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**Fundamentals of Engineering**

Isometric Sketching and Coordinate Systems GSMST Objectives:

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**Objectives Define 2D and 3D coordinate systems**

Determine coordinates of objects in: 2D views 3D views Practice drawing isometric from orthographic Objectives: Co-ordinate systems & object design - At the end of the session, students should be able to: Determine coordinates of vertices in 3-D space, given 2-D orthographic projection sketches Develop 3-D isometrics given coordinate of vertices in 3-D spaces Apply coordinate systems to effectively transform orthographic projections to isometrics Demonstrate the knowledge of isometric and orthographic projection by creating a problem

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**Pictorial Sketching: Coordinate Systems Y**

Used to define the locations of points, lines, and planes in 2 or 3 dimensions. "Cartesian Coordinate system" Y X

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Coordinate Space in 2-D A 2-D coordinate system locates the origin at the intersection of the X axis (horizontal axis or abscissa) and the Y axis (vertical axis or ordinate). These are called View Coordinates. X -X -Y Y

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**Determine the Coordinates**

B C

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Coordinate Space in 3-D Z X Y -Z -X -Y (0,0,0) In the 3-D coordinate system (world coordinate system) the axes are mutually perpendicular. The origin (0,0,0) is usually taken at the intersection of these axes.

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3-D Coordinate Systems Consist of three, mutually perpendicular axes used to define space Positive or negative based on the axes Right Hand Rule determines if a coordinate system is positive (right-handed) or negative (left- handed) 3-D Coordinate systems are generally positive (right-handed)

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**Coordinate Systems: Right Hand Rule**

Place your fingers in the direction of the positive x-axis and rotate them in the direction of the y-axis. Your thumb will point in the direction of the positive z-axis.

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**Left or Right-Handed? The systems are right-handed (positive).**

Z X Y Y Z X These systems are left-handed (negative). Z X Y Y X Z

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Orthographic Projection: Missing Views Constructing the third view helps visualization skills. When constructing the third view, recall: Points project perpendicularly from one view to the next. Object dimensions (height, width and depth) are preserved from one view to the next. 17

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**Orthographic Projection: Missing Views Two Solutions**

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Pictorial Sketching Used to portray a 3-D object on a 2-D sheet of paper. 3-D axes appear differently when shown on a 2-D surface. Standard axes: Isometric Oblique

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Oblique Sketching Since one face of the object is undistorted, the most irregular face is usually shown in the plane of the paper.

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**Oblique Sketching 3 types of oblique pictorials.**

Cabinet pictorials are the most common.

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**Oblique Coordinate Axes**

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**Oblique Coordinate Axes**

Note: Surface parallel to the plane of the paper (the XY plane) is shown in its true shape. Oblique sketches are made perpendicular to an edge on the object 34

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Oblique Sketching Oblique sketch from edge DC:

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**To draw oblique sketches: 1. Draw the first surface completely**

2 Oblique Sketching 3 1 To draw oblique sketches: 1. Draw the first surface completely Add lines showing the receding dimension (depth) 3. Repeat until the object is complete Notice: All receding lines are parallel to one another

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Oblique Practice Task: Using engineering paper, draw both these coded sketches. 3 World coordinates are tied the 3D representation of the object. Each orthographic view shows only 2 of the three coordinates at a time. 1

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**Isometric Coordinate Axes**

Isometric sketches are made as if you’re looking down a diagonal a cube

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**Isometric Coordinate Axes**

Note: all isometric object surfaces will appear distorted. Square surface appears as a rhombus Isometric sketches are made as if you were looking down a diagonal of a cube

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**Isometric Coordinate Axes**

Isometric grid paper/dot paper is useful for constructing isometric drawings. We'll use grid paper in class and dot here in the PowerPoint

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**Coded Plans Pictorial sketches can be made from coded plans.**

Coded plans define the shape of a block building. "Arrow" shows the corner you are drawing from Coded Plan Building

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**Coded Plans: Isometric Sketch**

From Corner C

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**Isometric Sketching 0.Draw edge "C“ 1.Sketch right or left surface.**

3 1 2 1 C Guidelines for constructing isometric drawings: C Step 1 & 2 Step 3 Step 4 ... 0.Draw edge "C“ 1.Sketch right or left surface. 2.Draw a surface that shares an edge with the surface just drawn. 3.Continue drawing one surface at a time until the object is complete. Step 4 ...

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Isometric Practice Task: Using isometric paper, draw these coded sketches. World coordinates are tied the 3D representation of the object. Each orthographic view shows only 2 of the three coordinates at a time.

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**Orthographic and Isometrics Coordinates**

X Z Y Task: Using the world coordinates convention for computers and CAD, determine the values of the coordinates for points in orthographic drawings and isometric drawings. Note the origin (0,0,0) can be set at an any point. World coordinates are tied the 3D representation of the object. Each orthographic view shows only 2 of the three coordinates at a time.

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**World Coordinates in Orthographic Projections**

B C D Y X A A X Y Z Take time to explain the oblique cut across the upper part of the body. Students have a difficult time when seeing this for the first time. Demonstrate how to identify its coordinates. Note C to D is a straight line. Note some students may find it easier to do the isometric for visualization and then do the coordinates. Encourage students to do it the way that works for them. Z X Z Y

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**World Coordinates in Isometric Projections**

B X Z Y B A C D Y X A A X Y Z Explain to the students how the coordinates are transformed from the 2D to the 3D drawing. Make it clear how to travel along each of the three axes to properly count coordinates in the 3D space. Z X Z Y

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**World Coordinates in the Isometric**

What are the Coordinates Of this point? X Y Z A X Z Y The solution appears with a second click of the mouse. This is helpful to students to visualize the 3D coordinates for oblique surfaces.

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**Orthographic Views from Isometric Sketches**

Orthographic Projection: Orthographic Views from Isometric Sketches Make an orthographic sketch, by sketching top, front and right side views of the object shown below. 2 3 1 1

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**Isometric Sketches from Orthographic Views**

Orthographic Projection: Isometric Sketches from Orthographic Views Sometimes you are asked to construct isometric sketches from orthographic views. Orthographic views develop visualization skills The box method is one way to do this. For some problems, the box method may not be very helpful.

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**Iso. Sketches from Ortho Views**

Orthographic Projection: Iso. Sketches from Ortho Views 1. Find the object's overall dimensions from the orthographic views and sketch that size box on isometric dot paper. W

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**Iso. Sketches from Ortho Views**

Orthographic Projection: Iso. Sketches from Ortho Views 2. Sketch the top, front, and right side views in their appropriate locations on the box.

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**Iso. Sketches from Ortho Views**

Orthographic Projection: Iso. Sketches from Ortho Views 3. Add/remove lines until the view is complete.

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ENGINEERING GRAPHICS 1E9

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