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Specifying Solid Inertia

The inertial properties of a rigid body influence its dynamic behavior. One example is the flywheel: the greater its inertia, the greater the rotational energy that it can store. In SimMechanics™, you specify the inertial properties using a Solid or Inertia block. Use a Solid block to specify geometry and color in addition to inertia. Use an Inertia block to specify only inertia. Both blocks provide multiple inertia types that you can select. You can represent a solid as a point mass or as a mass distribution (3-D solid).

To use the blocks, drag them from the Body Elements library.

Point Mass

A point mass occupies an infinitesimally small volume. When you treat a solid as a point mass, you assume its total mass exists at its center of mass. The moments and products of inertia of a point mass are zero, and you need only specify the total mass.

Adding a Point Mass to a Model

To position a point mass in a model, connect the block reference frame port (R) to the frame of your choice. A frame port, line, or node represents the frame. The point mass coincides with the origin of this frame. For example, connect the Solid block R frame port to the World Frame block W frame port to represent a point mass that coincides with the World frame origin.

For more information about frames, see Representing Frames.

Specifying Point Mass Inertia

To specify the inertial parameters of a point mass:

  1. In the block dialog box, expand Inertia.

  2. In Type, select Point Mass.

  3. In Mass, enter the total mass of the solid.

Mass Distribution

A mass distribution occupies a measurable region of space. All rigid bodies are 3-D mass distributions. To completely describe a mass distribution, you specify the total mass, center of mass, moments of inertia, and products of inertia.

You can use two inertia types to represent a mass distribution. Select Calculate from Geometry to automatically calculate the center of mass, moments of inertia, and products of inertia from the solid geometry. Select Custom to manually specify all inertial properties. The Solid block provides both inertia types. The Inertia block provides only Custom.

Adding a Mass Distribution to a Model

To position a mass distribution, connect the block reference frame port (R) to the frame of your choice. A frame, line, or node represents the frame. The reference frame origin coincides with the origin of this frame. For example, connect the Solid block R frame port to the World Frame block W frame port to represent a 3-D mass distribution whose reference frame origin coincides with the World frame origin.

The center of mass of the solid depends on the inertia type you use. If you select Custom, the center of mass depends on the coordinates that you manually specify with respect to the solid reference frame. If you select Calculate from Geometry, the center of mass depends on the geometry that you use. For more information, see the Solid block reference page.

Automatically Calculating Inertia

To automatically calculate the center of mass, moments of inertia, and products of inertia of a mass distribution:

  1. In the Solid block dialog box, expand Inertia.

  2. In Type, select Calculate from Geometry.

  3. Specify the remaining parameters as defined in the Solid block reference page.

    Note:   To automatically calculate the inertia of a solid from its geometry, you must specify a valid SimMechanics shape. If you specify a geometry from a file, you must manually enter all inertia parameters using inertia type Custom.

Specifying Custom Inertia

To manually specify all inertia parameters of a mass distribution:

  1. In the block dialog box, expand Inertia.

  2. In Type, select Custom.

  3. Specify the remaining parameters as defined in the Solid block reference page.

Related Examples

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