2D Essentials

Instructor: Laura Gerold, PECatalog #10614113Class # 22784, 24113, 24136, & 24138Class Start: January 18, 2012 Class End: May 16, 2012

Reminders• 50% Project Plans are due next TODAY!• Final Project is due on May 9th.• Optional extra credit is due next week on April 11th

• Find other countries where 1st and 3rd angle projections are used for 5 extra points

• Details are on blackboard in class materials / extra credit folder

Chapter 3 – Isometric Drawing

Group Project• Individually Create an object using your blocks.• Draw an isometric drawing of your creations.• Trade your drawing with someone in a different row.• With a new drawing in hand from someone else, create the

object on the plan using your blocks.• Questions • Can you create the object with an isometric drawing only? • Was it easier or harder than creating an object using the

orthographic plans?• Which method would you prefer, or would you like both for

creating a part in the “real-world?”

Axonometric Drawings• Axonometric projection is a type of

parallel projection, more specifically a type of orthographic projection, used to create a pictorial drawing of an object, where the object is rotated along one or more of its axes relative to the plane of projection.

• Different from orthographic because of the angle the object is “tipped”

• "Axonometric" means "to measure along axes". There are three axes.

• There are three main types of axonometric projection: isometric, dimetric, and trimetric projection.

Axonometric Drawings• Foreshortening – reducing the length of a line to create an

illusion of an object being in 3D• Isometric Projection – equal foreshortening along each of the

three axis• Isometric is the most common form of axonometric projection

used.

Axonometric Drawings• Dimetric Projection – equal foreshortening along two axis, and

a different along the third axis. Not “tipped” evenly on all planes of projection.

Source: http://draftingmanuals.tpub.com/14276/css/14276_326.htm

Axonometric Drawings• Trimetric projection – different foreshortening along all three

axis directions

Source: http://draftingmanuals.tpub.com/14276/css/14276_327.htm

Isometric Lines• The projections of the edges of a cube make angles of 120

degrees to each other (isometric axes)• Any line parallel to one of these lines is called an isometric

line• Isometric Lines are used to draw normal edges

Non-Isometric Lines• Non-Isometric Lines are lines that are not parallel to the

isometric axes • The lengths of non-isometric lines cannot be measured

directly with a scale• Non-isometric lines are used to draw inclined & oblique

surfaces

Oblique Surfaces in Isometric• Step 1: Find the intersections of the oblique surfaces with the

isometric planes. • Note that for this example, the oblique plane contains point A,

B, and C

Oblique Surfaces in Isometric• Step 2: To draw the plane, extend line AB to X and Y, in the

same isometric plane as C• Use lines XC and YC to locate points E and F

Oblique Surfaces in Isometric• Step 3: Finally draw AD and ED using the rule that parallel

lines appear parallel in every orthographic or isometric view

Group Project - Oblique Surfaces in Isometric

• Create a simple isometric sketch of an oblique surface. Use items you brought, items in the room, or go on a quick scavenger hunt around the 2nd floor

• Label the isometric and non-isometric lines• Shade in the oblique planes• Present your drawing as a group to the class

Hidden Lines and Centerlines• Hidden lines are omitted from pictorial drawings unless they

are needed to make the drawing clear• Draw centerlines locating the center of a hole only if they are

needed to indicate symmetry or for dimensioning• Use centerlines sparingly in isometric drawings - “If in doubt,

leave them out”

Angles in Isometric• Angles project true size only when the plane containing the

angle is parallel to the plane of projection• An angle may project to appear larger or smaller than the true

angle depending on its position

Drawing Angles in Isometric• The multi-view below shows three 60 degree angles. None of

the three angles will be 60 degrees in the isometric drawing.

Drawing Angles in Isometric• Step 1. Lightly draw an enclosing box

using the given dimensions, except for dimension X, which is not given.

• Step 2. To find X, draw triangle BDA from the top view full size as shown.

• Step 3. Transfer dimension X to the isometric drawing to complete the enclosing box Find dimension Y by a similar method and then transfer it to the isometric.

• Step 4. Use dimension K to locate point E. A protractor can’t be used to measure angles in a isometric drawing . Convert angular measurements to linear measurements along isometric axes.

Group Project - Angles in Isometric

• Draw a multi-view (orthographic) sketch of a triangle with three angles, 30, 60, and 90 on the front view, with a depth and width of your choice.

• Create an isometric drawing using your orthographic sketch• Present

Drawing Curves in Isometric• Draw curves using a series of offset measurements• Select points in random along curve in top view and correlate

in front view

Drawing Holes in Isometric• When a circle lies in a plane that is not parallel to the plane of

projection, the circle projects as an ellipse.• The ellipse can be constructed using offset measurements.• There are several different methods that can be used to draw

an isometric ellipse . . . We’ll cover a couple in class.

