# MODELING AND DESIGN C H A P T E R F O U R

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1 MODELING AND DESIGN C H A P T E R F O U R

2 OBJECTIVES 1. Identify and specify basic geometric elements and primitive shapes. 2. Select a 2D profile that best describes the shape of an object. 3. Identify mirrored shapes and sketch their lines of symmetry. 4. Identify shapes that can be formed by extrusion and sketch their cross sections. 5. Identify shapes that can be formed by revolution techniques and sketch their profiles. 6. Define Boolean operations. 7. Specify the Boolean operations to combine primitive shapes into a complex shape. 8. Work with Cartesian coordinates and user coordinate systems in a CAD system. 9. Identify the transformations common to CAD systems.

3 COORDINATES FOR 3D CAD MODELING Most CAD systems use the right hand rule for coordinate systems; if you point the thumb of your right hand in the positive direction for the X axis and your index finger in the positive direction for the Y axis, your remaining fingers will curl in the positive direction for the Z axis Z Y X Z The Z Axis. In systems that use the right hand rule, the positive Z axis points toward you when the face of the monitor is parallel to the X Y plane.

4 COORDINATES FOR 3D CAD MODELING Axis of Rotation. The curl of the fingers indicates the positive direction along the axis of rotation. 2D CAD Drawing. the X true shape because the viewing direction is perpendicular to the X Y plane straight down the Z axis.

5 Specifying Location Even though the model is ultimately stored in a single Cartesian coordinate system, you may usually specify the location of features using other location methods as well. The most typical of these are relative, polar, cylindrical, and spherical coordinates. These coordinate formats are useful for specifying locations to define your CAD drawing geometry. 3DCoordinates for Vertices

6 COORDINATES FOR 3D CAD MODELING Absolute Coordinates Relative Coordinates Polar Coordinates

7 Object snaps are aids for selecting locations on existing CAD drawing geometry. (Autodesk screen shots reprinted courtesy of Autodesk, Inc.) Object Snaps are Aids

8 GEOMETRIC ENTITIES Points Lines Planes Specifying Points. Point 1 was added to the drawing by typing the absolute coordinates 3,4,7. Point 2 was added relative to Point 1 with the relative Specifying Lines. (a) This 2D line was drawn from endpoint (3,2) to (6,6). (b) This 3D line was drawn from endpoint (3,2,0) to (5,4,6). Defining a Plane in CAD. define a plane in this Pro/ENGINEER model.

9 GEOMETRIC ENTITIES Circles A circle is a set of points that are equidistant from a center point. The distance from the center to one of the points is the radius AutoCAD Circle Construction Options (Autodesk screen shots reprinted courtesy of Autodesk, Inc.) AutoCADArc Construction Options (Autodesk screen shots reprinted courtesy of Autodesk, Inc.) Arcs following

10 CIRCULAR ARC Bisecting a Line or a Circular Arc

11 DRAWING TANGENTS TO TWO CIRCLES Drawing Tangents to Two Circles Tangency constraints shown in AutoCAD for two identical sets of circles

12 ARC AND THROUGH A POINT Tangents. These are often easy constructions using CAD and object snaps.

13 BISECTING AN ANGLE Below shows the given angle BAC to be bisected. Step 1. Lightly draw large arc with center at A to intersect lines AC and AB. Step 2. Lightly draw equal arcs r with radius slightly larger than half BC, to intersect at D. Step 3. Draw line AD, which bisects the angle.

14 PARALLEL TO A LINE With given point P as center, and any convenient radius R, draw arc CD to intersect the given line AB at E Using AutoCAD, you can quickly draw a new line parallel to a given line and through a given point using the Offset command with the Through option. Another method is to use the Parallel object snap while drawing the line

15 LAYING OUT AN ANGLE Many angles can be laid out directly with the triangle or protractor DRAWING A TRIANGLE WITH SIDES GIVEN DRAWING A RIGHT TRIANGLE WITH HYPOTENUSE AND ONE SIDE GIVEN

16 DRAWING AN EQUILATERAL TRIANGLE lines AC and BC to complete the triangle. Alternative Method Draw lines through points A and B, making angles of 60 with the given line and intersecting C

17 POLYGONS A polygon is any plane figure bounded by straight lines. If the polygon has equal angles and equal sides, it can be inscribed in or circumscribed around a circle and is called a regular polygon. Polygons can be defined by the number of sides and whether they are inscribed or circumscribed in a circle. (Autodesk screen shots reprinted courtesy of Autodesk, Inc.)

18 DRAWING A REGULAR PENTAGON Dividers Method Divide the circumference of the circumscribed circle into five equal parts with the dividers, and join the points with straight lines. Step 1. Bisect radius OD at C. Step 2. Use C as the center and CA as the radius to lightly draw arc AE. With A as center and AE as radius, draw arc EB. Step 3. Draw line AB, then measure off distances AB around the circumference of the circle. Draw the sides of the pentagon through these points.

19 DRAWING A HEXAGON Each side of a hexagon is equal to the radius of the circumscribed circle. To use a compass or dividers, use the radius of the circle to mark the six points of the hexagon around the circle. Connect the points with straight lines. Check your accuracy by making sure the opposite sides of the hexagon are parallel. Centerline Variation Draw vertical and horizontal centerlines. With A and B as centers and radius equal to that of the circle, draw arcs to intersect the circle at C, D, E, and F, Measurement Across Flats vs. Across Corners

20 ELLIPSES An ellipse can be defined by its major and minor axis distances. The major axis is the longer axis of the ellipse; the minor axis is the shorter axis. Major and Minor Axes of Some Ellipses * Most CAD systems provide an Ellipse command that lets you enter the major and minor axis lengths, center, or the angle of rotation for a circle that is to appear elliptical.

21 SPLINE CURVES or freeform, curves. Many surfaces cannot be easily defined using simple curves such as circles, arcs, or ellipses. For example, the flowing curves used in automobile design blend many different curves into a smooth surface. Creating lifelike shapes and aerodynamic forms may require spline curves

22 Drawn in AutoCAD Approximated Spline. This spline drawn in AutoCAD is pulled toward the defined control points. The Properties dialog box at the right allows you to change the weighting factor for each control point. (Autodesk screen shots reprinted courtesy of Autodesk, Inc.)

23 GEOMETRIC RELATIONSHIPS Tangency. Lines that are tangent to an entity have one point in common but never intersect. 3D objects may be tangent at a single point or along a line.

24 SOLID PRIMITIVES

25 Operations Complex Shapes. The 3D solid primitives in this illustration show basic shapes that make up a telephone handset. (Shutterstock.)

26 Subtraction Boolean Operations

27 RECOGNIZING SYMMETRY 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. Right and Left hand Brake Levers (Using symmetry requires it)

28 EXTRUDED FORMS

29 REVOLVED FORMS

30 IRREGULAR SURFACES

31 USER COORDINATE SYSTEMS

32 USER COORDINATE SYSTEMS Drawing on an Inclined Plane. A new coordinate system is defined relative to the slanted surface to make it easy to create the hole.

33 TRANSFORMATIONS

34 Changing the View. Changing the View. Note that the location of the model relative to the coordinate axes does not change in any of the different views. Changing the view does not transform the model itself.

35 Geometric or Viewing Transformation? Geometric or Viewing Transformation? Three of these models are the same, but the viewing location, zoom, or rotation has changed. Three have been transformed to different locations on the coordinate system.

36

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