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**Techniques and Applications**

Technical Illustration Techniques and Applications PowerPoint by Anthony J. Panozzo Publisher The Goodheart-Willcox Co., Inc. Tinley Park, Illinois

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**Axonometric Drawing Techniques**

Chapter 5 Axonometric Drawing Techniques

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Learning Objectives Identify and explain the different types of pictorial and axonometric drawings. Plan, lay out, and draw isometric views of objects containing normal, inclined, skewed, irregularly curved, and circular surfaces. Use isometric ellipse templates, isometric protractors, and angle ellipse templates as drawing aids.

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Learning Objectives Identify and explain the primary applications of computer-generated axonometric drawings. Develop drawings using the isometric, dimetric, and trimetric methods of pictorial drawing.

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Pictorial Drawing A style used to show all three dimensions of an object in a single view. Used in technical illustration almost exclusively. Each pictorial style can be further divided into specific classifications.

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Pictorial Drawing

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**Axonometric Drawings There are three drawing types. Isometric Dimetric**

Refers to equal measure. Dimetric Refers to two measures. Trimetric Refers to three measures.

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Axonometric Drawings In an isometric drawing, equal angles (120°) are used between each of the primary axes. The scales used for each axis are also equal. In a dimetric drawing, two of the angles used between the primary axes are equal. Two of the scales for the axes are equal. In a trimetric drawing, the axis intersections produce three different angles. Three different scales are used for the axes.

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Axonometric Drawings

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Oblique Drawings An oblique drawing is similar to an axonometric drawing. A front view is parallel to the projection plane and top and side views are viewed at an oblique angle. The width and height axes are full scale. The receding axis scale varies depending on the type of drawing. The receding axis angle can be any angle between 0 and 90.

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**Oblique Drawings There are three types. Cavalier oblique**

The receding axis is full scale. Cabinet oblique The receding axis is half scale. General oblique The receding axis is drawn at a scale other than one-half or full size.

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Oblique Drawings Common receding axis angles and scale factors are typically used.

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Perspective Drawings Used to represent what is normally seen from a given viewing point. Receding axis lines converge to a vanishing point as they recede. There are three types related to the number of vanishing points. One-point perspective Two-point perspective Three-point perspective

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Perspective Drawings

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**Applications of Pictorial Drawings**

Each style has advantages and limitations. Select the most appropriate method for a given illustration. Proper selection enhances viewer understanding and saves drawing time.

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**Axonometric Drawing Applications**

Primary use is for rectangular objects with flat plane surfaces. Curved and irregular shapes are difficult to show because of receding object faces. Isometric drawings are the most used. Advantages include ease of layout and scaling. Disadvantages include a slight oversizing and distortion of proportion. Dimetric and trimetric views can produce more realism but take longer to draw.

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**Oblique Drawing Applications**

Primary use is for objects with circular, cylindrical, or irregular shapes easier to draw with a normal front view. Also used for objects with one long axis.

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**Perspective Drawing Applications**

Primary use is in architectural and interior design. Very realistic views are used to show a specific viewing location and elevation. More drawing time is required. Most suitable for flat-surface objects with rectangular shapes.

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**Advantages of Pictorials**

Provide the best way to represent an object. Simplify what is shown for the viewer. Quicker to draw than multiview drawings. Hidden lines are normally excluded. Placing part labels and notes is much quicker than dimensioning orthographic views.

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**Disadvantages of Pictorials**

Present difficulty when dimensions are required for manufacturing. The viewing angle may cause distortion in the object. Hidden details may be difficult to visualize. Complex shapes may be difficult to draw.

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Isometric Projection The object is rotated 45 to the frontal plane and tipped forward 35°16 from the horizontal plane. Horizontal lines are drawn at 30 from the X axis. In comparison to an isometric drawing, measurements are foreshortened by approximately 82%. Foreshortening all measurements can make a true-scaled view difficult to draw.

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Isometric Projection

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**Isometric Drawing An isometric drawing is made at full scale.**

The object is approximately 1.22 times larger than an isometric projection.

