Notes

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Module 4 CAD & Geometric Constraints
4.1 Introduction
All designs and machines begin with a series of drawings depicting the parts and assemblies of
the finished machine, device, or construction. To accomplish this, engineers have traditionally
used a method called geometric construction to create all of their designs. This 2 dimensional
(2D) method is a process that uses a series of geometric shapes to create the more complex
geometry of any given drawing and in turn any part or machine. In this module you will take the
basics of geometric construction and expand these skills into 3Dimensional (3D) modeling as
this is the standard industrial process in designing and engineering of parts and machines. The
exercises are designed to be non-application (software) specific but, to require a demonstration
of the principles and skills necessary for an engineer to create any number of designs and three
dimensional shapes that will make up a part and eventually an assembly. Also, it will be expected
that the engineering student has a working and functional knowledge of the basic geometric 2D
shapes as well as the ability to create these at will.


Figure 4.1 – The completed wheel project. Shown beginning at the top and moving
downward are the top plate, Axle Supports, Wheel, and Bushings (Brass)

Module 4 4.2

4.2 Outcome
Upon completion of this module, you will be able to create and analyze 3 dimensional (3D)
models created with the use of the Extrude and Revolve Tools. You will be competent in the
creation of sketching on the correct plane within the software to generate the proper geometry to
create the model at the proper dimensional sizes and within the correct geometric and
dimensional constraints by completing the review questions, worksheets/ quizzes, application
assignments and comprehensive module assessment.
4.3 Objectives
1. After completion of the application assignments in this module you will be able to apply
correct geometric construction techniques in 2D/ 3D at an intermediate level.
2. After completion of the application assignments in this module you will be able to use
coordinate systems to identify points in space in 2D & 3D.
3. After completion of this module the student will understand and discuss the terminology
used in 2D drafting & 3D modeling by completing a worksheet with a proficiency of
80%.
4. After completion of this module the student will be able to define the difference between
geometric and dimensional constraints by completing a worksheet with a proficiency of
80%.
4.4 Assignments
All assignments need to be filed in engineering notebook as shown in module 2

4.8 CAD & Geometric Constraints Review Questions

4.9.1 Geometric Identification Worksheet
4.9.2 Geometric Shapes Worksheet
4.9.3 Geometric Terms Worksheet
4.9.4 Geometric Constraints & CAD Worksheet

4.10.1 Sketching Models
4.10.2 Extrusion Models
4.10.3 Revolution Models
4.10.4 Puzzle Block Models
4.10.5 Wheel Assembly Models

4.11 CAD & Geometric Constraints Assessment

4.3 Geometric Construction
4.5 Terms to Know
Tool Term Definition

Axis A line used in a coordinate system to measure or
determine relative locations of intersection and
lengths of lines and planes. See Reference
Document B for additional Information.

Concentric Circular Shapes that share a common center point.
See Reference Document B for additional
Information.

Dimensional
Constraint
Used to create length, distance and angle
dimensions. See Reference Document B for
additional Information.
Geometric Constraint Used to create all the Geometrical Constraints.
.See Reference Document B for additional
Information.

Coordinate A set of numbers designating a location based
from a common accepted reference point. See
Reference Document B for additional
Information.

Extrude A tool that stretches a 2D drawing into the third
dimension. See Reference Document B for
additional Information.

Fillet An inside rounded corner between two
intersecting planes. Typical command in CAD for
and rounded corner between two planes.

Horizontal This constraint tool allows you to lock a line into
a horizontal position (orientation).
Module 4 4.4


Parallel This constraint allows you to keep two lines
parallel to each other (have the same orientation).

Perpendicular This constraint allows you to keep two lines at 90°
angle to each other.

Plane A flat 2D surface upon which an engineer can
draw or sketch. See Reference Document B for
additional Information.

Revolve A sketch or drawing that is rotated around a
central axis to create a 3D model. See Reference
Document B for additional Information.

Sketch A free hand drawing used to develop geometry in
a drawing or CAD model. Will typically have
dimensional and geometric constraint information
included. See Reference Document B for
additional Information.

Tangent This constraint allows you to make a circle and a
line (or two circles) so that they both intersect (or
touch) at exactly one point. See Reference
Document B for additional Information.

