CHAPTER 4

GEOMETRIC CONSTRUCTIONS AND

MODELING BASICS

4.1 Points and Lines

4.2 Angles

4.3 Triangles

4.4 Quadrilaterals

A polygon that is bounded by four straight lines.

4.5 Polygons

A polygon is any plane figure bounded by straight lines.

Regular Polygons

• Regular polygons have equal angles and equal sides.

• They are often created and described by inscribing them in a circle,

or circumscribing them about a circle.

• Hex head bolts are a typical example

4.6 Circles

• A circle is a closed curve, all points of which are equally distant

from the center.

• Circumference equals pi times the diameter C = p d

4.7 Creating a Triangle

4.10 Constructing a Bisector

4.11 Constructing a Circle

4.*. General Method to Construct Polygons

Inscribing a Pentagon to a Circle

Inscribing a Hexagon to a Circle

Inscribing a Octagon to a Circle

How would you inscribe a octagon to a given circle?

Dividing a Line into a Proportion

How would you divide a line into a given proportion?

4.12 Tangency

Step-by-Step 4.3

Conic Sections

Conics sections are generated when a plane meets with a right cone.

There are four different curves that can be obtained depending on

the angle the plane makes with the cone axis.

They are circle, ellipse, parabola, and hyperbola that are basic

geometries in engineering graphics.

These curves also appear in describing orbits of satellites in

dynamics.

Click the figure to see the simulation. If it does not start right away, click one more time.

4.13 Ellipse

4.15 Creating a Tangent to an Ellipse

4.16 Creating an Approximate Ellipse

Parabola: Appication 1

Radio telescope

Many bridges use parabolic supports like this.

Application 2

4.17 Drawing an Helix

Details

4.18 Drawing an Involute

An involute is generated when a string is unwound tightly from a point

on the polygon. This curve is used in many places like gear profiles,

specially, for gears that require to transmit large forces and moments.

Involute around a circle

The radius changes slowly to the arc length at the end of the unwinding.

4.19 Cycloid

A cycloid is generated when a circle rolls on a plane. This curve is used

in many places like gear profiles, specially, for gears that does not

require to transmit large forces and moments like in watches.

• If the generating point is on the circumference of a circle that rolls along

the convex side of a larger circle, the generated curve is called

epicycloid, otherwise, hypocycloid.

• Epicycloids and hypocycloids in rotary pump.

Application

4.22 Solids

CAD: Extruded Solid

• CAD construction for a 3D part having a

uniform cross section.

• Named for the manufacturing process of

forming material by forcing it through a

shaped opening.

CAD: Revolved Solid

construction by revolving a uniform cross-

section along a circular path.

CAD: Boolean Operators

• Venn diagrams can be used to

show Boolean operations.

• Union (addition)

• Difference (subtraction)

• Intersection

CAD: Boolean Operations of Solids

Summary

• Points, lines, and circles are the basic geometric elements used to

make 2D sketches.

• Using CAD you can create 3D models.

• Understanding geometric solids can help you create CAD models

and interpret and visualize from 2D sketches and drawings.

Geometric Construction Projects

Spanner

Shaft Hanger Casting

Form Roll Lever