2D EssentialsInstructor: Laura Gerold, PECatalog #10614113Class # 22784, 24113, 24136, & 24138Class Start: January 18, 2012Class 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
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
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 thickdashed line called the cutting-plane line. The arrowsat the ends of the cutting-plane line indicate thedirection of sight for the sectional view. The Cutting Plane
Visible Edges on Cutting PlanesNewly visible edges cut by cutting plane arecrosshatched with section lining.
LABELING CUTTING PLANES Note that each section (A-A and B-B) is completely independent.
RULES FOR LINES IN SECTION VIEWS • Show edges and contours that are now visible behind the cutting plane. • Omit hidden lines in section views.
RULES FOR LINES IN SECTION VIEWS• Show edges and contoursthat are now visible behind thecutting plane.• Omit hidden lines in sectionviews.• A sectioned area is alwayscompletely bounded by avisible outline—never by ahidden line.• A visible line can nevercross a sectioned area in aview 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 formworks especially well for drawings. The alternative style, uses alternating long dashes and pairsof short dashes and ends with arrowheads. This style has been in general use for a long time, soyou may still see it on drawings. Both lines are drawn the same thickness as visible lines. Thearrowheads at the ends of the cutting plane line indicate the direction in which the cutaway objectis viewed. Alternative Methods for Showing a Cutting Plane A 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