Ellipsoidal Solid

Solid ellipsoidal element with geometry, inertia, and color

Libraries:
Simscape / Multibody / Body Elements

Description

The Ellipsoidal Solid block is a three-dimensional extension of the ellipse with geometry center coincident with the reference frame origin and semi-principal axes coincident with the reference frame x, y, and z axes.

The Ellipsoidal Solid block adds to the attached frame a solid element with geometry, inertia, and color. The solid element can be a simple rigid body or part of a compound rigid body—a group of rigidly connected solids, often separated in space through rigid transformations. Combine Ellipsoidal Solid and other solid blocks with the Rigid Transform blocks to model a compound rigid body.

Geometry parameters include shape and size. You can choose from a list of preset shapes or import a custom shape from an external file in STL or STEP format. By default, for all but STL-derived shapes, the block automatically computes the mass properties of the solid from the specified geometry and either mass or mass density. You can change this setting in the Inertia > Type block parameter.

A reference frame encodes the position and orientation of the solid. In the default configuration, the block provides only the reference frame. A frame-creation interface provides the means to define additional frames based on solid geometry features. You access this interface by selecting the Create button in the Frames expandable area.

Derived Properties

You can view the calculated values of the solid mass properties directly in the block dialog box. Setting the Inertia > Type parameter to Calculate from Geometry causes the block to expose a new node, Derived Values. Click the Update button provided under this node to calculate the mass properties and display their values in the fields below the button.

Derived Values Display

Visualization Pane

The block dialog box contains a collapsible visualization pane. This pane provides instant visual feedback on the solid you are modeling. Use it to find and fix any issues with the shape and color of the solid. You can examine the solid from different perspectives by selecting a standard view or by rotating, panning, and zooming the solid.

Select the Update Visualization button to view the latest changes to the solid geometry in the visualization pane. Select Apply or OK to commit your changes to the solid. Closing the block dialog box without first selecting Apply or OK causes the block to discard those changes.

Ellipsoidal Solid Visualization Pane

Right-click the visualization pane to access the visualization context-sensitive menu. This menu provides additional options so that you can change the background color, split the visualization pane into multiple tiles, and modify the view convention from the default +Z up (XY Top) setting.

Examples

Fairground Carousel Ride

A fairground carousel ride. A torque applied to the wheel causes the carousel to rotate and a hydraulic actuator provides the force to lift the arm. The cabs are free to rotate about an axis approximately tangential to the wheel radius. When the wheel is near vertical, the centrifugal acceleration acting on the cabs (caused by the rotation of the wheel) ensures that the cabs are close to a near vertical position. Consequently, the riders are close to 'up-side-down' at the top of the rotation.

Open Model

Ports

Frame

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R — Reference frame
frame

Local reference frame of the solid. This frame is fixed with respect to the solid geometry. Connect this port to a frame entity—port, line, or junction—to resolve the placement of the reference frame in a model. For more information, see Working with Frames.

Geometry

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G — Geometry
geometry

Geometry that represents the solid. Connect this port to a Spatial Contact Force block to model contacts on the solid.

Dependencies

To enable this port, under Geometry, expand Export and select Entire Geometry.

Parameters

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Geometry

Radii — Ellipsoid radii along the x, y, and z semiprincipal axes
`[1 1 2] m` (default) | scalar with units of length

Ellipsoid radii along the x, y, and z axes of the solid reference frame. The ellipsoid becomes a sphere if all radii are equal.

Entire Geometry — Export the true geometry of the block
`off` (default) | `on`

Select Entire Geometry to export the true geometry of the Ellipsoidal Solid block which can be used for other blocks, such as the Spatial Contact Force block.

Dependencies

To enable this option, select Entire Geometry under the Export.

Inertia

Type — Inertia parameterization to use
`Calculate from Geometry` (default) | `Point Mass` | `Custom`

Inertia parameterization to use. Select Point Mass to model a concentrated mass with negligible rotational inertia. Select Custom to model a distributed mass with the specified moments and products of inertia. The default setting, Calculate from Geometry, enables the block to automatically calculate the rotational inertia properties from the solid geometry and specified mass or mass density.

Based on — Parameter to base inertia calculation on
`Density` (default) | `Mass`

Parameter to use in inertia calculation. The block obtains the inertia tensor from the solid geometry and the parameter selected. Use Density if the material properties are known. Use Mass if the total solid mass if known.