Isometric Ellipse – Random Line Method

• Step 1: Draw parallel lines spaced at random across the circle

• Step 2: Transfer these lines to the isometric drawing

Isometric Ellipse in a non-isometric plane

• If the curve lies on a non-isometric plane (it is inclined or oblique), can not directly apply offset measurements

• Step 1. Draw lines in the orthographic view to locate points

Isometric Ellipse in a non-isometric plane

• Step 2 Enclose the cylinder in a construction box and draw the box in the isometric drawing

• Draw the base using offset measurements• Construct the inclined ellipse by locating points and drawing

the final curve through them

Isometric Ellipse in a non-isometric plane

• Step 3: Darken the final lines

Orienting Ellipses in Isometric• All diagonals on an isometric cube are horizontal or are at 60

degrees to the horizontal• Approximate ellipses drawn using the four center method are

accurate enough for most isometric drawings

Drawing a 4-Center Ellipse• Step 1. Draw or

imagine a square enclosing the circle in the multi-view drawing

• Draw the isometric view of the square (with sides equal to the diameter of the circle).

Drawing a 4-Center Ellipse• Step 2. Mark the

midpoint of each line• Step 3. Draw two

large arcs with radius R, from the intersections of the perpendiculars in the closest corners

• Step 4. Draw the two small arcs with radius, r

• Demonstration

Group Project - Isometric Ellipses

• Use your blocks to build a simple object• Draw the object in isometric complete with holes show as

isometric ellipse• If you brought an item with holes , you can draw that item

instead• Present drawings

Isometric Cylinders• To create an isometric cylinder, connect two ellipses with

parallel lines tangent to the appropriate axis

Group Project – Isometric Cylinders

• Use an object you brought, that I have, or that you find in a room and draw an isometric cylinder

• Present results

Screw Threads in Isometric• Use parallel partial ellipses equally spaced at the symbolic

thread pitch to represent the crests of a screw thread in isometric

Visualization Exercise• http://

www.wisc-online.com/objects/ViewObject.aspx?ID=ENG20004

Chapter 7 – Section Views

Why do we need Section Views?

• To see what is “hidden” within a item to be able to build it• To show the material that the item is built out of• How-To Architect

UNDERSTANDING SECTIONSSection views are used for three main purposes:

• To document the design and manufacture of single parts that are manufactured as one piece.

• To document how multiple parts are to be assembled or built.

• To aid in visualizing the internal workings of a design.

When the part is cut fully in half, the resulting view is called a full section.

The Cutting PlaneThe cutting plane appears edgewise as a thick dashed line called the cutting-plane line. The arrows at the ends of the cutting-plane line indicate the direction of sight for the sectional view.

The Cutting Plane

Visible Edges on Cutting Planes

Newly visible edges cut by cutting plane are crosshatched with section lining.

LABELING CUTTING PLANES

Note that each section (A-A and B-B)is completely independent.

RULES FOR LINES IN SECTIONVIEWS

• Show edges andcontours that are

now visible behind the cutting plane.

• Omit hidden lines in section views.

RULES FOR LINES IN SECTIONVIEWS

• Show edges and contours that are now visible behind the cutting plane.

• Omit hidden lines in section views.

• A sectioned area is always completely bounded by a visible outline—never by a hidden line.

• A visible line can never cross a sectioned area in a view of a single part.

CUTTING-PLANE LINE STYLEIt is made up of equal dashes, each about 6 mm (1/4“) long ending in arrowheads. This form works especially well for drawings. The alternative style, uses alternating long dashes and pairs of short dashes and ends with arrowheads. This style has been in general use for a long time, so you may still see it on drawings. Both lines are drawn the same thickness as visible lines. The arrowheads at the ends of the cutting plane line indicate the direction in which the cutaway object is viewed.

Alternative Methods for Showing a Cutting PlaneA and B.

Visualizing Cutting-Plane Direction

Correct and Incorrect Cutting-Plane Line Placement

SECTION-LINING TECHNIQUE• Uniformly spaced by an interval of about 2.5 mm

• Not too close together

• Uniformly thin, not varying in thickness

• Distinctly thinner than visible lines

• Neither running beyond nor stopping short of visible outlines

SECTION-LINING TECHNIQUE continued….

Group Project - Section Views• Draw a section view of a simple object (blocks?) in the room

Section Views Visualization Exercise

• http://www.wisc-online.com/objects/ViewObject.aspx?ID=ENG19804

What’s Next?• Finish Chapter 7 – Section Views

Questions?• On one of your sketches, answer the following two questions:• What was the most useful thing that you learned today?• What do you still have questions about?

Homework

Chapter 3 Exercises: 3.1 (h, i – isometric sketch only)Chapter 7 Review Questions: 1