# Solid

Rigid solid with geometry, inertia, and color

Body Elements

## Description

This block represents a rigid solid with geometry, inertia, and color. The solid 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 Solid and 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. The block can automatically compute the inertial properties of the solid based on the geometry you specify given its mass or mass density.

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.

## Dialog Box and Parameters

### Geometry

Shape

Select a solid shape. The table summarizes the various shapes that you can select. The default shape is `Brick`.

ShapeDescriptionExample
`Cylinder`

Cylindrical shape with geometry center at the reference frame origin and symmetry axis aligned with reference frame Z axis

`Sphere`

Spherical shape with geometry center at the reference frame origin.

`Brick`

Prismatic shape with geometry center at the reference frame origin and faces normal to X, Y, Z axes.

`Ellipsoid`

3-D extension of ellipse with geometry center at the reference frame origin and semi-principal axes aligned with reference frame X, Y, Z axes.

`Regular Extrusion`

3-D sweep of regular polygon cross-section along an extrusion axis.

Shape has geometry center at the reference frame origin, and extrusion axis aligned with reference frame Z axis. Cross-section is constant along extrusion length.

`General Extrusion`

3-D sweep of general cross-section shape along an extrusion axis.

Reference frame origin coincides with cross-section (0,0) coordinate, halfway along extrusion length. Reference frame Z axis aligns with extrusion axis.

Cross-section lies in reference frame XY plane. Cross-section shape and dimensions are constant along extrusion length.

`Revolution`

3-D sweep of general cross-section about a revolution axis.

Reference frame origin coincides with cross-section (0,0) coordinate. Reference frame Z axis aligns with revolution axis.

Cross-section lies in reference frame XZ plane. Revolutions can be full (revolution angle = 360°) or partial (0°<revolution angle<360°). For partial revolutions, the reference frame X axis splits the revolution into two symmetric halves.

`From File`3-D shape loaded from STL (Standard Tessellation Language) or STEP (Standard for the Exchange of Product Data) file.

The reference frame has the origin and orientation defined in the file.

`Cylinder`: Radius

Enter the cylinder radius. This is the distance between the origin and circumference of the transverse cross-section. The default value is `1`. Select or enter a physical unit. The default is `m`.

`Cylinder`: Length

Enter the cylinder length. This is the distance between the two flat surfaces measured along the symmetry axis. The default value is `1`. Select or enter a physical unit. The default is `m`.

`Sphere`: Radius

Enter the spherical radius. This is the distance between the origin and surface of the sphere. The default value is `1`.

`Brick`: Dimensions

Enter a three element vector [a b c] with the brick dimensions along the reference frame X, Y, and Z axes, respectively. The default vector is `[1 1 1]`. Select a physical unit. The default unit is `m`.

`Ellipsoid`: Radii

Enter a three element vector [a b c] with the ellipsoid semi-principal axes along the reference frame X, Y, and Z axes, respectively. The default vector is `[1 1 1]`. Select a physical unit. The default unit is `m`.

`Regular Extrusion`: Number of Sides

Enter the number of sides for the polygonal cross-section. The minimum number of sides is `3`. The default value is `3`.

`Regular Extrusion`: Outer Radius

Enter the radius of the smallest circle required to completely enclose the polygonal cross-section. This is equal to the distance from the polygon center to the intersection of any two polygon edges. The default value is `1`. Select a physical unit. The default unit is `m`.

`Regular Extrusion`: Length

Enter the extrusion length. This is the distance along which to sweep the 2-D cross-section. The default value is `1`. Select a physical unit. The default unit is `m`.

`General Extrusion`: Cross-section

Enter the cross-section coordinate matrix. This is a matrix with N rows, each with the [X Y] coordinates of a single cross-section point. Coordinates must define a single closed loop. The loop must not self-intersect. The closed loop divides dense and empty regions according to the following rule: as viewed at each point along the cross-section, the dense region lies to the left of the cross-section segment, while the empty region lies to the right. Select a physical unit. The default unit is `m`.

`General Extrusion`: Length

Enter the extrusion length. This is the distance along which to sweep the 2-D cross-section. The default value is `1`. Select a physical unit. The default unit is `m`.

`Revolution`: Cross-section

Enter the cross-section coordinate matrix. This is a matrix with N rows, each with the [X Z] coordinates of a single cross-section point. Coordinates must define a closed loop. The loop must not self-intersect. X-coordinate values must be greater than or equal to zero. The closed loop divides dense and empty regions according to the following rule: as viewed at each point along the cross-section, the dense region lies to the left of the cross-section segment, while the empty region lies to the right. Select a physical unit. The default unit is `m`.

`Revolution`: Extent of Revolution

Specify the angle to revolve the cross-section through. Select `Full` for a 360 degree revolution. Select `Custom` and enter a revolution angle for partial revolutions. The revolution angle must lie between `0` and `360` degrees.

`From File`: File Type

Select the format of the source file with the solid geometry data. Formats include `STL` and `STEP`.

STL (Standard Tessellation Language) files represent the surface geometry of a 3-D solid as a matrix of 2-D triangular elements. A normal vector and three vertex coordinate sets, included in the STL file, fully define each triangular element in the tessellated surface. Selecting `STL` exposes an additional option, Units.

STEP (Standard for the Exchange of Product Data) files represent the surface geometry of a 3-D solid using a set of analytical curves. These files can include additional information about a solid, such mass density and physical units.

The block provides automatic inertia computation from geometry only for STEP-derived geometries. For STL-derived geometries, you must manually enter the solid inertia parameters.