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**Isometric Drawing Types**

Regular isometric drawing Horizontal axes are drawn at 30° (most common). Reversed axis isometric drawing The orientation of the axes is the exact opposite of the regular axis isometric orientation. Used to show details on the bottom of an object. Long axis isometric drawing Includes a major horizontal axis and two axes inclined at 60°. Used to show features along one axis.

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**Isometric Drawing Types**

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**Object Orientation in Isometric Views**

Choose the best view where the desired features are emphasized. The object should be drawn in its operating position orientation. Select a different view if the most natural has many hidden features.

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**Drawing Isometric Lines and Nonisometric Lines**

Horizontal and vertical isometric lines are always parallel to the isometric axes. Nonisometric lines are inclined to the isometric axes. To draw, each endpoint is first plotted on isometric lines. Plotted points are then connected. The block-in technique is useful and accurate.

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Block-in Technique First, draw an isometric block with light construction lines and the overall dimensions. “Block in” the individual points of the profile and connect the points with isometric lines until the shape is defined. Develop all normal isometric lines first, then one nonisometric surface at a time.

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**Block-in Technique Locate the step features on the front face first.**

Locate the corresponding points on the back plane of the block. Connect the points with isometric lines.

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Block-in Technique Nonisometric lines and surfaces require additional steps. Draw an isometric block with the overall dimensions. Measure distances on each orthographic view and transfer to points on isometric lines parallel to axis lines on the block. Connect the points with nonisometric lines. Nonisometric lines are not true length and cannot be measured directly with a scale.

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**Block-in Technique (Nonisometric Surfaces)**

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**Drawing Isometric Arcs, Circles, and Irregular Curves**

Circles and arcs appear as ellipses in an isometric drawing. The coordinate method simplifies the drawing process for arcs. Points are located on curves using isometric lines as reference lines. An orthographic view is commonly used to transfer coordinate points.

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**Coordinate Method First, “block in” the basic object shape.**

Identify coordinate points on the curved shape in the orthographic projection. Transfer coordinates from the orthographic view to the corresponding points in the isometric view. Connect the points in a smooth curve with an irregular curve or spline. Locate points on the closest surface first, then background features.

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Coordinate Method

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**Constructing Isometric Circles**

The four-center method is more efficient than the coordinate method. Plotting coordinates for a circle requires many points to provide a good shape definition. Using arcs and center points on an isometric plane simplifies the process.

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Four-Center Method Locate the center of the isometric circle and draw a square around it with isometric lines. Locate the midpoint on each side. Draw lines from the corners to the opposite midpoints. Draw the ellipse sides using the necessary radii and the corners as the centers. Draw the ends using the necessary radii and the line intersections as the centers. Check for smoothness before darkening.

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Four-Center Method The radius values labeled R1 are for the ellipse sides. The radius values labeled R2 are for the ellipse ends.

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Four-Center Method If the arcs do not meet properly, draw a correction arc. Reset the compass to the proper radius of the small arc. Draw arcs from the ends of the large arcs to locate a new center. Draw the arc.

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**Centering Isometric Views**

Regular isometric drawing Locate the center of the drawing area. Drop a vertical line from the center point one-half the maximum height of the object. Draw a 30° line one-half the width of the object. To show the front face on the left, draw to the right. To show the back, draw to the left. Draw a 30° line one-half the depth of the object in the opposite direction of the line drawn in Step 3. The endpoint is the bottom front or bottom rear corner of the object.

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**Centering Isometric Views**

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**Centering Isometric Views**

Reversed axis isometric drawing Locate the center of the drawing area. Draw a vertical line up from the center point one-half the maximum height of the object. Draw a 30° line one-half the width of the object. To show the front face on the left, draw to the right. To show the back, draw to the left. Draw a 30° line one-half the depth of the object in the opposite direction of the line drawn in Step 3. The endpoint is the top front or top rear corner of the object.

