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Chapter 2 - Part 1 The Language and Terminology of Technical Drawing Chapter Objectives - at the completion of this chapter students will be able to: •Define the terminology used to describe the geometry of multiview drawings •Describe points, lines, angles •Describe polygons •Describe 3D objects •Describe projection planes •Describe normal, inclined and oblique surfaces Supplemental Files •Describe line types •Describe line weights •Interpret the multiviews of graphic primitives •Describe orthographic projection including miter line technique © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. Supplemental files are available for download inside the Chapter 2 folder of the book’s file downloads. Please see the inside front cover for further details. 2.1 THE TERMINOLOGY OF MULTIVIEW DRAWING Multiview drawings are created by configuring the points, lines and planes of an object to create views that represent the object’s features as they would appear if viewed from different points of view. For example, a mechanical drafter might construct the front, top, and side views of a machine part. An architectural drafter may draw the front, sides, and rear views of a building. Before learning the techniques involved in the creation of the multiviews of an object, students should be familiar with the terminology used to describe the features of an object. © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. 2.2 POINTS, PLANES, COORDINATE SYSTEMS, AND LINES Points A point is an exact “location” in space that is defined by coordinates that are located relative to a known origin point. Points are often represented in technical drawings by a visible “dot”, and while the dot representing a point is visible, the point has no dimensional size. Locating Points in Two Dimensional (2D) Coordinate Systems In a two dimensional (2D) coordinate system, points are defined on a 2D flat surface that represents a plane. The coordinates of the point are located by measuring from two perpendicular lines that represent the X (horizontal) and Y (vertical) axes. The intersection where the X and Y axes meet is called the origin. In technical drawings, the X and Y axes represent a 2D area referred to as the “XY plane”. In the example below, the origin point’s value would be stated as “zero comma zero”, or (0,0), which means the location of the origin is zero units (0) on the X axis and zero units (0) on the Y axis. A point, represented by a green dot, is located at coordinate 2,3. This means that the point’s location is 2 units to the right of the origin on the X axis and 3 units above the origin on the Y axis. Because points 0,0 and 2,3 are both located on the XY plane they are considered to be coplanar. Point located at 2,3 2.1 Two Dimensional Coordinate System with X and Y Axes Noted Note: Coordinates that are defined relative to a 0,0 origin are also referred to as absolute coordinates. Origin (0,0) © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. In the example below, two points (in red) are defined on the XY plane at coordinates 1,2 and 4,3 respectively. Points that lie on the same plane are referred to as coplanar. Points that share the same location are referred to as coincident. 2.2 Points on a Two Dimensional Coordinate System Origin Point (0,0) Points that lie on the same plane are referred to as coplanar. Points that share the same location are referred to as coincident. © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. Negative Values in Two Dimensional (2D) Coordinate Systems Points that are located below the X axis, or to the left of the Y axis, are described with negative coordinate values (a minus sign precedes the coordinate). In the example below, two points are defined at coordinates -3,1 and -1.5,-2.5 respectively. Origin Point (0,0) © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. Three Dimensional (3D) Coordinate Systems In a three dimensional (3D) coordinate system, a Z axis is added to the X and Y axes. Using this system, points can be located relative to the origin along the X, Y and Z axes. The Z axis represents the height of the point above or below the X,Y plane (see figure below). For example, a 3D coordinate might be defined with the coordinates 1,1,1. This coordinate would lie one unit to the right of the origin along the X axis, one unit from the origin along the Y axis, and one unit above the X,Y plane. 2.3 Three Dimensional Coordinate System Origin Point (0,0,0) of a 3D coordinate system © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. Lines To a mathematician, a line is a set of continuous points that extend indefinitely in either direction. In technical drawing terminology, a line is a segment defined by two points, the start point and the endpoint. These endpoints are defined with coordinates. In technical drawing terminology, a line is a segment defined by two endpoints. The endpoints are defined with coordinates. Points that lie on the same line are referred to as collinear. Noncollinear points do not lie on the same line. In the example below, a red line begins at a start point located at coordinate 2,2 and ends at a point located at coordinate 8,7 (relative to the origin). These points are collinear. A point located exactly halfway between the start and end points would be the line’s midpoint. 