- 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

## Chapter Exercises

*Exercise 4.1* Draw inclined line *AB* 65 mm long. Bisect it with line *CD*.

*Exercise 4.2* Draw any angle. Label its vertex *C.* Bisect the angle and transfer half the angle to place its vertex at arbitrary point *D.*

*Exercise 4.3* Draw an inclined line *EF.* Use distance *GH* equal to 42 mm. Draw a new line parallel to *EF* and distance *GH* away.

*Exercise 4.4* Draw line *JK* 95 mm long. Draw a second line *LM* 58 mm long. Divide *JK* into five equal parts. Use a different method than you selected to divide line *JK* to divide line *LM* into three equal parts.

*Exercise 4.5* Draw line *OP* 92 mm long. Divide it into three proportional parts with the ratio 3:5:9.

*Exercise 4.6* Draw a line 87 mm long. Divide it into parts proportional to the square of *x*, where *x* = 1, 2, 3, and 4.

*Exercise 4.7* Draw a triangle with the sides 76 mm, 85 mm, and 65 mm. Bisect the three interior angles. The bisectors should meet at a point. Draw a circle inscribed in the triangle, with the point where the bisectors meet as its center.

*Exercise 4.8* Draw a right triangle that has a hypotenuse of 65 mm and one leg 40 mm. Draw a circle through the three vertices.

*Exercise 4.9* Draw inclined line *QR* 84 mm long. Mark point *P* on the line 32 mm from *Q.* Draw a line perpendicular to *QR* at point *P*. Select any point *S* 45.5 mm from line *QR.* Draw a line perpendicular from *S* to line *QR*.

*Exercise 4.10* Draw two lines forming an angle of 35.5°.

*Exercise 4.11* Draw two lines forming an angle of 33.16°.

*Exercise 4.12* Draw an equilateral triangle with sides of 63.5 mm. Bisect the interior angles. Draw a circle inscribed in the triangle.

*Exercise 4.13* Draw an inclined line *TJ* 55 mm long. Using line *TJ* as one of the sides, construct a square.

*Exercise 4.14* Create a 54-mm-diameter circle. Inscribe a square in the circle, and circumscribe a square around the circle.

*Exercise 4.15* Create a 65-mm-diameter circle. Find the vertices of an inscribed regular pentagon. Join these vertices to form a five-pointed star.

*Exercise 4.16* Create a 65-mm-diameter circle. Inscribe a hexagon, and circumscribe a hexagon.

*Exercise 4.17* Create a square with 63.5 mm sides. Inscribe an octagon.

*Exercise 4.18* Draw a triangle with sides 50 mm, 38 mm, and 73 mm. Copy the triangle to a new location and rotate it 180°.

*Exercise 4.19* Make a rectangle 88 mm wide and 61 mm high. Scale copies of this rectangle, first to 70 mm wide and then to 58 mm wide.

*Exercise 4.20* Draw three points spaced apart randomly. Create a circle through the three points.

*Exercise 4.21* Draw a 58-mm-diameter circle. From any point *S* on the left side of the circle, draw a line tangent to the circle at point *S.* Create a point *T*, to the right of the circle and 50 mm from its center. Draw two tangents to the circle from point *T*.

*Exercise 4.22* Open-Belt Tangents. Draw a horizontal centerline near the center of the drawing area. On this centerline, draw two circles spaced 54 mm apart, one with a diameter of 50 mm, the other with a diameter of 38 mm. Draw “open-belt”-style tangents to the circles.

*Exercise 4.23* Crossed-Belt Tangents. Use the same instructions as Exercise 4.22, but for “crossed-belt”-style tangents.

*Exercise 4.24* Draw a vertical line *VW*. Mark point *P* 44 mm to the right of line *VW*. Draw a 56-mm-diameter circle through point *P* and tangent to line *VW.*

*Exercise 4.25* Draw a vertical line *XY*. Mark point *P* 44 mm to the right of line *XY*. Mark point *Q* on line *XY* and 50 mm from *P.* Draw a circle through *P* and tangent to *XY* at point *Q.*

*Exercise 4.26* Draw a 64-mm-diameter circle with center *C.* Create point *P* to the lower right and 60 mm from *C*. Draw a 25-mm-radius arc through *P* and tangent to the circle.