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**Centering Isometric Views**

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**Centering Isometric Views**

Long axis isometric drawing Locate the center of the drawing area. Drop a line from the center point one-half the width of the object at a 60° angle to horizontal. To show the front face on the left, draw to the right. To show the back, draw to the left. Draw a 60° line one-half the object height in the opposite direction of the line drawn in Step 2. Draw a horizontal line one-half the object depth in the same direction as the line in Step 3. The endpoint is the bottom front or rear of the object.

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**Centering Isometric Views**

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**Isometric Drawing Aids**

More types of templates are available for isometric drawing than for any other type of drawing. US Customary and metric sizes are available. There are three major types of templates. Isometric ellipse template Angle ellipse template Isometric protractor

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**Isometric Ellipse Templates**

Made of plastic with precise holes for tracing. Used to draw ellipses on normal isometric surfaces. Holes are 22% oversized (no calculations are needed). Templates are labeled Isometric or 35°16.

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**Angle Ellipse Templates**

Used for circular shapes inclined or skewed to the principal projection planes. Holes are true size. Use a larger ellipse to compensate for isometric oversizing. For US Customary sizes, multiply the true size by 1 1/4 (1.25) and round to the closest size available. For metric sizes, multiply the true size by 1.22 and round to the closest size available.

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**Angle Ellipse Templates**

Full sets normally consist of a series of 10 separate templates. Viewing angles range from 10° (very flat) to 55° (almost circular). Templates progress in increments of 5°. Templates are selected for different isometric surfaces with an isometric protractor.

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**Using Isometric Ellipse Templates**

Align the proper axis lines with construction lines on the drawing. The ellipse must have three-axis alignment. The ellipse center is first aligned with the center of the hole or cylinder. The ellipse is turned to align with the vertical axis and the appropriate horizontal axis.

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**Using Isometric Ellipse Templates**

On vertical surfaces, the minor ellipse axis is parallel to the horizontal axis on the other side of the vertical axis and one axis line is vertical. On horizontal surfaces, the minor axis is vertical and the major axis is horizontal.

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**Using Angle Ellipse Templates**

Orient the ellipse center on the construction line center point on the drawing. Rotate the ellipse so the minor axis is parallel to the centerline (thrust line) of the circular shape. Determining the angle of the ellipse and drawing the thrust line present difficulty. An isometric protractor is typically used to identify the angle ellipse and thrust line.

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**Using Angle Ellipse Templates**

A 1 ellipse is used for a diameter hole (.8125 1.22 = 1.01 or 1). The ellipse minor axis is aligned parallel to the thrust line.

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**Using Ellipse Templates**

Isometric ellipses can be used to measure distances along nonisometric lines and surfaces. Any point on the ellipse perimeter represents the same distance from the center. To measure, the ellipse must always be properly oriented on the drawing plane.

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**Using Ellipse Templates**

After isometric lines are drawn, a 1 isometric ellipse sets the thickness of the inclined face. A 1/2 ellipse tangent to the top edge sets the thickness of the upper nonisometric face.

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**Isometric Protractor Used to measure nonisometric angles.**

Readings are divided into four quadrants. Angular values progress from 0 to 90 and reverse back to 0. To use, the minor axis of the template is aligned with an appropriate isometric axis.

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Isometric Protractor

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Isometric Protractor Elliptical shapes identify the different angle ellipses. A line through each ellipse aligns with the minor axis and represents the thrust line. The reading along the edge identifies the thrust line angle. Use the angle to determine the angle ellipse required. Use the closest ellipse to the reading for thrust lines that do not align precisely with an ellipse.

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**Developing Nonisometric Features**

Measure the angle to draw the nonisometric line. Draw the horizontal line for the top surface and then complete the front face.

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**Developing Nonisometric Features**

To draw the top surface, align the protractor with the top vertex point and measure 90 to establish the line perpendicular to the front face. Center and align the protractor on the front face and draw the thrust line parallel to a perpendicular axis line.

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**Developing Nonisometric Features**

Calculate the thrust line angle in the proper direction by counting degrees toward the “open air” side of the object. For the thrust line angle reading of 60, a 50 angle ellipse is used.

