Activity 8.2 Parametric Constraints
Introduction
Have you ever received an advertisement in the mail that looked like it was tailored
specifically for you? How could the company afford to spend so much time and
money entering your name and other personal information into the various locations
of the advertisement? In order to create such advertisements, the company will store
your personal information within a database. A computer will then plug specific
pieces of your personal information into various locations on a generic document
with links to the database. The same thing happens with email advertisements. This
type of work takes a great deal of preplanning to pull off, but the efforts are worth it if
a number of customers respond.
Engineers perform similar types of plug and produce operations, specifically in the
area of 3D CAD solid modeling. Numeric constraints, also referred to as parametric
dimensions, may not always have a fixed number value. Some objects must be
customized, like a tailored suit or dress. If you were to return to one of your
elementary school classrooms, you would think that someone took normal-sized
furniture and uniformly scaled it down. That could very well have been the case. If
designed correctly in a 3D CAD solid modeling program, the furniture that you
interact with as a young adult can be scaled down by changing one or more
dimensions. Companies are beginning to build this type of design flexibility into their
internet-based customer ordering systems. If the customer enters specific
dimensional values, colors, and sometimes materials into the online database, the
computer updates the sizes and features of the various associated parts, and then
places and delivers an order to the company staff. This is only one example of the
power of parametric modeling.
In this activity you will learn how algebraic formulas can be used to replace numeric
values in a 3D CAD solid model.
Equipment



Computer with 3D CAD solid modeling software
Engineering notebook
Number 2 pencil
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 1
Procedure
1. Study the image below and table on the next page. Complete the following tasks.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 2
a. Use the given information to fill in the missing parametric equations and missing
numeric values for each parameter in the table below.
Dimension
Description
Geometric
Relationship
Parametric
Equation
Value
d0
Overall Plate
Depth
--
--
3 in.
5:3 ratio;
Overall Plate
overall plate
d1
d0*(5/3)
Width
width to overall
plate depth
20 times
Plate
smaller than
d2
d1/20
Thickness
the overall
width
perpendicular
Plate Taper
to the top and
d3
-0°
Angle
bottom plate
surfaces
½ the overall
d4
Slot Width
d0/2
plate depth
4/5 of the
Slot Width
d5
overall plate
Location
width
1/3 of the
Slot Depth
d6
overall plate
Location
depth
same as the
d7
Slot Radius
d2
plate thickness
Slot Extruded
same as the
d8
Height
plate thickness
same as the
Slot Taper
d9
plate taper
d3
Angle
angle
Hole Width
¼ of the overall
d10
Location
plate width
2/3 of the
Hole Depth
d11
overall plate
Location
depth
twice the slot
d12
Hole Diameter
2*d7
radius
Hole Extruded
same as the
d13
Height
slot height
Small Hole
same as the
d14
d9
Taper Angle
slot taper angle
b. Use your parametric equations to create the object above in a 3D CAD solid
modeling program per the instructions below. Be sure to use the same parameter
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 3
names for each dimension as identified in the table in number 1 above. The only
numeric values that you should enter are 3 inches for dimension d0, and 0° for
dimension d3. All other parameters should be defined using a formula. When
finished, save the file and identify its name and location in your student folder.
NOTE: The hole (diameter d12) was created using the CIRCLE tool.
File name: ______________________
Location: _________________________
1. Sketch a rectangle. Dimension
the depth first (d0) and then the
width (d1).
2. Extrude the rectangle the
appropriate distance (d2) using a
formula. Note that a parameter
will automatically be assigned for
the taper angle (d3) of the
extrusion. The default taper
angle is zer0 degrees.
3. Sketch and dimension the slot
on the top surface of the plate
using the parameter names
shown and the appropriate
formulas. Be sure that the
semicircular ends of the slot are
tangent to the straight edges of
the slot.
4. Extrude Cut the slot the
appropriate distance (d8).
Again, a parameter will
automatically be assigned for the
taper angle of the extrusion (d9).
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 4
5. Sketch and dimension a circle on
the top surface of the plate to
represent the hole using the
parameter names shown and
appropriate formulas.
6. Extrude Cut the hole the
appropriate distance (d14).
Again, a parameter will
automatically be assigned for the
taper angle (d13).
c. Record the physical properties of the part below.
Volume: _________________
Surface Area: __________________
d. Change the overall plate depth to 1.5 inches, that is d0 = 1.5 in. Be
prepared to demonstrate the change to your teacher.
i. Describe what happens to the plate and the features when you revised
the dimension.
ii. Record the physical properties of the part after it is resized.
Volume: ________________
Surface Area: __________________
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 5
2. An aluminum (density 2.710 g/cm3) part is represented in the image below.
This part must be created using parametric constraints so that it can be
quickly and accurately resized when necessary. Complete each of the follow
tasks.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 6
a. What drawing views are displayed above? How does each view help
describe the part?
b. Create the part as a 3D CAD solid model. Use the following parametric
constraints to dimension the model.

