# Fundamentals of Engineering

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Fundamentals of Engineering
Isometric Pictorials and Ellipses GSMST Objectives: Sketching and Isometric Pictorials - At the end of the session, students should be able to: Infer that technical drawings are effective tools for communication of technical ideas Differentiate between multi-view and isometric drawings Develop isometric sketches of tangible objects on isometric grid sheet

Objectives Projections: The Four Basic Types
Creating Isometric sketches Sketching Ellipses

Projections: Four Basic Types
Note: Isometric is a special case of Axonometric Orthographic Projections Axonometric Course emphasizes on multi-view (orthographic) and isometric (one type of axonometric pictorial) projections only Multiview projections are a collection of 2-D views Pictorials are 3-D Pictorials Oblique Perspective

Introduction to Isometric Projection
CUBE Isometric Projection: One type of axonometric pictorial (3-D) projection ‘Iso-’ means ‘equal ‘metric projection’ means ‘a projection to a scaled measure’ The three dimensions are not only shown in one view, but also the dimensions can be scaled from this drawing START WITH A CUBE All of the normal drawing planes (top, front, side) are equally foreshortened or tilted, and all of the major axes (X, Y, Z) are at equal rotations from each other (120 degrees apart), as in the illustration above. And, because all of the major planes are equally foreshortened, all of the measurements in these planes are equal as well as shown above. This means that the same measuring scale may be used in drawing both the width, height, and depth of objects. Isometric means equal measure All planes are equally or proportionately shortened and tilted All the major axes (X, Y, Z) are 120 degrees apart

Making an Isometric Sketch
Defining Axis 30o 60o Isometric Axis Derive the axes from a vertex of the cube

Making an Isometric Sketch
Axis Convention Height Choose the longest dimension to be the width or the depth for optical stability Depth Width The above slide is used to indicate the manner in which the width, depth and height of a 3-dimensional object is seen in an Isometric Sketch. Note the assignments of height, width, and depth to the axis. The front view direction is shown. Please emphasize this convention to the students. Front view Isometric Axis Convention

Incorrect orientation Note the alignment of the axes
Usage of the Grid Paper Explain the usage of grid paper – (Many student make a mistake in choosing the correct orientation of the grid paper ) Instructions on the grid paper used for isometric sketches indicate to turn paper sideways. Students are required to follow that guideline when instructed. This will ensure proper axes conventions Inform students that during the exam the isometric grid given in the question paper is with correct orientation and it is not required to turn the paper for correct orientation of grid. Correct orientation Incorrect orientation Note the alignment of the axes

Going From Isometric to Rectilinear
See how the face of the cube in the isometric transforms in to the square in the rectilinear grid – The axes that are 60 apart widens in to 90 - hence only 2-axes at a time could be represented in any orthographic projection

Object for Practice How to derive this object from a rectangular piece of wood? Shape it in to a rectangle with maximum dimensions (so as to fit the required object) on the three axes Chisel out the unwanted parts…. Slides follow. NOTE: No scale provided due to lack of measurements of blocks.

Making an Isometric Sketch
Axis Convention Height Choose the longest dimension to be the width (or the depth) for optical stability Width Depth The above slide is used to indicate the manner in which the width, depth and height of a 3-dimensional object is seen in an Isometric Sketch. Note the assignments of height, width, and depth to the axis. The front view direction is shown. Emphasize this convention to the students. Isometric Axis Convention Front view 10 10

Blocking in the Object Begin with Front Face Front Face Height Width
Identify the size of the front view of the object and sketch its outside dimensions on the Isometric view.

Blocking in the Object: Add Side Face
Height Depth Side Face Once the front view outside dimensions are added on the isometric sketch, add the side view dimensions.

Blocking in the Object: Add Top Face
After front and side views are sketched on the isometric drawing, then add the top view.

Adding Detail Cut Outs – Part 1
The order of adding the details is important. They build upon each other.

Adding Detail Cut Outs – Part 2
Note that lines parallel to axes

Adding Detail Cut Outs – Part 3
Note that lines parallel to axes are drawn first, then oblique lines are determined from their intersections.

Darken Final Lines - Part 4
Note: All visible edges will be darkened Construction lines can be left in but must be much lighter than the final lines.

Draw the Isometric Use Isometric Grid Paper Block is 6 x 3 x 3

Isometric View

Draw the Isometric Allow the student approximately 10 minutes to work on this in class. The next slide has the solution which can be discussed with the students. The instructor may choose to have volunteers bring their solutions to the front of class to explain prior to showing the solution. The homework for this lecture involves transforming orthographic to isometric drawings. This exercise is to help students understand how to do this.

