- Coordinates for 3D CAD Modeling
- Geometric Entities
- 4.1 Manually Bisecting a Line or Circular Arc
- 4.2 Drawing Tangents to Two Circles
- 4.3 Drawing an Arc Tangent to a Line or Arc and Through a Point
- 4.4 Bisecting an Angle
- 4.5 Drawing a Line through a Point and Parallel to a Line
- 4.6 Drawing a Triangle with Sides Given
- 4.7 Drawing a Right Triangle with Hypotenuse and One Side Given
- 4.8 Laying Out an Angle
- 4.9 Drawing an Equilateral Triangle
- 4.10 Polygons
- 4.11 Drawing a Regular Pentagon
- 4.12 Drawing a Hexagon
- 4.13 Ellipses
- 4.14 Spline Curves
- 4.15 Geometric Relationships
- 4.16 Solid Primitives
- 4.17 Recognizing Symmetry
- 4.18 Extruded Forms
- 4.19 Revolved Forms
- 4.20 Irregular Surfaces
- 4.21 User Coordinate Systems
- 4.22 Transformations
- Key Words
- Chapter Summary
- Skills Summary
- Review Questions
- Chapter Exercises

## 4.17 Recognizing Symmetry

An object is symmetrical when it has the same exact shape on opposite sides of a dividing line (or plane) or about a center or axis. Recognizing the symmetry of objects can help you in your design work and when you are sketching or using CAD to represent an object. Figure 4.63 shows a shape that is symmetrical about several axes of symmetry (of which two are shown) as well as about the center point of the circle.

**4.63** Symmetrical Part. *Symmetrical parts can have symmetry about a line or point, or both.*

Mirrored shapes have symmetry where points on opposite sides of the dividing line (or mirror line) are the same distance away from the mirror line. For a 2D mirrored shape, the axis of symmetry is the mirror line. For a 3D mirrored shape, the symmetry is about a plane. Examples of 3D mirrored shapes are shown in Figure 4.64.

**4.64** 3D Mirrored Shapes. *Each of these symmetrical shapes has two mirror lines, indicated by the thin axis lines. To create one of these parts, you could model one quarter of it, mirror it across one of the mirror lines, then mirror the resulting half across the perpendicular mirror line.*

To simplify sketching, you need to show only half the object if it is symmetrical (Figure 4.65). A centerline line pattern provides a visual reference for the mirror line on the part.

**4.65** *Orthographic sketches of symmetrical parts may show only half of the object.*

Most CAD systems have a command available to mirror existing features to create new features. You can save a lot of modeling time by noticing the symmetry of the object and copying or mirroring the existing geometry to create new features.

### Right- and Left-Hand Parts

Many parts function in pairs for the right and left sides of a device. A brake handle for the left side of a mountain bike is a mirror image of the brake handle for the right side of the bike (Figure 4.66). Using CAD, you can create the part for the left side by mirroring the entire part. On sketches you can indicate a note such as RIGHT-HAND PART IS SHOWN. LEFT-HAND PART IS OPPOSITE. Right-hand and left-hand are often abbreviated as RH and LH in drawing notes.

**4.66** Right- and Left-hand Brake Levers

### Parting-Line Symmetry

Molded symmetrical parts are often made using a mold with two halves, one on each side of the axis of symmetry. The axis or line where two mold parts join is called a ** parting line**. When items are removed from a mold, sometimes a small ridge of material is left on the object. See if you can notice a parting line on a molded object such as your toothbrush or a screwdriver handle such as the one shown in Figure 4.67. Does the parting line define a plane about which the object is symmetrical? Can you determine why that plane was chosen? Does it make it easier to remove the part from the mold? As you are developing your sketching and modeling skills think about the axis of symmetry for parts and how it could affect their manufacture.

**4.67** Parting Line. *The parting line on a molded part is often visible as a ridge of material.*

**4.68** Two Halves of a Mold Used to Form a Strap (shown at left). *(Two straps can be molded at once.)*