`From File`: File Name

Enter the name of the geometry source file. The name must include the file path, provided relative to the working directory.

`From File`: Units

Select or enter the desired unit of length. The default is `m`. This option appears when you select `STL` as the geometry source file type.

### Inertia

Type

Select a method to specify the inertial properties of the solid. The default is `Calculate from Geometry`.

TypeDescription
`Calculate from Geometry`Automatically compute moments and products of inertia based on solid geometry and either mass or density.
`Point Mass`Treat the solid as an idealized mass occupying an infinitely small volume in space. The inertia tensor about the center of mass is always zero for a point mass. The position of the point mass coincides with the origin of the reference port frame. Select the Point Mass method to represent a simple mass disturbance on a rigid body.
`Custom`Manually specify the inertial properties of the solid, including moments and products of inertia as well as center of mass.

`Calculate from Geometry`: Based on

Select the quantity to base inertia calculations on. Options are `Density` and `Mass`. Depending on the method you choose, enter the average mass density or the total mass of the solid. Select a physical unit.

`Point Mass`/`Custom`: Mass

Enter the total mass of the solid. Select a physical unit. The default is `1 Kg`.

`Custom`: Center of Mass

Enter the center of mass coordinates with respect to the solid reference frame in the order [X Y Z]. In a uniform gravitational field, the center of mass coincides with the center of gravity. Select a physical unit. The default is `[0 0 0]`.

`Custom`: Moments of Inertia

Enter the mass moments of inertia of the solid element in the order [Ixx, Iyy, Izz]. Each moment of inertia must refer to a frame whose axes are parallel to the block reference frame axes and whose origin is coincident with the solid center of mass. The moments of inertia are the diagonal elements of the solid inertia tensor,

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

where:

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

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

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

Select a physical unit. The default is `[1 1 1] kg*m^2`.

`Custom`: Products of Inertia

Enter the mass products of inertia of the solid element in the order [Iyz, Izx, Ixy]. Each product of inertia must refer to a frame whose axes are parallel to the block reference frame axes and whose origin is coincident with the solid center of mass. The products of inertia are the off-diagonal elements of the solid inertia tensor,

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

where:

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

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

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

Select a physical unit. The default is `[0 0 0] kg*m^2`.

### Graphic

Type

Select a method to represent the solid in Mechanics Explorer. The default is `From Geometry`.

TypeDescription
`From Geometry`Shape specified in Geometry section
`Marker`Simple icon such as `Sphere`, `Cube`, or `Frame`
`None`No visualization

`Marker`: Shape

Geometric shape of the graphic marker. Options include `Cube`, `Frame`, and `Sphere`. The default setting is `Sphere`.

`Marker`: Size

Absolute size of the graphics marker in pixels. Changing the zoom level in the model visualization pane has no effect on the apparent marker size. The default value is `10`.

Visual Properties

Color specification type. Options include `Simple` and `Advanced`. Select `Simple` to specify the solid color and opacity. Select `Advanced` to add lighting effects such as specular reflections and light emission.

`Simple`: Color

[R G B] color vector. This vector contains the red (R), green (G), and blue (B) contents of the solid color on a scale of 0–1. The default vector is `[0.5 0.5 0.5]`. A color picker provides an alternative means of defining the solid color.

`Simple`: Opacity

Degree to which the solid obscures model components positioned behind it. The opacity value can range from 0 to 1. An opacity of 0 makes the solid completely translucent, while an opacity of 1 makes the solid completely opaque. The default value is `1.0`.

`Advanced`: Diffuse Color

[R G B] or [R G B A] diffuse color vector. The diffuse color is the apparent color of the solid under direct white light. The color vector contains the red (R), green (G), and blue (B) contents of the diffuse color on a scale of 0–1. It can include an optional opacity value (A), also on a scale of 0–1. The default vector is `[0.5 0.5 0.5]`.

`Advanced`: Specular Color

[R G B] or [R G B A] specular color vector. The specular color is the color of the glossy highlights on the solid surface. The color vector contains the red (R), green (G), and blue (B) contents of the specular color on a scale of 0–1. It can include an optional opacity value (A), also on a scale of 0–1. The default vector is `[0.5 0.5 0.5 1.0]`.

`Advanced`: Ambient Color

[R G B] or [R G B A] ambient color vector. The ambient color is the apparent color of the solid under indirect ambient light. The color vector contains the red (R), green (G), and blue (B) contents of the ambient color on a scale of 0–1. It can include an optional opacity value (A), also on a scale of 0–1. The default vector is `[0.15 0.15 0.15 1.0]`.

`Advanced`: Emissive Color

[R G B] or [R G B A] emissive color vector. The emissive color is the color of light generated by the solid. The color vector contains the red (R), green (G), and blue (B) contents of the emissive color on a scale of 0–1. It can include an optional opacity value (A), also on a scale of 0–1. The default vector is ```[0.0 0.0 0.0 1.0]```.

`Advanced`: Shininess

Sharpness of the specular highlights on the solid surface. The shininess value can range from 0 to 128. A low shininess value produces large specular highlights with a gradual falloff in intensity. A large shininess value produces small specular highlights with a sharp falloff in intensity. The default value is `75`.

### Visualization Pane

So that you can visually check the solid you are modeling, the Solid block dialog box provides a visualization pane. This pane enables you to view the solid shape, color, and reference frame location from various 3-D perspectives. You can select a standard view point or rotate, pan, and zoom the solid view. Select the Update Visualization button to view the latest changes to the solid.

Solid Visualization Pane

## Ports

Frame port R identifies the solid reference frame.