2012

3D Solids
The following table shows the mass properties that are displayed for solids.
Mass properties for solids
DescriptionMass property
The measure of inertia of a body. Because a density of one is used,
mass and volume have the same value.
Mass
The amount of 3D space that a solid encloses.Volume
The diagonally opposite corners of a 3D box that encloses the solid.Bounding box
A 3D point that is the center of mass for solids. A solid of uniform
density is assumed.
Centroid
The mass moments of inertia, which is used when computing the
force required to rotate an object about a given axis, such as a wheel
rotating about an axle. The formula for mass moments of inertia is
Moments of in-
ertia
mass_moments_of_inertia = object_mass * radius
axis
2
Mass moments of inertia unit is mass (grams or slugs) times the dis-
tance squared.
Property used to determine the forces causing the motion of an object.
It is always calculated with respect to two orthogonal planes. The
formula for product of inertia for the YZ plane and XZ plane is
Products of iner-
tia
product_of_inertia
YZ,XZ
= mass * dist
centroid_to_YZ
* dist
centroid_to_XZ
This XY value is expressed in mass units times the length squared.
Another way of indicating the moments of inertia of a solid. The for-
mula for the radii of gyration is
Radii of gyra-
tion
gyration_radii = (moments_of_inertia/body_mass)
1/2
Radii of gyration are expressed in distance units.
Calculations that are derived from the products of inertia and that
have the same unit values. The moment of inertia is highest through
Principal mo-
ments and
a certain axis at the centroid of an object. The moment of inertia isX,Y,Z directions
about centroid lowest through the second axis that is normal to the first axis and
that also passes through the centroid. A third value included in the
results is somewhere between the high and low values.
1086 | Chapter 13 M Commands