2.4 Coordinates for the Start and End Points of a Two-dimensional Line Drawn on the X-Y Plane Parallel Lines Parallel lines run side by side at a uniform distance and never intersect, even if extended. Two or more planes can be parallel relative to each other. Lines can be parallel to planes. Spline A smooth curve that passes through, or near, specified points. © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. Angles 2.5 Two Lines Meeting to Form an Angle Angle An angle is formed when two, noncollinear lines have the same endpoint. The angle at right is formed by sides BA and BC. The angle formed by these lines is referred to as angle ABC. Vertex In 2D space, the common point where two lines meet is called a vertex. The plural of vertex is vertices. In the example at right, angle ABC’s vertex is point B and the its sides are lines BA and BC. Note: When specifying an angle using letters or numbers, the vertex should be the middle letter in the series. The angle formed by the lines above is referred to as angle ABC. Note: The point where two lines cross is referred to as an intersection - as opposed to a vertex. In 3D objects, a vertex is where the object’s edges meet. In the object at right, all of the vertices have been assigned a number. This object has a total of 17 vertices. © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. 2.6 Three Dimensional Object with Multiple Vertices Types of Angles Right Angle Acute Angle Obtuse Angle The angle between the sides measures exactly 90 degrees. The angle between the sides measures less than 90 degrees. The angle between the sides measures greater than 90 degrees but less than 180 degrees. 2.7(a) Right Angle 2.7(b) Acute Angle Perpendicularity When two lines meet to form a right angle, they are perpendicular. In the example above, line BA is perpendicular to line BC. Planes that meet at right angles to each other are considered to be perpendicular (see example at right), Lines can also be perpendicular to planes. © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. 2.7(c) Obtuse Angle Types of Angles Complementary Angles Supplementary Angles If two angles have a total measurement of 90 degrees they are complementary angles. If two angles have a total measurement of 180 degrees they are supplementary angles. 2.8(b) Supplementary Angles 2.7(c) Obtuse Angle Opposite Angles Adjacent Angles When two lines cross, they form 4 angles. The opposite angles have the same measure. Where two lines cross, angles that share a common side and common vertex, are called adjacent angles. The sum of any two adjacent angle equals 180 degrees. Therefore: Angle A = Angle B and Angle C = Angle D 2.9(a) Opposite Angles Therefore, Angles A + C = 180 degrees and Angle C + B = 180 degrees, Angle B + D = 180 degrees and Angle D + A = 180 degrees. 2.9(b) Adjacent Angles © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. 2.3 TERMINOLOGY OF GEOMETRIC SHAPES Tangent When a line touches a circle at only one point. Circles 2.11(a) Lines Tangent to a Circle A circle can be defined by its center point and either a diameter or radius (diameter/2) Tangency Point Diameter Symbol Radius Center Point 2.10 Circle Terminology Two circles that touch at only one point are tangent. Flat surfaces can also be tangent to curved surfaces. 2.11(b) Circle Tangent to a Circle Concentricity When two or more circles share a common center point they are concentric. 2.12(a) Concentric Circles © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. Eccentricity When two or more circles do not share a common center point they are eccentric. 2.12(b) Eccentric Circles Polygons Polygons are multi-sided, 2D figures composed of straight line segments. The polygon’s start and end points meet at the same point which creates a “closed” figure. Polygons are classified by the number of sides they contain. Triangles - Three sided polygons. Quadrilaterals - Four sided polygons. Right Triangle Rectangle Square One right angle. 2.13(b) Quadrilaterals Equilateral Three equal angles. Scalene No equal angles. 2.13(a) Triangles Hexagons - Six sided polygons. Hexagon constructed by inscribing it within a circle. Hexagon constructed by circumscribing it around a circle. Pentagons - Five sided polygons. Heptagon - Seven sided polygons. Octagons - Eight sided polygons. Nonagons - Nine sided polygons. Decagons - Ten sided polygons. Dodecagons - Twelve sided polygons. 2.13(c) Hexagons © Technical Drawing 101 with AutoCAD Smith, Ramirez & Schmidt Cylinders A cylinder is a three-dimensional object that is defined by its the diameter or radius, its length, and the location of its center axis. See Figure below. Flat surfaces can also be tangent to curved surfaces. Plane tangent to a cylinder 2.14(a) Cylinder Coaxial When two or more cylinders are aligned along the same center axis they are coaxial. Center planes meeting along center axis. 2.14(b) Coaxial Cylinders © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. 3D SHAPES Rectangular Prism Rectangular Prism Shown with a center plane. SymmetryWhen the features of an object are exactly the same on both sides of the object’s center plane, the object is symmetrical. © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. 3D SHAPES Triangular Prism Triangular Prism Triangular Prism Shown with center plane. © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. Sometimes referred to as a wedge. 3D SHAPES Sphere Sphere Shown with 2 center planes. Shown with 3 center planes. Sphere Cone Shown with center plane. Torus © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved. Cone Truncated Cone Open Chapter 2 Lecture – Part 2 © Technical Drawing 101 with AutoCAD Smith & Ramirez – All rights reserved.