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Rigid solid element with geometrical, inertial, and graphical properties

This block represents a rigid solid element with geometrical,
inertial, and graphical properties. Geometrical properties include
dimensions and shape, which can range from simple (e.g., `Sphere`)
to complex (e.g., `General Extrusion`).

Inertial properties include the center of mass and the inertia tensor, which the block can automatically compute from geometry and mass/density data. Graphical properties include color which, in conjunction with shape and dimensions, fully defines the solid appearance in the Mechanics Explorer visualization window.

Combine multiple Solid and Rigid Transform blocks to model complex-shaped rigid bodies.

Specify solid shape and dimensions. Shapes can be standard,
such as `Sphere`, or custom, such as `Revolution`.

**Shape**Select a solid shape. The default shape is

`Brick`. For shape definitions and examples refer to the table.Shape Description Example `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.

Specify the solid inertial parameters. Depending on the specification type, parameters can include mass, density, center of mass, and moments and products of inertia.

**Type**Select a method to specify the inertial properties of the solid. The default is

`Calculate from Geometry`.Type Description `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 [I

_{xx}, I_{yy}, I_{zz}]. 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,where:

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 [I

_{yz}, I_{zx}, I_{xy}]. 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,where:

Select a physical unit. The default is

`[0 0 0] kg*m^2`.

Specify solid graphic properties. These include color, opacity, and shininess.

**Type**Select a method to represent the solid in Mechanics Explorer. The default is

`From Geometry`.Type Description `From Geometry`Shape specified in **Geometry**section`Marker`Simple icon such as `Sphere`,`Cube`, or`Frame``None`No visualization `Marker`:**Shape**Marker shape used to represent the solid in Mechanics Explorer. Options include

`Sphere`,`Cube`, and`Frame`. The default is`Sphere`.`Marker`:**Size**Marker absolute size in screen pixels. The default is

`10`.

**Visual Properties**Select the method used to specify the color and opacity of the solid. For the most realistic graphical appearance, select

`Advanced`. The default method is`Simple`.Method Parameters `Simple`Color and opacity. `Advanced`Color (ambient, diffuse, specular, and emissive) and shininess. `Simple`:**Color**Enter the color RGB vector. This is a three-element vector with the red, green, and blue components of a color. Values must lie in the range 0–1. You can also select a color directly from the color palette.

`Simple`:**Opacity**Enter the solid opacity. This is a measure of how much light the material blocks. Values must lie in the range 0–1.

`Advanced`:**Diffuse Color**Diffuse color RGBA vector. This is a four-element vector with the red, green, blue, and opacity color components. Values must lie in the range 0–1.

The diffuse color is the apparent color of a rough surface exposed to direct white light. Light scatters equally in all directions in accordance with Lambert's law, causing the intensity and color of the scattered light to appear the same from all angles. The diffuse color normally provides the dominant contribution to the color of a solid surface. The default diffuse color, given in the form of a three element vector, is

`[0.5 0.5 0.5]`.`Advanced`:**Specular Color**Diffuse color RGBA vector. This is a four-element vector with the red, green, blue, and opacity color components. Values must lie in the range 0–1.

The specular color is the apparent color of the glossy highlights arising from a solid surface exposed to direct light. The size of the specular highlights depends on the value of the

**Shininess**parameter. The intensity of the specular color is not uniform and has a strong dependence on the viewing angle. The default specular color is`[0.5 0.5 0.5 1.0]`.`Advanced`:**Ambient Color**Diffuse color RGBA vector. This is a four-element vector with the red, green, blue, and opacity color components. Values must lie in the range 0–1.

The ambient color is the apparent color of a solid surface exposed only to indirect light. The default ambient color is

`[0.15 0.15 0.15 1.0]`.`Advanced`:**Emissive Color**The emissive color is the apparent color of direct light produced by the solid surface. The default emissive color is

`[0.0 0.0 0.0 1.0]`.`Advanced`:**Shininess**Scalar quantity that encodes the size and rate of decay of the specular highlights arising from the solid surface. The scalar value must fall in the range 0–128.

A small shininess value corresponds to a specular highlight with large area and gradual falloff in the highlight intensity. A large shininess value corresponds to a specular highlight with small area and sharp falloff in the highlight intensity. The default value is

`75`.

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