Documentation

# Spherical Solid

Solid spherical element with geometry, inertia, and color

• Library:
• Simscape / Multibody / Body Elements

## Description

The Spherical Solid block is a spherical shape with geometry center coincident with the reference frame origin.

The Spherical 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 Spherical 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 or causes the block to discard those changes.

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.

## Ports

### Frame

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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.

## Parameters

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#### Geometry

Distance between the center of the sphere and its surface.

Select Export: Entire Geometry to export the physical properties of the Spherical Solid block to a Spatial Contact Force block.

#### Inertia

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.

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.

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.

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.

[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.

Three-element vector with the [Ixx Iyy Izz] 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:

• ${I}_{xx}=\underset{V}{\int }\left({y}^{2}+{z}^{2}\right)\text{\hspace{0.17em}}dm$

• ${I}_{yy}=\underset{V}{\int }\left({x}^{2}+{z}^{2}\right)\text{\hspace{0.17em}}dm$

• ${I}_{zz}=\underset{V}{\int }\left({x}^{2}+{y}^{2}\right)\text{\hspace{0.17em}}dm$

Three-element vector with the [Iyz Izx Ixy] 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:

• ${I}_{yz}=-\underset{V}{\int }yz\text{\hspace{0.17em}}dm$

• ${I}_{zx}=-\underset{V}{\int }zx\text{\hspace{0.17em}}dm$

• ${I}_{xy}=-\underset{V}{\int }xy\text{\hspace{0.17em}}dm$

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

Choice of graphic to use in the visualization of the solid. The graphic is by default the geometry specified for the solid. Select `Marker` to show instead a simple graphic marker, such as a sphere or cube. Change this parameter to `None` to eliminate this solid altogether from the model visualization.

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

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.

Parameterization for specifying visual properties. Select `Simple` to specify color and opacity. Select `Advanced` to add specular highlights, ambient shadows, and self-illumination effects.

RGB color vector with red (R), green (G), and blue (B) color amounts specified on a 0–1 scale. A color picker provides an alternative interactive means of specifying a color. If you change the Visual Properties setting to `Advanced`, the color specified in this parameter becomes the Diffuse Color vector.

Graphic opacity specified on a scale of 0–1. An opacity of `0` corresponds to a completely transparent graphic and an opacity of `1` to a completely opaque graphic.

True color 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 specifies the color opacity also on a scale of 0–1. Omitting the opacity element is equivalent to specifying a value of `1`.

Color of specular highlights specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of `1`.

Color of shadow areas in diffuse ambient light, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of `1`.

Surface color due to self illumination, specified as an [R,G,B] or [R,G,B,A] vector on a 0–1 scale. The optional fourth element specifies the color opacity. Omitting the opacity element is equivalent to specifying a value of `1`.

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.

#### Frames

Clear the check box to hide the reference frame port in the Solid block. Hiding the reference frame port suppresses the frame visualization in Mechanics Explorer. You must expose the reference frame port if the block has no custom frames.

Select the Create button to define a new frame using the frame-creation interface. Each new frame appears on a row above the New Frame parameter. To edit an existing frame, select the Edit button . To delete an existing frame, select the Delete button .

#### Frame Creation Interface

Frame identifier specified as a MATLAB string. This string identifies the frame port in the block diagram and in the tree view pane of Mechanics Explorer. Keep the frame name short to ensure it fits in the block icon width.

Select the location of the frame origin. Options include:

• At Reference Frame Origin — Make the new frame origin coincident with the reference frame origin. This is the default option.

• At Center of Mass — Make the new frame origin coincident with the solid center of mass. The reference frame origin is located at the center of mass in symmetrical shapes such as spheres and bricks but not in certain extrusions or revolutions.

• Based on Geometric Feature — Place the new frame origin at the center of the selected geometry feature. Valid geometry features include surfaces, lines, and points. You must select a geometry feature from the visualization pane and then select the Use Selected Feature button. The name of the selected geometry feature appears in the field below this option.

Select the axis of the new frame that you want to set as the primary axis. The primary axis constrains the possible orientations of the remaining two axes. Specify the orientation of the primary axis by selecting from the following options:

• Along Reference Frame Axis — Align the primary axis with the selected axis of the reference frame.

• Along Principal Inertia Axis — Align the primary axis with the selected principal inertia axis. The principal inertia axes are those about which the products of inertia are zero.

• Based on Geometric Feature — Align the primary axis with the vector associated with the selected geometric feature. Valid geometric features include surfaces and lines.

Select the axis of the new frame that you want to set as the secondary axis. The secondary axis is the projection of the selected direction onto the normal plane of the primary axis. Select the direction to project from the following options:

• Along Reference Frame Axis — Project the selected reference frame axis onto the normal plane of the primary axis. Align the secondary axis with the projection.

• Along Principal Inertia Axis — Project the selected principal inertia axis onto the normal plane of the primary axis. Align the secondary axis with the projection. The principal inertia axes are those about which the products of inertia are zero.

• Based on Geometric Feature — Project the vector associated with the selected geometry feature onto the normal plane of the primary axis. Align the secondary axis with the projection. Valid geometry features include surfaces and lines. You must select a geometry feature from the visualization pane and then select the Use Selected Feature button.