Vertical This constraint tool allows you to lock a line into
a vertical position (orientation).See Reference
Document B for additional Information.
4.5 Geometric Construction
4.6.1 Cartesian Coordinates
The process of locating and drawing the lines
that create an image using this system is
relatively simple but we must follow some
specific rules and conventions. The process that
is applied is that the corners on a plane of the
object to be drawn can be plotted on that
Cartesian grid. These points can then be
connected like a child’s dot to dot puzzle to
create the image or view of the object. This form
of application for the coordinate system is used
in many industries and particularly in CNC
(Computer Numerical Control) and CAM
(Computer Aided Manufacture) processes. It is a
relatively simple process to go from a CADD
file to a rapid prototype process without having
to do more than simply save the model or
drawing file as a specific type.

4.6.2 3D (Three Dimensional)
Coordinates
In a Cartesian system adding the third dimension
is as simple as adding a third coordinate/axis.
The process of determining a location is the
same but with a simple additional step that
follows the same pattern as the 2D process. That
process is to plot the x axis first then the y
followed by the z. This process is consistent and
easily applied. An example of this is shown in
figure 4.3


Figure 4.2 2D Rectangular or Cartesian
coordinate examples

Figure 4.3 3D Coordinate example

Module 4 4.6

4.6.3 Geometric Construction and Modeling
The engineer designs parts and
machines in answer to a question or
problem that is to be solved in the
function of the final product. To do
this the industry standard is to
design in a CAD system. There are
various applications that can be
applied. The most common are
Autodesk’s Inventor, Dassault
Systems’ Solidworks, and PTC’s
Creo. The choice of software is up to
the engineer as each package has
positive and negatives to the
application.
4.6.4 Creating an
Extrusion (Extruded
Solid)
The first piece that will be used in
this module will be created using extrusions only. An extrusion is a shape that has been pressed,
pulled, or stretched into the third dimension. One of the simplest ways to view this process is to
think of it like it is a child’s “Play Dough” set. The desired shape is place in the press, such as a
star, and then the “dough” is placed in the press’ compartment. The handle presses down into the
compartment forcing the “dough” out through the desired shapes cut-out forming a “worm of
dough” in that shape. This is what an extrusion does but, it is in the CAD system, it is straight
and at a specific length.
This same process, in essence, is what each of the software packages that the engineer might be
using begins with. By sketching the outline of the part to be modeled they can then use the
proper tool to extrude it into the third dimension. The sketch has a feature tool applied to it
creating the virtual 3 dimensional model of that shape.
Once an engineer has determined the form or shape of the part that they are designing, they then
begin the process of creating the CAD file of the parts. These files are used to describe the parts
to the end user or the builder of the part. For example, if an engineer/designer is to design a
simple plate such as the one above (figure 4.4) they still begin with a sketch in the CAD system.
This sketch is as simple as the rough outline of the part to be modeled. Once this outline is
created a designer will usually begin with dimensions that are geometric constraints. These are
Figure 4.4 – Top Plate of wheel project

4.7 Geometric Construction
dimensions that act as control for the overall form of
the part. From there most designers and engineers
work the part just as a machinist would. That is
cutting away in a virtual sense from the CAD
model.
The process that will be included in this module will
create the models for the base plate and the bushing
shown in figure 4.1 on the first page of this module.
Step 1 To begin draw a rectangle using the sketch
tool in the “sketch” mode of the software. This
process begins with the engineer selecting a plane
upon which to draw. Typically, this is the front plane
in the software that is being used. The lower left
corner should be placed at the origin of the plane
upon which you are drawing. Make sure that the
rectangle is truly square and that the sides are
parallel to the opposing side and that the intersecting
lines are perpendicular by using the proper
geometric constrains. In most CAD software the
engineer will apply size dimensions to the sketch to ensure that the extrusion that will be created
from the sketch will be the proper size. The sizes for this sketch are 5.25 inches wide by 3.25
inches high. Once this sketch is complete the engineer will close the sketch at which point it
should appear like figure 4.5 as shown here.




Figure 4.5 – Sketch of top plate after
sketch is complete. Blue lines
indicate that this is a fully constrained
sketch.