Density — Mass per unit volume of material
`1000 kg/m^3` (default)

Mass per unit volume of material. The mass density can take on a positive or negative value. Specify a negative mass density to model the effects of a void or cavity in a solid body.

Mass — Total mass of the solid element
`1 kg` (default) | scalar with units of mass

Total mass to attribute to the solid element. This parameter can be positive or negative. Use a negative value to capture the effect of a void or cavity in a compound body (one comprising multiple solids and inertias), being careful to ensure that the mass of the body is on the whole positive.

Custom: Center of Mass — Center-of-mass coordinates
`[0 0 0] m` (default) | three-element vector with units of length

[x y z] coordinates of the center of mass relative to the block reference frame. The center of mass coincides with the center of gravity in uniform gravitational fields only.

Custom: Moments of Inertia — Diagonal elements of inertia tensor
`[1 1 1] kgm^2` (default) | three-element vector with units of masslength^2

Three-element vector with the [I_xx I_yy I_zz] moments of inertia specified relative to a frame with origin at the center of mass and axes parallel to the block reference frame. The moments of inertia are the diagonal elements of the inertia tensor

$(\begin{matrix} I_{x x} \\ I_{y y} \\ I_{z z} \end{matrix}),$

where:

$I_{x x} = \int_{m} (y^{2} + z^{2}) d m$
$I_{y y} = \int_{m} (x^{2} + z^{2}) d m$
$I_{z z} = \int_{m} (x^{2} + y^{2}) d m$

Custom: Products of Inertia — Off-diagonal elements of inertia tensor
`[0 0 0] kgm^2` (default) | three-element vector with units of masslength^2

Three-element vector with the [I_yz I_zx I_xy] products of inertia specified relative to a frame with origin at the center of mass and axes parallel to the block reference frame. The products of inertia are the off-diagonal elements of the inertia tensor

$(\begin{matrix} I_{x y} & I_{z x} \\ I_{x y} & I_{y z} \\ I_{z x} & I_{y z} \end{matrix}),$

where:

$I_{y z} = - \int_{m} y z d m$
$I_{z x} = - \int_{m} z x d m$
$I_{x y} = - \int_{m} x y d m$

Calculate from Geometry: Derived Values — Display of calculated values of mass properties
button

Display of the calculated values of the solid mass properties—mass, center of mass, moments of inertia, and products of inertia. Click the Update button to calculate and display the mass properties of the solid. Click this button following any changes to the block parameters to ensure that the displayed values are still current.

The center of mass is resolved in the local reference frame of the solid. The moments and products of inertia are each resolved in the inertia frame of resolution—a frame whose axes are parallel to those of the reference frame but whose origin coincides with the solid center of mass.

Dependencies

The option to calculate and display the mass properties is active when the Inertia > Type block parameter is set to Calculate from Geometry.

Graphic

Type — Graphic to use for visualization
`From Geometry` (default) | `Marker` | `None`

Type of the visual representation of the solid, specified as From Geometry, Marker, or None. Set the parameter to From Geometry to show the visual representation of the solid. Set the parameter to Marker to represent the solid as a marker. Set the parameter to None to hide the solid in the model visualization.

Visual Properties — Parameterizations for color and opacity
`Simple` (default) | `Advanced`

Parameterizations for specifying visual properties. Select Simple to specify Diffuse Color and Opacity. Select Advanced to specify more visual properties, such as Specular Color, Ambient Color, Emissive Color, and Shininess.

Dependencies

To enable this parameter, set Type to From Geometry or Marker.

Shape — Shape of marker to represent to the solid
`Sphere` (default) | `Cube` | `Frame`

Shape of the marker by means of which to visualize the solid. The motion of the marker reflects the motion of the solid itself.

Dependencies

To enable this parameter, set Type to Marker.

Size — Width of the marker in pixels
10 `pixels` (default) | scalar

Width of the marker in pixels. This width does not scale with zoom level. Note that the apparent size of the marker depends partly on screen resolution, with higher resolutions packing more pixels per unit length, and therefore producing smaller icons.

Dependencies

To enable this parameter, set Type to Marker.

Color — Color of light due to diffuse reflection
[0.5 0.5 0.5] (default) | 3-by-1 or 1-by-3 vector with values in the range of 0 to 1 | 4-by-1 or 1-by-4 vector with values in the range of 0 to 1

Color of the graphic under direct white light, specified as an [R G B] or [R G B A] vector on a 0–1 scale. An optional fourth element (A) specifies the color opacity on a scale of 0–1. Omitting the opacity element is equivalent to specifying a value of 1.