1. CE En 112 Engineering Drawing with CAD Application Manual Drafting Supplement (Lecture C) Engineering Geometry and Construction

2. 2 of 21 Lecture Outline Engineering geometry (3.1, p.192) Coordinate spaces (3.3, p.194, we will refer to this one when we learn UCS), Geometric elements (3.4, p.200) Points, lines, surfaces & arcs (3.5, p.202) Conic curves (3.6, p.207) Surfaces (3.10, p.218) will be covered as part of AutoCAD 3D lectures We cannot cover all materials in this chapter in one lecture. But, some of the definitions and concepts have been covered in your education up to this point (from elementary school). We place emphasis on quickly constructing necessary geometric elements. Terms you learn from this chapter have direct relevance to CAD.

3. 3 of 21 Engineering Geometry (Supp. 3.1) Geometric construction: Act of constructing a geometry, especially using hand tools Engineering geometry: Basic geometric elements and forms used in engineering design e.g., dividing a line Points, Lines, Surfaces, and Solids

4. 4 of 21 Geometric Elements (Supp. 3.4) Manual drafting AutoCAD

5. 5 of 21 Points, Lines, Surfaces, and Arcs (Supp. 3.5) Point: Theoretical location that has neither width, height, nor depth and describes an exact location in space

6. 6 of 21 Points, Lines, Surfaces, and Arcs (con’t) Line: Geometric primitive that has length and direction but not thickness –May be straight, curved, or a combination

7. 7 of 21 Points, Lines, Surfaces, and Arcs (con’t) Tangencies: Exists when a straight line is in contact with a curve at a single point; that is, a line is tangent to a circle if it touches the circle at one and only one point

8. 8 of 21 Points, Lines, Surfaces, and Arcs (con’t) Circles: Single curved surface primitive, all points of which are equidistant from one point, the center

9. 9 of 21 Points, Lines, Surfaces, and Arcs (con’t) –Center –Circumference –Radius –Chord –Diameter –Secant –Arc –Semicircle –Minor arc –Major arc –Central angle –Sector –Quadrant –Segment –Tangent The elements of a circle are as follows (outlined in previous slide): The slides that follow provide examples of manual drafting points, lines, surfaces, and mostly, arcs

10. 10 of 21 Points, Lines, Surfaces, and Arcs (con’t) Constructing arcs tangent to two lines

11. 11 of 21 Points, Lines, Surfaces, and Arcs (con’t) Constructing an arc tangent to a line and another arc

12. 12 of 21 Points, Lines, Circles, and Arcs (con’t) Constructing an arc tangent to two given arcs or circles

13. 13 of 21 Points, Lines, Circles, and Arcs (con’t) Constructing an arc tangent to two given arcs Please note that we should avoid this kind of reverse curve in highway alignment design.

14. 14 of 21 Constructing an arc tangent to a given arc Points, Lines, Circles, and Arcs (con’t) Observe the signs carefully to place the center of a new circle that contacts the two existing circles.

15. 15 of 21 Points, Lines, Circles, and Arcs (con’t) Constructing lines tangent to two circles or arcs, using a straightedge (a trial and error method)

16. 16 of 21 Conic Curves (Supp. 3.6) Parabola: Curve created when a plane intersects a right circular cone parallel to the side (elements) of the cone

17. 17 of 21 Conic Curves (con’t) Engineering Applications of Parabolas Parallelogram Method of Drawing Parabolas

18. 18 of 21 Conic Curves (con’t) Hyperbola: Curve of the intersection created when a plane intersects a right circular cone and makes a smaller angle with the axis than do the elements

19. 19 of 21 Conic Curves (con’t) Ellipse: Single-curved- surface primitive – created when a plan passes through a right circular cone at an angle to the axis that is greater than the angle between the axis and the sides (a circle when viewed at an angle appears as an ellipse)

20. 20 of 21 Conic Curves (con’t) Constructing a Foci Ellipse

21. 21 of 21 Next Class Pictoral drawings Next Week, Midterm 1 at the Testing Center (25 AutoCAD questions, to be answered on the bubble sheet, and manual drafting related questions – up to dimensioning). Bring your drafting tools. Midterm 1 is a timed exam. 120 min. But anticipating a few minutes differences between your watch and Testing Center’s clock, actual max time allowed is 125 minutes.