Engineering Drawing: Projections

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1. Fundamentals of Projection Orthographic Projection: A method of representing 3D objects in 2D by projecting points onto planes. Planes of Projection: HP (Horizontal Plane): Represents the top view. VP (Vertical Plane): Represents the front view. PP (Profile Plane) / AVP (Auxiliary Vertical Plane): Represents the side view. Reference Line (XY Line): Intersection of HP and VP. Quadrants: The space is divided into four quadrants by HP and VP. Engineering drawings primarily use the First Angle Projection (First Quadrant) or Third Angle Projection (Third Quadrant). First Angle Projection: Object between observer and planes. HP below XY, VP above XY. (ISO Standard) Third Angle Projection: Planes between observer and object. HP above XY, VP above XY. (ANSI Standard) 2. Projection of Points A point has three coordinates: $(x, y, z)$. $x$: distance from PP $y$: distance from VP (front/back) $z$: distance from HP (above/below) Front View (FV): Projects onto VP. Shows distance from HP ($z$) and PP ($x$). Plotted above/below XY. Top View (TV): Projects onto HP. Shows distance from VP ($y$) and PP ($x$). Plotted below/above XY. Side View (SV): Projects onto PP. Shows distance from HP ($z$) and VP ($y$). Key Rule: When HP is rotated clockwise $90^\circ$ to align with VP, points above HP are above XY, points below HP are below XY. Points in front of VP are below XY (for TV), points behind VP are above XY (for TV). 3. Projection of Lines A line is defined by two points. Projecting a line involves projecting its endpoints. True Length (TL): The actual length of the line in 3D space. True Inclination: The actual angle a line makes with HP ($\theta$) or VP ($\phi$). Line Parallel to Both HP & VP: FV and TV are parallel to XY, and show TL. Line Perpendicular to HP (Parallel to VP): FV shows TL and is perpendicular to XY. TV is a point. Line Perpendicular to VP (Parallel to HP): TV shows TL and is perpendicular to XY. FV is a point. Line Parallel to HP, Inclined to VP: TV shows TL and true inclination $\phi$ with XY. FV is shorter than TL, parallel to XY. Line Parallel to VP, Inclined to HP: FV shows TL and true inclination $\theta$ with XY. TV is shorter than TL, parallel to XY. Line Inclined to Both HP & VP: Neither FV nor TV shows TL or true inclinations. To find TL: Rotate the line in one view until it's parallel to the reference plane, then project to the other view. Traces of a Line: Where a line intersects HP (Horizontal Trace, HT) or VP (Vertical Trace, VT). 4. Projection of Planes A plane is a 2D surface. Its projection is defined by the projection of its boundaries (e.g., vertices of a polygon). Types of Planes: Perpendicular Planes: Perpendicular to one plane and parallel or inclined to another. Perpendicular to HP, Parallel to VP: FV shows true shape. TV is a line perpendicular to XY. Perpendicular to VP, Parallel to HP: TV shows true shape. FV is a line perpendicular to XY. Perpendicular to Both HP & VP (Profile Plane): FV and TV are lines. SV shows true shape. Perpendicular to HP, Inclined to VP: FV is shorter than true shape, inclined to XY. TV is a line shorter than true length, inclined to XY. Perpendicular to VP, Inclined to HP: TV is shorter than true shape, inclined to XY. FV is a line shorter than true length, inclined to XY. Oblique Planes: Inclined to both HP and VP. Neither FV nor TV shows the true shape. Steps for Oblique Planes: Assume the plane is parallel to one plane (e.g., HP). Draw its true shape in TV. Draw its corresponding FV (a line parallel to XY). Incline the FV to the desired angle with HP. Project to get the new TV. Incline the TV from step 3 to the desired angle with VP. Project to get the final FV. Edge View: When a plane is seen as a line. This occurs when the plane is perpendicular to the projection plane. True Shape: Can be found using auxiliary views or by rotation method. 5. Projection of Solids Solids have three dimensions. Their projections are defined by projecting their bases and apex/top. Types of Solids: Polyhedra: Prisms, Pyramids (bases are polygons). Solids of Revolution: Cylinders, Cones, Spheres (formed by rotating a 2D shape). Axis: Line connecting centers of bases (prism, cylinder) or apex to center of base (pyramid, cone). Resting Position: How the solid is placed relative to HP and VP. On its base on HP: Base true shape in TV. Axis perpendicular to HP. On its base on VP: Base true shape in FV. Axis perpendicular to VP. On one of its edges on HP/VP: Edge view. On one of its corners on HP/VP: Point view. Projection Methods: Usually a two-stage process. Assume the solid is in a simple position (e.g., axis perpendicular to HP). Draw FV and TV. Incline the solid's axis/base to the given angle with HP or VP. Project the first views to get the final views. Visible/Invisible Edges: Determine which edges are visible from the observer's position and draw them as continuous lines; hidden edges as dashed lines. 6. Sectioning of Solids When a solid is cut by an imaginary cutting plane, the exposed surface is called a section . Cutting Plane Line: Represented by a thick long-dash-short-dash line with arrows indicating viewing direction. Sectional View: The view showing the cut surface. Parallel lines (hatching) are drawn on the sectioned area. True Shape of Section: Can be found by projecting perpendicularly from the cutting plane line onto an auxiliary plane parallel to the cutting plane. Types of Cutting Planes: Perpendicular to VP, Parallel to HP: Cuts seen as true shape in TV. Perpendicular to HP, Parallel to VP: Cuts seen as true shape in FV. Perpendicular to VP, Inclined to HP: Cutting plane appears as a line in FV. Perpendicular to HP, Inclined to VP: Cutting plane appears as a line in TV. Oblique to Both HP & VP: Requires two auxiliary views to determine true shape. 7. Development of Surfaces Unfolding the 3D surface of a solid into a 2D plane without stretching or tearing. Used for manufacturing sheet metal objects (e.g., ducts, containers). Methods: Parallel Line Development: For prisms and cylinders (solids with parallel bases). Radial Line Development: For pyramids and cones (solids with an apex). Triangulation Development: For transition pieces or complex shapes (dividing surfaces into triangles). Key Principle: True lengths of edges and elements are crucial for accurate development. Steps (e.g., Cylinder): Draw FV and TV of the cylinder. Divide the base circle in TV into equal parts. Project these divisions to the FV. Draw a rectangle with width equal to the circumference of the base ($2\pi r$) and height equal to the cylinder's height. Transfer the divisions and any cut points onto this rectangle. Steps (e.g., Cone): Draw FV and TV of the cone. Draw the development as a sector of a circle with radius equal to the cone's slant height ($L$). The angle of the sector is $\alpha = (R/L) \times 360^\circ$, where $R$ is base radius. Transfer any cut points or features by projecting them onto the slant height in FV, then marking them on the developed sector.