Chapter 04 ppt - Ivy Tech -

GEOMETRIC

CONSTRUCTION

C H A P T E R F O U R

OBJECTIVES

1. Identify the geometry that makes up basic 2D drawings.

2. Use board drafting or 2D CAD skills to create technical figures.

3. Describe the advantages of CAD contrasted with drawing with manual instruments

Technical Drawing with Engineering Graphics, 14/e

Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman 2

© 2012, 2009, 2003, Pearson Higher Education,

Upper Saddle River, NJ 07458. • All Rights Reserved.

GEOMETRY REVIEW

• Triangles

• Quadrilaterals

• Polygons

• Circles

• Arcs





BISECTING A LINE OR

CIRCULAR ARC

Triangle and T-Square System



Compass system



BISECTING A LINE WITH TRIANGLE

AND T-SQUARE

From endpoints A and B, draw construction lines at 30 °, 45°, or 60° with the given line.

Then, through their intersection, C, draw a line perpendicular to the given line to locate the center D…





Triangles

Inclined lines can be drawn at standard angles with the 45 ° triangle and the

30 ° x 60° triangle. The triangles are transparent so that you can see the lines of the drawing through them. A useful combination of triangles is the 30 ° x 60° triangle with a long side of 10" and a 45 ° triangle with each side 8" long.





Any Angle in 15° Increments

With only a 30

° x 60° triangle and a 45 ° triangle, you can draw any angle in 15 ° increments

The bottom of the triangle in each case is resting on the blade of the

T-square. Twenty-four 15

° sectors are possible with just these two triangles used singly or in combination.





Protractors

For measuring or setting off angles other than those obtainable with triangles, use a protractor.

Plastic protractors are satisfactory for most angular measurements

Nickel silver protractors are available when high accuracy is required





BISECTING AN ANGLE

ANGLES…

TRANSFERRING AN

ANGLE





DRAWING A LINE PARALLEL TO A

LINE AND AT A GIVEN DISTANCE

T-square Method For Curves





DRAWING A LINE THROUGH A POINT

AND PERPENDICULAR TO A LINE

When the Point Is Not on the Line When the Point Is on the Line T-square Method





DRAWING A TRIANGLE

WITH SIDES GIVEN

TRIANGLES…

DRAWING A RIGHT

TRIANGLE WITH

HYPOTENUSE AND ONE

SIDE GIVEN





LAYING OUT AN ANGLE

• Tangent Method

• Sine Method

• Chord Method

Many angles can be laid out directly with the triangle or protractor.





DRAWING AN EQUILATERAL

TRIANGLE

Alternative Method





DRAWING A SQUARE

• T-square Method

• Diameters Method

• Inscribed Circle Method

You can use the AutoCAD Polygon command to draw squares. The

Rectangle command is another quick way to make a square in AutoCAD.





DRAWING A REGULAR PENTAGON

Dividers Method



Geometric Method



DRAWING A HEXAGON

Each side of a hexagon is equal to the radius of the circumscribed circle

Use a compass

Centerline Variation

Steps





Drawing an Octagon

Given an inscribed circle, or distance

“across flats”, use a T-square or straightedge and a 45 ° triangle to draw the eight sides tangent to the circle.

Given a circumscribed square, (the distance

“across flats”) draw the diagonals of the square. Then, use the corners of the square as centers and half the diagonal as the radius to draw arcs cutting the sides





FINDING THE CENTER OF A CIRCLE

This method uses the principle that any right triangle inscribed in a circle cuts off a semicircle.

Another method, slightly longer, is to reverse the procedure. Draw two nonparallel chords and draw perpendicular bisectors. The intersection of the bisectors will be the center of the circle.





DRAWING TANGENTS TO TWO

CIRCLES

AutoCAD software provides a convenient object snap for finding tangency.





DRAWING AN ARC TANGENT TO A

LINE OR ARC

AND THROUGH A POINT

Tangents





DRAWING AN ARC TANGENT TO TWO

LINES AT RIGHT ANGLES


Giesecke, Hill, Spencer, Dygdon, Novak, Lockhart, Goodman

For small radii, such as 1/8R for fillets and rounds, it is not practicable to draw complete tangency constructions. Instead, draw a 45

° bisector of the angle and locate the center of the arc by trial along this line

22




LINES AT ACUTE OR

OBTUSE ANGLES





DRAWING AN ARC TANGENT TO AN

ARC AND A STRAIGHT LINE






ARCS





Drawing an Arc Tangent to Two Arcs and

Enclosing One or Both





DRAWING AN OGEE CURVE

Connecting Two Parallel Lines Connecting Two Nonparallel Lines





THE CONIC SECTIONS

The conic sections are curves produced by planes intersecting a right circular cone.

Four types of curves are produced: the circle, ellipse, parabola, and hyperbola, according to the position of the planes.





DRAWING A FOCI ELLIPSE





DRAWING A CONCENTRIC CIRCLE

ELLIPSE

If a circle is viewed with the line of sight perpendicular to the plane of the circle…

…the circle will appear as a circle, in true size and shape





DRAWING A PARALLELOGRAM

ELLIPSE

The intersection of like-numbered lines will be points on the ellipse. Locate points in the remaining three quadrants in a similar manner. Sketch the ellipse lightly through the points, then darken the final ellipse with the aid of an irregular curve.





ELLIPSE TEMPLATES

These ellipse guides are usually designated by the ellipse angle, the angle at which a circle is viewed to appear as an ellipse.





Irregular Curves

The curves are largely successive segments of geometric curves, such as the ellipse, parabola, hyperbola, and involute.





DRAWING AN APPROXIMATE ELLIPSE

For many purposes, particularly where a small ellipse is required, use the approximate circular arc method.





DRAWING A PARABOLA

The curve of intersection between a right circular cone and a plane parallel to one of its elements is a parabola.





DRAWING A HELIX

A helix is generated by a point moving around and along the surface of a cylinder or cone with a uniform angular velocity about the axis, and with a uniform linear velocity about the axis, and with a uniform velocity in the direction of the axis





DRAWING AN INVOLUTE

An involute is the path of a point on a string as the string unwinds from a line, polygon, or circle.





DRAWING A CYCLOID

A cycloid is generated by a point P on the circumference of a circle that rolls along a straight line

Cycloid





DRAWING AN EPICYCLOID OR A

HYPOCYCLOID

Like cycloids, these curves are used to form the outlines of certain gear teeth and are therefore of practical importance in machine design.





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