisecting an Angle
- 4.4 Bisecting an Angle
- 4.5 Drawing a Line through a Point and Parallel to a Line
- 4.5 Drawing a Line through a Point and Parallel to a Line
- 4.6 Drawing a Triangle with Sides Given
- 4.6 Drawing a Triangle with Sides Given
- 4.7 Drawing a Right Triangle with Hypotenuse and One Side Given
- 4.7 Drawing a Right Triangle with Hypotenuse and One Side Given
- 4.8 Laying Out an Angle
- 4.8 Laying Out an Angle
- 4.9 Drawing an Equilateral Triangle
- 4.9 Drawing an Equilateral Triangle
- 4.10 Polygons
- 4.10 Polygons
- 4.11 Drawing a Regular Pentagon
- 4.11 Drawing a Regular Pentagon
- 4.12 Drawing a Hexagon
- 4.12 Drawing a Hexagon
- 4.13 Ellipses
- 4.13 Ellipses
- 4.14 Spline Curves
- 4.14 Spline Curves
- 4.15 Geometric Relationships
- 4.15 Geometric Relationships
- 4.16 Solid Primitives
- 4.16 Solid Primitives
- 4.17 Recognizing Symmetry
- 4.17 Recognizing Symmetry
- 4.18 Extruded Forms
- 4.18 Extruded Forms
- 4.19 Revolved Forms
- 4.19 Revolved Forms
- 4.20 Irregular Surfaces
- 4.20 Irregular Surfaces
- 4.21 User Coordinate Systems
- 4.21 User Coordinate Systems
- 4.22 Transformations
- 4.22 Transformations
- Key Words
- Key Words
- Chapter Summary
- Chapter Summary
- Skills Summary
- Skills Summary
- Review Questions
- Review Questions
- Chapter Exercises
- Chapter Exercises
This chapter is from the book
This chapter is from the book
This chapter is from the book
4.3 Drawing an Arc Tangent to a Line or Arc and through a Point
Given line AB, point P, and radius R (Figure 4.25a), draw line DE parallel to the given line and distance R from it. From P draw an arc with radius R, cutting line DE at C, the center of the required tangent arc.
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4.25 Tangents. These are often easy constructions using CAD and object snaps.
Given line AB, with tangent point Q on the line and point P (Figure 4.25b), draw PQ, which will be a chord of the required arc. Draw perpendicular bisector DE, and at Q draw a line perpendicular to the line to intersect DE at C, the center of the required tangent arc.
Given an arc with center Q, point P, and radius R (Figure 4.25c), from P, draw an arc with radius R. From Q, draw an arc with radius equal to that of the given arc plus R. The intersection C of the arcs is the center of the required tangent arc.
STEP BY STEP DRAWING AN ARC TANGENT TO TWO ARCS: CREATING CONSTRUCTION GEOMETRY
CAD software typically provides a command option to draw a circle or arc tangent to two entities (any combination of arcs, circles, or lines) given the radius. For example, the AutoCAD Circle command has an option called Ttr (tangent, tangent, radius). When you use this command, you first select the two drawing objects to which the new circle will be tangent and then enter the radius.
Take a look at the shift lever drawing. To draw this figure you must use a geometric construction to find the center of the 1.00-radius tangent arc. Before the lower 4.20-radius arc can be drawn, the smaller 1.00-radius arc must be constructed tangent to the 1.50 diameter circle. When an arc is tangent to a circle, its center must be the radius distance away from that circle.
Use basic CAD commands to draw the portions shown.
Construct circle B with a radius 1.00 larger than circle A. You can use the AutoCAD Offset command to do this quickly. The desired tangent arc must have its center somewhere on circle B. The vertical dimension of 1.25 is given between the two centers in the drawing. Construct line C at this distance. The only point that is on both the circle and the line is the center of the desired tangent arc.
Draw the 1.00-radius circle tangent to the 1.50-diameter circle and centered on the point just found.
Next, construct the lower 4.20-radius arc to be tangent to the lower curve at the left and to the 1.00-radius circle. Then, trim the circles at their intersections to form the desired arcs.
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Geometric Constraints
Using geometric constraints is another way to create this CAD geometry. When geometric constraints are used, a general-case arc can be drawn that is not perfectly tangent. Then, a tangent constraint, the vertical dimension between the arc center and the circle, and the required radius can be applied to the arc as drawn. The software will then calculate the correct arc based on these constraints.
If the desired distance changes, the dimensional constraint values can be updated, and the software will recalculate the new arc. Not all software provides constraint-based modeling, especially in a 2D drafting context. The AutoCAD software has had this feature since release 2010.
When using constraint-based modeling, you still must understand the drawing geometry clearly to create a consistent set of geometric and dimensional constraints.