Draw The Isometric This object can be used to explain how triangular shapes in all three orthographic views result in an oblique surface in the isometric view. It also allow some discussion of the undercut oblique surface producing the hidden line on the orthographic view.

Sketching a Circle Draw a square whose sides are the diameter of the circle. At the center of each side define the point of tangency for the circle. Draw the diagonals of the square. Orient the paper so you can draw equal arcs to construct the circle

Isometric ellipses In an isometric drawing, the object is viewed at an angle, which makes circles appear as ellipses. Holes Cylinders Example object – focus on eye piece. Inside (hole) and outside (cylinder) both appear elliptical in this sketch.

Ellipses Can be in Any of Three Planes
Ellipse could appear in any one of the three planes (front, profile or side, horizontal or top) Major axis (long axis) of the ellipse will be along the long diagonal of the rectangle Minor axis (short axis) along the shorter diagonal. Note ellipse must have the correct orientation in the box. (Almost fills the box, if rotated 90 degrees, it would be incorrect for the plane of view.)

Sketching an Isometric of a Hollow Pipe
Isometric object without construction lines Note: Student product will have construction lines.

Step 1 – Creating the Base Box
Length Diameter Recall that the proper way to start an isometric sketch is to lightly sketch in the box within which the object will fit. Process will fairly closely follow that described in of Bertoline.

Step 2 – Ellipse on Front Face
- Corner to corner to get center Lines to Tangent Points - Lines to tangent points Tangent Points Note for students that just front part of box will be shown to keep it simple in the visuals. Sketch in lines corner to corner (along major and minor axis of ellipse) to get center point Sketch perpendicular lines through center point to get tangent points on outside box.

Step 3 – Ellipse on Front Face
Sketch in Arcs Tangent Points Sketch in smooth arcs to join the Tangent points on Major axis and minor axis. Radius of arc on the longer diagonal is shorter than the radius of arc on the shorter diagonal.

Step 3 – Ellipse on Back Face and Profile
Repeat for ellipse on rear face Draw Tangent Lines for Profile Complete Visible Part of Back Ellipse Note that in case on the rear side of the pipe, only a part of the ellipse is visible. So only the part which is visible is drawn with dark lines

Step 4 – Ellipse for Hole on Front Face
Create Box for Hole Sketch Ellipse Encourage student to leave in their light construction lines. Constructions lines not shown here to just add focus to what is being added at this step. Note that the construction line should be much lighter and thinner than the main object lines.

Isometric of Hollow Pipe
Isometric object without construction lines Note: Student product will have construction lines.

Summary Technical drawings are an effective communication media
Projections of various types can be used Isometric projections and creating isometric sketches has been introduced Assignments will emphasize simple isometric sketches Summarize the objectives of the session Will introduce more advanced isometrics and orthographics drawing in next class

Review Questions _______ sketches present the object in a single view, with all three dimensions represented _______ sketches present the object in a series of projections, each one showing only two of the objects’ three dimensions Which among the following is NOT an isometric axes (Hint: Use the Isometric Grid paper for reference)? Note on all REVIEW QUESTIONS slides: Have the students do individually and check with their partner. Will not be graded. This is for better understanding and making the students read the text book. Students could expect such questions in their mid-term and final. Answers will also be posted on WebCT. Answers: Pictorial (Axonometric/Isometric, Perspective, Oblique) Multiview/orthographic c) => spacing between any two axes can be 30, 60, 120, 240 only a) b) d) c) 120° 60° 240° 90°

Tips for Drawing Assignments
Follow Sketching and Text conventions. Title Information is required. Avoid labels on the sketch. Leave the construction lines – MUCH lighter and thinner than the finished lines Include centerlines on isometrics

Tips for Drawing Assignments
Do not try to shade drawing – this is not a pencil sketching class. Use grid paper. Try to sketch along grid lines. Practice sketching straight lines and curves on a grid sheet.

Tips for Pictorial Views
In pictorial views, hidden lines are not shown unless absolutely required for clarity, such as; Non-visible bottom of a blind hole Important feature of object not in direct view In pictorial views, holes or notches without bottom/end visible should be assumed to go completely through the object. Centerlines are to be shown on all isometric pictorials.

In Class Assignment Use Isometric Sketch Paper (ISP)