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**Isometric Drawing with Computer-Aided Drafting (CAD)**

CAD programs typically provide tools and features that simplify isometric drawing. Isometric grid A 30 dot pattern establishes the drawing axes. Used for layout, blocking in, and drawing. Grid and snap spacing is set based on divisions related to major drawing features. Isometric cursor Provides a visual aid for axis alignment.

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Isometric Grid

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Isometric Axes In a CAD system, isometric lines are easily drawn using angle entries. Each axis line can be drawn with one of two angles. Angles are typically measured counterclockwise from 0 horizontal. Isometric axis angles are useful to know when the grid is not suitable. Other angles are used for nonisometric lines.

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**Isometric Axis Drawing Angles**

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**Isometric Line Drawing Functions in CAD**

Absolute and relative coordinates are used to a lesser extent in isometric drawing. Polar coordinate entry is an essential tool. Coordinates are normally located from a previous point using a distance and angle Drawing typically begins in the lower-middle portion of the screen. The drawing is centered once complete.

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**Drawing Isometric Lines**

The left face begins with the Line command at the origin. Point Point Point Point Point or Close

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**Drawing Isometric Lines**

The top-left face begins at Point 2. Point Point Point

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**Drawing Isometric Lines**

The top-right face begins at Point 5. Point Point Point

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**Drawing Isometric Lines**

To complete the upper portion of the right face, pick Point 8 and To complete the lower-right face, pick the origin and (Point 10) and (Point 9).

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Isometric Planes The three normal isometric planes are identified with different cursors. Left isoplane Right isoplane Top isoplane The isoplane cursors are used for regular or reversed axis isometric drawing. A different cursor is required for long axis isometric drawing.

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Isometric Planes

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**Isocircle and Ellipse Functions**

CAD systems typically provide tools for drawing isometric ellipses (isocircles) automatically. To draw, select the desired isoplane, then enter the center point and radius or diameter. Drawing procedures vary for nonisometric ellipses.

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**Isometric Editing and Illustrating Techniques**

Trimming or clipping allows removal of lines for hidden features. A cutting edge is used. The Erase command is also useful. Lines may be added or deleted to enhance visualization or save time while leaving design requirements unchanged. Try different editing functions if those used in orthographic views are not useful.

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**Trimming Isometric Features**

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Dimetric Drawing Often used as a compromise between isometric and trimetric drawing. Isometric oversizing may be undesirable. Less time is required than in trimetric drawing. Common axis angles and scales are used.

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**Dimetric Drawing Axis Combinations (Regular Axis)**

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**Dimetric Drawing Axis Combinations (Reversed Axis)**

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**Dimetric Drawing Principles**

Circular features may require special methods. Angle ellipse templates can be used for features lying between axes with the same scale. Coordinate layout is used for features lying between axes with different scales.

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**Coordinate Layout for Circular Shapes (Dimetric Drawing)**

Draw an orthographic view and divide with grid lines to locate points on the perimeter. Draw a grid aligned with an axis in the dimetric view. Use the appropriate scale for the grid lines along the foreshortened axis. Transfer points to the dimetric view. Fit the points.

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**Coordinate Layout for Circular Shapes (Dimetric Drawing)**

A 10 left and 40 right axis layout is used in the example. The scales are 1 for the left and vertical axes and .5 for the right axis. The left face does not require coordinate layout.

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**Dimetric Drawing Applications**

Use when appearance and proportion are more important than drawing time. Avoid when the drawing has circular or irregular shapes. Objects with rectangular or normal surfaces are most suitable.

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Trimetric Drawing Typically provides the most realism of the axonometric drawing styles. Requires more time to develop and is used less than isometric and dimetric drawing. Drawings have three different axis angles and scales. There are two major horizontal axis angle orientations. 45/15 35/25

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**Trimetric Drawing Axis Angle Orientations**

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**Trimetric Drawing Principles**

Measures along each axis can be developed using angle ellipse sizing rather than specific scales. For 45/15 axis orientations, use 25, 35, and 55 angle ellipses for the three faces. For 35/25 axis orientations, use 30, 40, and 35 angle ellipses. Block in the object first, then locate features using angle ellipses or scales.