*Exercise 4.27* Draw intersecting vertical and horizontal lines, each 65 mm long. Draw a 38-mm-radius arc tangent to the two lines.

*Exercise 4.28* Draw a horizontal line. Create a point on the line. Through this point, draw a line upward to the right at 60° from horizontal. Draw 35-mm-radius arcs in an obtuse and an acute angle tangent to the two lines.

*Exercise 4.29* Draw two intersecting lines to form a 60° angle. Create point *P* on one line a distance of 45 mm from the intersection. Draw an arc tangent to both lines with one point of tangency at *P.*

*Exercise 4.30* Draw a vertical line *AB*. In the lower right of the drawing, create a 42-mm-radius arc with its center 75 mm to the right of the line. Draw a 25-mm-radius arc tangent to the first arc and to line *AB*.

*Exercise 4.31* With centers 86 mm apart, draw arcs of radii 44 mm and 24 mm. Draw a 32-mm-radius arc tangent to the two arcs.

*Exercise 4.32* Draw a horizontal centerline near the center of the drawing area. On this centerline, draw two circles spaced 54 mm apart, one with a diameter of 50 mm, the other with a diameter of 38 mm. Draw a 50-mm-radius arc tangent to the circles and enclosing only the smaller one.

*Exercise 4.33* Draw two parallel inclined lines 45 mm apart. Mark a point on each line. Connect the two points with an ogee curve tangent to the two parallel lines. (An ogee curve is a curve tangent to both lines.)

*Exercise 4.34* Draw a 54-mm-radius arc that subtends an angle of 90°. Find the length of the arc.

*Exercise 4.35* Draw a horizontal major axis 10 mm long and a minor axis 64 mm long to intersect near the center of the drawing space. Draw an ellipse using these axes.

*Exercise 4.36* Create six equal rectangles and draw visible lines, as shown. Omit dimensions and instructional notes.

*Exercise 4.37* Create six equal rectangles and draw lines as shown. In the first two spaces, draw examples of the standard line patterns used in technical drawings: visible, hidden, construction, centerlines, cutting-plane lines, and phantom. In the remaining spaces, locate centers *C* by diagonals, and then work constructions out from them. Omit the metric dimensions and instructional notes.

*Exercise 4.38* Draw the figures as shown. Omit all dimensions.

*Exercise 4.39* Draw the friction plate. Omit dimensions and notes.

*Exercise 4.40* Draw the Geneva cam. Omit dimensions and notes.

*Exercise 4.41* Draw accurately in pencil the shear plate. Give the length of *KA*. Omit the other dimensions and notes.

*Exercise 4.42* Draw the ratchet wheel using pencil. Omit the dimensions and notes.

*Exercise 4.43* Draw the latch plate using pencil. Omit the dimensions and notes.

*Exercise 4.44* Draw the parabolic floodlight reflector shown.

*Exercise 4.45* Identify the solid primitives and Boolean operations you could use to create the following objects.

*Exercise 4.46* Use an isometric grid to help sketch the solids formed by revolving the following shapes about the axis shown. Coordinates are defined by the X-Y-Z icon, with positive X to the right, positive Y up, and positive Z out of the page.

*Exercise 4.47* Use an isometric grid to help sketch the solids formed by extruding the following shapes along the axis specified. Coordinates are defined by the X-Y-Z icon, with positive X to the right, positive Y up, and positive Z out of the page.

*Exercise 4.48* Starting at point A in each of the figures, list the coordinates for each point in order as relative coordinates from the previous point.

*Exercise 4.49* Plot the coordinates in each of the lists on grid paper. Each point represents the endpoint of a line from the previous point, unless otherwise indicated. Relative coordinates are preceded by @.

*Exercise 4.50* Using the information provided on the drawing, determine the coordinates you would use (absolute, relative, or polar) and the order in which you would enter them to create the figure.

*Exercise 4.51* Using the information provided on the drawing, determine the coordinates you would use (absolute, relative, or polar) and the order in which you would enter them to create the figure.

*Exercise 4.52* Using the information provided on the drawing, determine the coordinates you would use (absolute, relative, or polar) and the order in which you would enter them to create the figure.