The overall height of the part is 2 inches

The top width is 0.5 inches

The right height is ¼ inch less than half of the overall height

The overall width is 50 percent larger than the overall height

The depth is 0.25 inches greater than the overall height

The upper hole diameter is 1/8 in. larger than the top width

The lower hole diameter is 1/16 in. less than the upper hole diameter

The edge distance (the distance from the outside circumference of the
hole to the edge of the part) from the lower hole to the right edge of the
part (along the inclined plane) is 1/8 in. greater than one quarter of
the upper hole diameter (see drawing). Note that you will dimension
to the hole center in the model but are given a constraint on the edge
distance. Call the distance from the lower hole center to the right edge
right to hole center distance in the parameter table.

The hole centers are aligned at the same distance from the back edge
of the included plane. The hole center-to-center distance is 1/8 in.
less than half of the overall width.

The distance from the back edge to the hole centers is one third of
the part depth.

The hole depth of both holes is half the diameter of the lower hole

The notch width is 35 percent of the overall width

The notch depth is always 0.25 inches.

The notch is centered in the front face from left to right. The notch
location is the distance from the right face to the right edge of the
notch (see drawing).

The inside vertical edges of the notch are filleted to a fillet radius of ¼
the top width.

The shell thickness is half of the hole depth.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 7
c. Edit the parameter table for your part in the 3D CAD solid modeling
software in order to identify each dimension that is underlined in the
constraints list. That is, either rename a parameter to match each
underlined label (Example 1, below) or add each underlined dimension
label in the comment column in the appropriate row (Example 2, below).
Example 1:
Example 2:
d. Find the following physical properties of the part as described above.
Overall Width: _____________
Right to Hole Center: ______________
Hole Center-to-Center: __________________
Volume: _________________
Surface Area: ___________________
Mass: __________________
e. Change the overall width of the part to 3.5 inches and the top width to 3/8
in. Be prepared to demonstrate the change in the part within the software
for your teacher. Find the following physical properties of the resized part.
Overall Width: ____________________
Right to Hole Center: __________________
Hole Center-to-Center: ___________________
Volume: __________________
Surface Area: _________________
Mass: _______________________
f. What view would be helpful in order to show and properly dimension the
shell thickness?
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 8
3. (Optional) An image of an Automoblox T9 vehicle (full size) and an image of
an Automoblox T9 Mini vehicle are shown below. Each image includes a
ruler. A multi-view drawing of a simplified Passenger Base for the full sized
vehicle is also provided. Assuming that the Mini vehicle is simply a scaled
down version of the full sized toy, create a CAD part file for the T9 that will
allow the user to create a part model of the Passenger Base for the Mini by
simply changing the overall width of the part. Note that the edge round radius
(0.02 inches) is a function of the equipment used to create the parts and will
remain the same for both vehicles. Also note that the holes for the connector
inserts are identical on opposite faces and that all holes (for the passengers
and for the connector inserts) are assumed to be centered on the part faces.
Automoblox T9
Automoblox T9 Mini
a. Create a part file for the full size T9 Passenger Base part. You may want
to make annotations in the comment column of the parameter table as you
create the part to document your dimensioning. Record the following
physical properties of the full-size Passenger Base. Note: Be sure to
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 9
create a new part file for the Passenger Base according to the given
dimensions. For the purposes of this exercise, do not use a previously
created part file.
Volume: ____________________
Surface Area: __________________
Mass: _________________
b. Revise your 3D solid modeling parameter table for the Passenger Base to
include parametric equations specifying the relationship among
parameters in order to allow a scaled resizing of the part.
c. By what factor should you multiply the overall width of the full-size part in
order to obtain the overall width of the Mini? Hint: Use approximate
measurements (see images) to approximate the relationship.
Full sized dimension x __________ = Mini dimension
d. If all of the parametric equations are written correctly, the object should
increase or decrease in size and maintain its geometric proportions. Test
your part file by scaling the object down to produce a T9 Mini Passenger
Base. Record the following physical properties for the Mini part.
Overall width: _____________________
Overall height: ______________________
Volume: ____________________
Surface Area: __________________
Mass: _________________
e. (Optional). Produce a fully dimensioned part drawing for the Passenger
Base for the T9 Mini.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 10
Conclusion
1. What is the difference between a numeric and a geometric constraint?
2. What advantages are there to using parametric equations instead of numeric
values?
3. What disadvantages are there to using parametric equations for numeric values?
4. Describe a situation in which using parametric equations to dimension an object
would be helpful.
© 2012 Project Lead The Way, Inc.
Introduction to Engineering Design Activity 8.2 Parametric Constraints – Page 11