Note: Images may not reflect the software package in use at your school. Images captures are
from Autodesk Inventor.
Module 4 4.8

Step 2 The next step is to
extrude the shape formed
in the sketch as shown in
figure 4.6 to the right. To
do this the engineer
proceeds in the model
menu to select the extrude
function. The engineer
then selects the sketch
from the previous step.
The shape will highlight
once it is selected. The
engineer now inputs the
depth the part is to be
extruded to. In this
situation the distance is
5/8 of an inch or, .625
inches. The engineer can
extrude forward into the
viewing plane, backward
in the same plane or in
both directions. For this
function the extrusion
should be done in only
one direction and that is
typically forward. Once the proper depth is set the engineer “clicks” the “ok” button on the
screen. At this point the part has now become a model as it now has width, height, and depth.

Figure 4.6 – The extrude function should look similar to this
preview.

4.9 Geometric Construction
Step 3 While still in the
model or feature menu the
engineer will create the fillets
that are on the outer corners
of the plate as shown in
figure 4.7 to the left. The
engineer selects the fillet tool
and selects the edges on
which to have the fillet
applied. Once the edges are
selected the engineer can
then specify the radius of the
fillets arc in the pop-up menu
for the feature. It is then a
simple “ok” or “apply” to
finish the feature. It is
important to understand that
if you specify too large a
radius that the software will
not allow the fillet to be
applied. In the case of the
part being used here the
radius is ½ or .5 inches and
this is easily handled with the
amount of material available.
The Engineer designing a
part or a machine will need to develop an understanding of the processes involved in the
machining of a part. Typically the process involved in the creating the models use the same basic
pattern as the actual machine processes. Most of the modeling processes can be done in any
order but often times they follow the machine processes. The next step will be to create the holes
for the bolts that will be used to attach the plate to the axle supports. To do this the engineer will
use a “Hole” wizard as shown in figure 4.8 of this module.

Figure 4.7 – Fillet preview from a modeling menu.

Module 4 4.10

Step 4 Making holes using a “Hole”
wizard. This process is available in
most CAD packages and is done
through the use of another sketch
and following model feature. To
begin the engineer selects the
“Sketch” or “2D Sketch” functions
in the software. They must then
select a surface or plane on which to
draw. For this feature the engineer
selects the broad surface that is 5.25
inches by 3.25 inches. It does not at
this time matter if it is the front
surface or the rear surface. The
engineer then uses the geometric
constraints of “Concentric” or
“center” to place points in the sketch
at the center of each of the arcs
created by the fillets on this surface.
The engineer now completes the
sketch and selects “Close” to finalize
this stage of the sketch.
Step 5 Now select the “Hole” option
from the model menu. The software
typically determines that the points
created in the previous step are the
centers of the hole or holes to be
created as shown in figure 4.8
above. A typical “pop up” window
appears to allow the engineer to
enter the specific information for the
hole(s) to be created as shown in
figure 4.9 to the left. This
information can include thread count
and type, counter-sink or counter-
bore information, and any other
information associated with a hole.
For our part the holes will be through holes of .375 inches in diameter with a 16 UNC 2B
Thread. (At this time in your modules the information about threads and fasteners have not been
Figure 4.8 – The hole wizard Function.

Figure 4.9 – Example of a hole wizard popup menu.

4.11 Geometric Construction
covered and will be covered in a later
module.) When the engineer has verified
that all of the information is correct they
will then click on the “apply” or “Ok”
option in the pop up.
On the completed part there are three (3)
recesses in the plate. Two (2) of these are
on the bottom of the plate and one (1) is
on the top as shown in the figure 4.10 to
the left. The following steps will explain
the process to create these recesses using
an extrude cut function.
The extrude cut function is essentially the
same as the extrude function with the
exception that it removes material from
the model instead of adding to the model.
Also it is often accomplished with a
single or minimal dimensional constraints
during the sketch portion of the process
with the sketch extending well beyond the
models own boundaries as seen in figure
4.11 of this module.

Step 6 To create a sketch you must first
select a plane or surface. To do this the
engineer uses their cursor to select the
desired surface on the object that they
wish to sketch on. They now select
“sketch” or “2D sketch” from the menu
ribbon. A pair of rectangular shapes to cut
out the recesses on the top plate can now
be sketched. The rectangle tool is now
used to create two rectangles that begin
outside of the plate and overlap the plate
as shown in figure 4.11 to the right.
These sketches each have a size constraint
placed on them to control the volume of
Figure 4.10 – The completed plate.

