Ellipsoidal Solid

Solid ellipsoidal element with geometry, inertia, and color

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Libraries:
Simscape / Multibody / Body Elements

Description

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

By default, the block has only one reference frame that defines the position and orientation of the solid. To create additional frames on the body, in the Frames section, select the Create button .

You can use the block to model a single rigid body or create a compound rigid body by combining it with other solids that are rigidly connected and positioned using Rigid Transform blocks.

Compute Inertia Properties

You can compute the inertia properties of a solid, if you set the Inertia > Type parameter to Calculate from Geometry. This setting exposes the Inertia button in the toolstrip of the Property Inspector. To compute the inertia properties, click the Inertia button and the visualization pane displays the computed values.

The block defines the center of mass in the reference frame of the solid and specifies the moments and products of inertia in the inertia frame of resolution, which aligns its axes with the reference frame and positions its origin at the center of mass of the solid.

Visualize Solid

The Property Inspector includes a visualization pane that provides instant visual feedback on the solid. Use the pane to check and adjust the shape and color of the solid. To inspect the solid from different angles, select a standard view, interact with the view selection cube or orientation triad, or rotate, pan, and zoom the display.

To view the latest changes to the solid geometry in the visualization pane, in the toolstrip, click Refresh. You can also display the frames on the solid and change the background color of the visualization pane by clicking Frames and Background in the toolstrip.

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

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

G — Geometry

geometry

Convex hull that represents the true geometry of 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

Geometry

Radii — Ellipsoid radii along the x, y, and z semiprincipal axes

[1 1 2] m (default) | three-element vector

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) | Custom | Point Mass

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.

Dependencies

To enable this parameter, set Type to Calculate from Geometry.

Density — Mass per unit volume of material

1000 kg/m^3 (default) | scalar

Mass per unit volume of material. The value is a scalar with units of density and can be positive or negative. Specify a negative mass density to model the effects of a void or cavity in a solid body.

Dependencies

To enable this parameter, set:

1. Type to Calculate from Geometry

2. Based on to Density

Mass — Total mass of the solid element

1 kg (default) | scalar

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.

Dependencies

To enable this parameter, set Type to Custom or Point Mass. Alternatively, set Type to Calculate from Geometry and then set Based on to Mass.

Center of Mass — Center-of-mass coordinates

[0 0 0] m (default) | three-element vector

[x y z] coordinates of the center of mass relative to the block reference frame.

Dependencies

To enable this parameter, set Type to Custom.

Moments of Inertia — Diagonal elements of inertia tensor

[1 1 1] kg*m^2 (default) | three-element vector

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

$$\left(\begin{array}{ccc}{I}_{xx}& & \\ & I_{yy}& \\ & & I_{zz}\end{array}\right),$$

where:

• $$I_{xx}={\displaystyle \underset{m}{\int }\left(y^2+z^2\right)dm}$$

• $$I_{yy}={\displaystyle \underset{m}{\int }\left(x^2+z^2\right)dm}$$

• $$I_{zz}={\displaystyle \underset{m}{\int }\left(x^2+y^2\right)dm}$$

Dependencies

To enable this parameter, set Type to Custom.

Products of Inertia — Off-diagonal elements of inertia tensor

[0 0 0] kg*m^2 (default) | three-element vector

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

$$\left(\begin{array}{ccc}& I_{xy}& I_{zx}\\ I_{xy}& & I_{yz}\\ I_{zx}& I_{yz}& \end{array}\right),$$

where:

• $$I_{yz}=-{\displaystyle \underset{m}{\int }yzdm}$$

• $$I_{zx}=-{\displaystyle \underset{m}{\int }zxdm}$$

• $$I_{xy}=-{\displaystyle \underset{m}{\int }xydm}$$

Dependencies

To enable this parameter, set Type to Custom.

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.

Diffuse 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.

Dependencies

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

Opacity — Graphic opacity

1.0 (default) | scalar in the range of 0 to 1

Graphic opacity, specified as a scalar in the range of 0 to 1. A scalar of 0 corresponds to completely transparent, and a scalar of 1 corresponds to completely opaque.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Simple.

