|
Introduction
Pro Engineer has a built-in feature which calculates
the center of gravity of a given model. The purpose of this tutorial is
to guide the user through the steps necessary to make that calculation.
Included is also a suggested method of parametrically marking the center
of gravity location using an additional set of data planes. The instructions
detailed here are for a particular version of Pro/E. The menus and messages
in your version of Pro/E may differ slightly.
The Preliminaries
In order to calculate the center of gravity of
a model, Pro Engineer requires a predefined coordinate system. To create
a default coordinate system named CS0 which is aligned with the default
datum planes, do the following. From the part menu make the following
selections:
#FEATURE
#CREATE
#DATUM
#COORD SYS
Select the default coord system choice. After generating
the default coordinate system, you should see a set of 3D cross hairs
labeled CS0, (these are the letters CS followed by the number zero, not
the capital letter O).
Determining the Center
of Gravity of Your Model
Calculation
of the center of gravity is initiated through commands located in the info
menu. Follow these steps to calculate the center of gravity:
#INFO
#MODEL ANALYSIS
#MODEL MASS PROPERTIES
#COMPUTE
You can see that you have options to change default
accuracy and and coordinate system from this window. COMMENT: Unless you
are concerned with high levels of accuracy, the default accuracy should
produce acceptable results. The cost of higher accuracy specifications
is an increase in the calculation time.
You can select or create the coordinate system in which
you would like the center of gravity to be located and also relative accuracy
if you want.
After making this selection you will be prompted to
enter the density of the material of your model. Pro Engineer needs this
information to compute other properties of your model, such as its total
mass.
=>Enter density of <the name of
your part> in POUNDS/CUBIC INCH [1]:
If you are unconcerned about total mass or other density
related properties, then hit return, which accepts the default value (the
value in brackets). If you are only concerned about locating the center
of gravity, you may also simply accept the default value by hitting return.
Parametrically Marking
The Center of Mass
Introduction To Parametric
Relations
The following is a suggestion of how to mark the
location of the center of gravity you just calculated above. The method
described below necessitates that you mark the center of gravity only
once in your model. Afterward, if you change the geometry of your model
and recalculate the location of the center of gravity, the position of
your center of gravity marker will automatically be moved to the new center
of gravity location.
This method exploits a useful feature provided in Pro
Engineer. Pro Engineer allows the user to create parametric relationships
between dimensions or other quantities which describe the model you are
creating. These relationships are simply called relations in Pro
Engineer. Relations can take the form of straight equalities such as:
d2="d1"
They can also take the form of more involved equations
like:
d2 ="d1*6 + sin(d1)"
In both these examples d2 (some dimension in your model)
is a function of d1 (some other dimension in your model). This means whenever
you change d1, d2 will automatically change according to the relation
you have written. Once you establish this relation, d2 may not be modified
independently of d1. It can only be changed as a function of d1. You may
always modify or delete any relation you have created.
NOTE: Refer to the Pro/E manuals or on-line
help system for more information and more detailed explanations concerning
relations.
Creating the Center
of Gravity (COG) Marker
Introduction
We suggest that you use datum planes to
mark your center of gravity. Since datum planes are features which have
no volume or mass, they make no "physical" change to your model when you
add them. To create your markers, create three new datum planes, each
of which are offset from a different default datum plane. If you created
a default coordinate system, CS0, along with your default datum planes,
the offset distance of each of the created datum planes will be its distance
from the CS0 origin along one of the coordinate axes.
Example 1
To
create a new datum plane (dtm4) as an offset from dtm2, you are making a
new datum plane which is parallel to dtm2 and set off of it by some distance
specified by you. If dtm2 lies in the x-z plane of the CS0 coordinate system,
then the offset specified for dtm4 is also the z coordinate of dtm4 in the
CS0 coordinate system.
Creating Offset Datum
Planes
In detail here is how to
create a new datum plane offset from one of the default datums:
Beginning from the feature menu make the following
selections:
#CREATE
#DATUM
#PLANE
#OFFSET
You should find the following in the message
window:
=>Select one of the following: Plane, Coordinate
System.
Select one of the default datum planes (e.g. DTM2).
The new datum plane you are creating will be parallel and offset from
the default datum plane you select.
You should then see this message:
=>Select location on model for offset value
or "Enter Value" from menu.
Select:
#ENTER VALUE
You should then see this message:
=>Enter offset in the indicated direction,
<ESC> to quit [0.161]:
Look for the arrow pointing away from the default datum
you original selected. If it points in the positive direction of one of
the axes of CS0, enter a positive value which is of the same order of
magnitude as the dimensions you used to create your model (e.g. 1.0).
If the arrow points in the negative direction of one of the axes of CS0,
enter a negative value of the same order of magnitude as the dimensions
of your model.
After entering this value you should see this message:
=>Datum Plane is fully constrained. Select
"Done", "Quit" or "Restart".
Select
#DONE
Repeat the above steps to create the other two datum
planes offset from the remaining default datum planes. If you are only
interested in the planar center of mass location, you need only to create
a total of two offset datum planes.
Relating Datum
Locations to Center of Gravity Coordinates
After creating the offset datum planes, you
can then redefine the offset distances by creating relations. A relation
applied to example 1 would equate the offset dimension for dtm4 to
the z coordinate of the center of gravity taken with respect to the CS0
coordinate system. What follows are the steps to creating these relations:
Starting from the part menu level:
Select:
#RELATIONS
You should see the following message in the message
window:
=>Select a feature to display parameters,
or select from Relation menu.
Select each of three datum planes you just
created. Each of their offset dimensions should appear after you select
them. If you look at the offset dimensions, you should note that their
numerical values have changed to expressions beginning with the letter
"d" followed by an integer. These expressions are the names of the dimensions.
Each dimension specified in Pro Engineer is given a unique name which
begins with the letter d.
Select:
#ADD
You should see the following message in the message
window:
=>Enter RELATION [QUIT]:
To relate the location of the plane offset in the z
direction to the z coordinate (in CS0) of the center of gravity enter
this expression:
< z offset dimension name > =mp_cg_z("","CS0","")
(the < z offset dimension name > might
be d6 or d8 for example. You will have to locate its name in the model
window of your own object.)
Then hit return.
You will receive the following warning.
=>WARNING: Model changed since mass props
calculated. May need to recalculate.
=>Enter RELATION [QUIT]:
Do not be concerned with this warning because
the datum planes are features that have no volume or mass, so they won't
change the location of the center of gravity when they move around.
Repeat the above expression for x an y offset dimensions.
< x offset dimension name > =mp_cg_x("","CS0","")
< y offset dimension name > =mp_cg_y("","CS0","")
After writing these three expressions hit return again
to quit adding relations.
If you get a "Invalid attempt to assign negative value..."
error message, put a minus sign in your relations equation.
After entering the relations, regenerate your model.
The offset datum planes should now intersect at the center of mass. If
they look way off, go back and check your relation equations.
If you modify the geomtry or dimensions of your part,
you must recalculate the location of the center of gravity and then regenerate
your model. After executing these two steps, the datum planes whose offsets
you linked to the center of gravity coordinates should relocate to coincide
with the new center of gravity coordinates.
To check if the COG is located accurately, try the
following. Print out a front view of your part with the datum planes visible
(the show/hide datum planes option is under the Environment menu). Glue
the printout onto a stiff backing such as the back to a pad of paper or
to foam-core. Cut around the outline of the part with an Xacto knife.
You should be able to balance the object on a pencil where the pencil
point is at the intersection of the two offset datum planes.
Back to the Index |
Return
to: U of M Home