Figure 4.11 – Example of extrudes cut option.


Module 4 4.12

material that will be removed from the
plate in creating the recesses. These size
constraints are 1.50 inches in from the
outside edge of the part to the interior
edge of the rectangle. The engineer now
closes the sketch to adjust the cut of
each of these recesses.
Step 7 Select from the model menu the
extrude tool. The engineer will then
select the two rectangles drawn in the
previous step. The engineer will then
select the cut option from the popup
menu and specify a depth of .125 or 1/8
of an inch. Using the preview the
engineer will verify that the cut is
correct then select the “ok” or “apply”
option of the popup to complete the step
as shown in figure 4.12 to the left.

Step 8 Now rotate the part to create a
sketch on the opposing surface or plane.
To do this the engineer typically uses
the free orbit tool or the view/plane tool.
This is often a cube with labeled sides
that the engineer can select a side on
this cube and the model will rotate to
match the alignment represented on the
cube.

Otherwise the free rotate tool is used to
spin the part so that the engineer can
select the surface on which the engineer
will create a sketch. An example of a
“view” cube can be seen in figure 4.13
to the right.

Figure 4.12 – Using the cut feature in the extrude
function.

Figure 4.13 – Example of a view cube.

4.13 Geometric Construction
Step 9 Making a third extrude cut.
This process is exactly the same as
the previous cut process except that
the sketch is completely inside of
original plate along the major or long
axis and protrudes from the piece in
the vertical or minor axis. To do this
the engineer again selects “Sketch”
or “2D Sketch” from the tools in the
ribbon menu. They will then select
the surface opposite the previous
cuts. This is the surface that was
rotated into view using the free rotate
tool. A sketch is now created using
the rectangle tool extending above
and below the minor axis or length
of the plate. The engineer will apply
two dimensional constraints. These
constraints are 1.75 inches and are
from the edges of the part to the
edges of the sketch as shown in
figure 4.14 to the left. The sketch is
now complete and the engineer
should close the sketch.
Step 10 The engineer will now select
the extrude tool again from the
model menu. The sketch will again
be selected and the engineer will
select the cut option and specify that
a depth of .125 is entered as shown
in figure 4.15 to the right. The
engineer will now verify using the
preview that the cut is correct before
selecting the “apply” or “ok” button
to complete the model.

Figure 4.14 – Extrude cut sketch

Figure 4.15 – Extrude Cut

Module 4 4.14

4.6.5 Creating a Revolved Solid
A revolved surface or revolution is the 3 dimensional
shape created when a profile, a 2 dimensional shape, is
rotated around a central axis creating a 3 dimensional
shape. This is sometimes described using an analogy
of a piece of pie that is cut to represent the profile. The
center of the pie is then used as a central axis that the
profile is rotated around. In figure 4.19 the process is
shown for clarity.
The Revolve, or revolution, is always used to make a
cylindrical part or shape in a larger part. As an
example we will demonstrate the creation of a simple
bushing using the revolve feature commands. To begin
all software starts with a blank part file (ipt for
inventor and prt for Solidworks.)
The part to be created is shown in figure 4.16 of this
section. The engineer needs to understand the part
before they begin modeling it. A cross section of this
part would look like a simple “L” with an ascender
that is much shorter than the base. The engineer needs
to also know what the dimensions of this profile or
section is.
Step 1 To begin with the modeling of this part start
with a default file. This file will be drawn in inches
and be done to ANSI standards. The first thing the
engineer will need to do is select a plane on which to
draw. It is recommended that the front plane be
selected.
Step 2 The first line drawn will be a center line that
will note the center of the part as it extends from the
origin in the software. Following this line the engineer
sketches in the outline or profile of the bushing. This shape appears roughly as an “L” with as
long base and short but wide vertical ascender as shown in figure 4.17 to the right.
The engineer will now apply dimensional constraints to the profile. The inner diameter; from the
centerline to the lower line of the profile is .75 Inches. The outer diameter is 1.0 inches and the
shoulder diameter is 1.375 inches as shown in figure 4.17. The Shoulder length is .25 inches and
Figure 4.16 – Example of a
Revolved part