Diffuse 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 light due to diffuse reflection, specified as an [R,G,B] or [R,G,B,A] vector with values in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

The diffuse color reflects the main color of the rendered solid and provides shading that gives the rendered object a three-dimensional appearance.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Specular Color — Color of light due to specular reflection

[0.5 0.5 0.5 1.0] (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 light due to specular reflection, specified as an [R,G,B] or [R,G,B,A] vector with values in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1. This parameter changes the color of the specular highlight, which is the bright spot on the rendered solid due to the reflection of the light from the light source.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Ambient Color — Color of ambient light

[0.15 0.15 0.15 1.0] (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 ambient light, specified as an [R,G,B] or [R,G,B,A] vector with values in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

Ambient light refers to a general level of illumination that does not come directly from a light source. The Ambient light consists of light that has been reflected and re-reflected so many times that it is no longer coming from any particular direction. You can adjust this parameter to change the shadow color of the rendered solid.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Emissive Color — Self-illumination color

[0.0 0.0 0.0 1.0] (default) | 3-by-1 or 1-by-3 vector with values in the range of 0 to 1

Color due to self illumination, specified as an [R,G,B] or [R,G,B,A] vector in the range of 0 to 1. The vector can be a row or column vector. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of 1.

The emission color is color that does not come from any external source, and therefore seems to be emitted by the solid itself. When a solid has an emissive color, the solid can be seen even if there is no external light source.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Shininess — Highlight sharpness

75 (default) | scalar with value constrained to 0–128

Sharpness of specular light reflections, specified as a scalar number on a 0–128 scale. Increase the shininess value for smaller but sharper highlights. Decrease the value for larger but smoother highlights.

Dependencies

To enable this parameter, set:

1. Type to From Geometry or Marker.

2. Visual Properties to Advanced.

Frames

Show Port R — Show reference frame port for connection to other blocks

on (default) | off

Select to expose the R port.

New Frame — Create custom frame for connection to other blocks

button

Click the Create button to open a pane for creating a new body-attached frame. In this pane, you can specify the name, origin, and orientation for the frame.

• To name the custom frame, click the text field of the Frame Name parameter. The name identifies the corresponding port on the solid block and in the tree view pane of the Multibody Explorer.

• To select the Frame Origin of the custom frame, use one of the following methods:

  • At Reference Frame Origin: Make the new frame origin coincident with the origin of the reference frame of the solid.

  • At Center of Mass: Make the new frame origin coincident with the center of mass of the solid.

  • Based on Geometric Feature: Make the new frame origin coincident with the center of the selected feature. Valid features include surfaces, lines, and points. Select a feature from the visualization pane, then click Use Selected Feature to confirm the location of the origin. The name of the origin location appears in the field below this option.

• To define the orientation of the custom frame, under the Frame Axes section, select the Primary Axis and Secondary Axis of the custom frame and then specify their directions.

  Use the following methods to select a vector for specifying the directions of the primary and secondary axes. The primary axis is parallel to the selected vector and constrains the remaining two axes to its normal plane. The secondary axis is parallel to the projection of the selected vector onto the normal plane.

  • Along Reference Frame Axis: Selects an axis of the reference frame of the solid.

  • Along Principal Inertia Axis: Selects an axis of the principal inertia axis of the solid.

  • Based on Geometric Feature: Selects the vector associated with the chosen geometry feature of the solid. Valid features include surfaces and lines. The corresponding vector is indicated by a white arrow in the visualization pane. You can select a feature from the visualization pane and then click Use Selected Feature to confirm the selection. The name of the selected feature appears in the field below this option.

FrameN — Edit or delete existing custom frame

frame name

Frames that you have created. N is a unique identifying number for each custom frame.

• Click the text field to edit the name of an existing custom frame.

• Click the Edit button to edit other aspects of the custom frame, such as origin and axes.

• Click the Delete button to delete the custom frame.

Dependencies

To enable this parameter, create a frame by clicking New Frame.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2019b