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**Trimetric Drawing Axis Measurements**

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**Trimetric Drawing Principles**

Common axis scales are used for drawings with 45/15 axis angle orientations. Vertical axis scale = 1 Scale for axis with smallest receding angle = .75 Scale for axis with largest receding angle = .5 Circular features must be developed using coordinate layout. Using specific scales for other configurations can cause object distortion.

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**Trimetric Drawing Principles**

Proper object orientation is important. For objects with a much longer axis for one side than others, rotate the view so the side aligns with the smaller receding angle.

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**Trimetric Drawing Applications**

Use when proportionate pictorial drawings are required. If drawing time is a factor, other methods are normally used. Objects with rectangular or normal surfaces are most suitable.

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**Parallelogram Construction of Arcs and Circles**

Sometimes required for dimetric and trimetric drawings. Used when a surface angle cannot be calculated or an angle ellipse protractor is not suitable. Used for circular shapes with different scales on their axes.

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**Parallelogram Construction of Arcs and Circles**

First, draw a parallelogram with sides parallel to the axis lines of the surface. Locate the ellipse center (use diagonal lines if the hole is centered on the surface). Locate the endpoints of the major axis along the longer diagonal. Select an angle ellipse. Draw the ellipse at true scale and tangent to the parallelogram sides.

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**Parallelogram Construction of Arcs and Circles**

The example uses 10 and 40 angles for the horizontal axes. The scale factors are 1 for the left and vertical axes and .5 for the right axis.

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**Computer-Aided Dimetric and Trimetric Drawing**

CAD systems provide numerous tools that simplify drawing methods. Ellipse construction is much simpler. Several CAD aids are particularly useful. Grid and snap rotations Modified scaling functions Editing options

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**Establishing Dimetric and Trimetric Axes**

Rotate the snap and grid to angles that set the horizontal axes. Set snap and grid distances to reflect object dimensions. Change axis alignments depending on the features to be constructed.

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**Scale Modification Functions**

Different methods can be used to simplify drawing based on the tools available. Enter the exact distances required by calculating scaled measures mathematically. Set the snap to an axis scale factor and the grid to a related value. Enter fractional values using polar coordinates based on the axis scales needed. Use mathematical expressions with the system calculator.

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**Object Snap Functions in Dimetric and Trimetric Drawing**

Several object snap modes are useful. Intersection Endpoint Midpoint Node (point) Tangent Box in the object to set reference points. Use construction lines or points as needed. Copy objects whenever possible.

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**Dimetric and Trimetric Drawing Editing Functions**

Several basic commands provide different ways to modify objects. Scale Copy Mirror Erase Trim and Extend Save before and after making edits.

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**Scale Command Apply after objects are first drawn full scale.**

Receding measurements can be scaled as needed. Using system calculations helps reduce mistakes.

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**Copy Command Use for lines or arcs that are repeated in a drawing.**

Make copies to avoid drawing the same object twice. Use snap functions to maximize productivity.

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Mirror Command Useful when a dimetric drawing has equal angles and scales for the horizontal axes. One side can be mirrored about the vertical axis to avoid redrawing features. Use endpoints rather than snap points or grid dots to select the mirror line.

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**Erase Command Use to remove construction lines and unwanted features.**

Place features to be removed on a single layer so it can be deleted.

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**Trim and Extend Commands**

Use to modify temporary construction lines and arcs into finished objects. Trimming removes portions of an object at a cutting edge. Extending adds to an object so it meets a boundary edge.

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**Questions What are the three types of axonometric drawings?**

Isometric, dimetric, and trimetric. At what scale is the receding axis drawn in a cavalier oblique drawing? Full scale. What is the primary use for perspective drawings? Architectural and interior design.

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Questions At what angle are horizontal lines drawn in a regular isometric drawing? 30° above horizontal. What types of shapes are drawn using the four-center method? Isometric circles.

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Questions What is the difference between isometric and nonisometric lines? Isometric lines are parallel to the isometric axes. Nonisometric lines are not parallel to an isometric axis. What is the difference between holes on isometric and angle ellipse templates? Holes on an isometric ellipse template are 22% oversized and no calculation is necessary to use them. On an angle ellipse template, holes are true size and larger ellipses must be used.

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**Questions How are ellipses aligned on vertical isometric surfaces?**

The minor ellipse axis is parallel to the horizontal axis on the other side of the vertical axis on the drawing. What is the purpose of an isometric grid in a CAD drawing? It establishes a 30 pattern for the isometric drawing axes.

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Questions What type of coordinate entry is an essential tool for pictorial drawing in a CAD system? Polar. What CAD editing function permits the removal of lines for hidden features and uses a cutting edge? Trimming. What types of objects lend themselves best to dimetric drawing? Objects with rectangular or normal surfaces.

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Questions What two horizontal axis angle orientations are most commonly used in trimetric drawing? 45/15 and 35/25.

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**Glossary Cabinet oblique Cavalier oblique Coordinate method**

An oblique drawing in which the receding axis is drawn at half scale. Cavalier oblique An oblique drawing in which the receding axis is drawn at full scale. Coordinate method A method of defining curves on foreshortened or angled surfaces in which points on a grid are transferred from an orthographic view.

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**Glossary Dimetric drawing Four-center method**

An axonometric pictorial drawing in which two of the three angles created by the intersections of the axes are equal, but the third angle is different. Measurements along two of the axes use the same scale, but the third axis is drawn at a different scale. Four-center method A method used to locate center points for arcs defining an isometric circle.

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**Glossary General oblique Isometric cursor Isometric drawing**

An oblique drawing in which the receding axis is drawn at a scale other than one-half or full size, typically a three-quarter scale. Isometric cursor In a CAD system, a set of crosshairs that are rotated to align with the isometric axis. Isometric drawing An axonometric pictorial drawing in which the axes form 120 angles and measurements along all axes are drawn to the same scale.

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**Glossary Isometric grid Isometric lines Isometric protractor**

In a CAD system, a series of dots that align on a 30 pattern to establish the left and right axes. Isometric lines Horizontal and vertical lines parallel to an isometric axis. Isometric protractor A drafting instrument used to measure angles inclined or skewed to the principal isometric planes.

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**Glossary Long axis isometric drawing Nonisometric lines**

An isometric drawing that has one major axis aligned horizontally and the other axes inclined at a 60° angle to horizontal. Nonisometric lines Lines in an isometric drawing that are not parallel to one of the isometric axes.

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**Glossary Oblique drawing One-point perspective**

A type of pictorial drawing in which the front face is parallel to the projection plane, and the top and side views are viewed at an oblique angle. A receding axis is used to measure the depth and extends away from the face. One-point perspective A type of pictorial drawing in which a front view is parallel to the picture plane and receding axis lines converge at a single vanishing point.

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**Glossary Operating position orientation Regular isometric drawing**

The position an object is in when a person is using, controlling, or viewing it in its natural environment. Regular isometric drawing A drawing in which the left and right horizontal axes are drawn at a 30° angle above horizontal. Reversed axis isometric drawing A drawing in which the axes are drawn in the exact opposite orientation as a regular axis isometric drawing.

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**Glossary Three-point perspective Trimetric drawing**

A type of pictorial drawing in which the principal planes are inclined to the picture plane and receding axis lines converge to three vanishing points. Trimetric drawing An axonometric pictorial drawing in which all three angles created by the intersections of the axes are unequal, and each axis uses a different scale.

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**Glossary Trimming Two-point perspective**

In a CAD system, removing a portion of an object using another object as a cutting edge. Also known as clipping. Two-point perspective A type of pictorial drawing in which the principal planes are inclined to the picture plane and receding axis lines converge to two vanishing points.

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**Glossary Vanishing point**

A point in a perspective drawing where receding lines converge.

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