Figure 4.17 – Center line and
profile of bushing sketch

4.15 Geometric Construction
the total length of the bushing is .75 inches. After these are applied
the engineer will finish the sketch and in doing so activate the
modeling menu. To close the sketch the engineer selects the “finish
sketch” button on the screen or ribbon bar as shown in figure 4.18
(Program icons may vary).
The engineer will follow the creation of the profile with the creation
of the bushing in a one-step modeling process. This process is called
a revolve or revolution. It will rotate the profile around the center line
also created in the previous step of this process. In all of the software
packages this part could also be
created using two extrusions but,
because it is a cylindrical part it
is typically create using the
method being shown here.
Step 3 The engineer will now
select the revolve tool from the
ribbon bar which will bring up a
popup menu, shown in figure
4.19. This menu allows the
engineer to select the profile as
well as the axis the profile will
be rotated around. In most
software the profile will
automatically give the engineer a
preview of the model being
created. For this part the angle
should be a full revolution or
360° making the bushing a
cylinder. Once those parameters
are set in the pop-up and the preview shows the part correctly select “ok” to complete the part.
All parts are initially drawn using the default materials in both Inventor and Solidworks but once
the engineer has determined what the part will be constructed of the properties of that material
can be assigned to the model. The menu is most commonly available on the feature history that
usually appears on the left side of the screen. Simply select the properties of the part. Then go to
the physical properties and from the listed materials select the appropriate material. This part is a
brass bushing within which the axle will be mounted and then be mounted into the caster braces
that will support the wheel as it is assembled into the completed model. The completed bushing
with the materials applied can be seen in figure 4.20 of this module.
Figure 4.18 –
Finish Sketch
Button

Figure 4.19 – Revolve menu popup and automatic
preview.

Module 4 4.16

4.6.6 Creating Geometry
As demonstrated in this module engineers
use whatever software is available to their
particular firm or company in developing
the shapes and parts that they will need. In
previous years this was done using hand
tools and drawing instruments. The
students first project in the creation of a
three dimensional shape will be to copy
and extrude the parts of the puzzle block as
designed and recorded in the students
engineering notebook from an earlier
module.
An example of the necessary product that
the engineering student will need to create
can be seen in figure 4.21 of this module.
The information must contain all on the
proper sizing and dimensional information
as well as meet the design requirements as
given in the previous modules. The
example given here has the block pieces in
an explode view that will be discussed in a
later module.

Figure 4.20 – Complete Bushing with
materials applied.

Figure 4.21 – Puzzle Block Pieces

4.17 Geometric Construction
4.7 Summary
The role of geometric constructions in the engineering and design disciplines cannot be over
stated. All designers begin every part of every project by developing the geometric shape that is
used to describe the object they are designing. These shapes must, by definition, adhere to the
rules of geometry and the forms that we have been developing though this module. It is just as
we learn in elementary art. That all things can be drawn when we simplify them down to their
geometric forms and then combine these forms to make the desired object. It really is no
different in designing or engineering. The geometry of an object will determine the function of
that object and its usefulness.
By developing and eventually mastering the skills in geometric constructions engineers develop
their own mental tools to define and create the world around us. Their knowledge of circles,
polygons, and all of the other forms makes it possible to create the designs needed to solve the
problems of today and those that we will find as we develop and progress.

Module 4 4.18

4.8 Review Questions
Directions: In blank provided, letter the correct name of the geometric shape depicted.
Directions: In blank provided sketch the correct geometric shape named in the box provided.
Trapezoid







Rhombus Parallelogram
Equilateral Triangle







Circle Acute Triangle










4.19 Geometric Construction
1. Name and depict in a simple sketch the basic geometric shapes.
2. What is a size or dimensional constraint?
3. What is a location Constraint?
4. What is a geometric constraint?
5. What is the process to create a simple extrusion?
6. What conditions must be met in a sketch to create an extrusion or revolution?
7. What shapes can be used in the creation of an extrusion?
8. What is created using revolve or revolution in CAD?
9. How does revolve differ from extrusion?
10. What shapes can be used in the creation of the revolve tool?
11. What conditions must be met to create a revolved shape?
12. What are the steps in the creation of a revolved model in CAD?
13. What are the proper terms for the 3 dimensions of a CAD model?
14. What geometric feature can be applied to a model in either the sketching stage or the
model stage in the model of a CAD drawing?
Module 4 4.20

Notes: