# Documentation

## Model Cone

### Model Overview

You can model solids of revolution using the Simscape™ Multibody™ `Revolution` shape. Examples of solids of revolution include cone and circular dome shapes. In this example, you model a simple solid with cone shape using the `Revolution` shape. For an example that shows you how to model a circular dome solid, see Model Dome.

### Modeling Approach

To represent the cone geometry, first identify its cross-section shape. This is the 2-D area that Simscape Multibody revolves to obtain the 3-D cone. Then, specify the cross-section coordinates in the Solid block dialog box. These coordinates must satisfy certain restrictions. See Revolution and General Extrusion Shapes.

The cone in this example has a trapezoidal cross-section. The figure shows this cross-section.

The [0 0] cross-section coordinate identifies the reference frame origin for this solid. To place the solid reference frame at the cone tip, you by specify the coordinates so that the [0 0] coordinate coincides with the tip. By parameterizing the cross-section coordinates in terms of the relevant cone dimensions, you can quickly change the cone dimensions without having to reenter the cross-section coordinates. The figure shows the parameterized cross-section coordinates points.

### Build Solid Model

1. At the MATLAB® command prompt, enter `smnew`. A new Simscape Multibody model opens with some commonly used blocks. Delete all but the Solid block.

2. In the Solid block dialog box, specify the following parameters. You later initialize the different MATLAB variables in a subsystem mask.

ParameterSelect or Enter
Geometry > Shape`Revolution`.
Geometry > Cross-Section`CS`, units of `cm`
Inertia > Density`Rho`
Graphic > Visual Properties > Color`RGB`

3. Select the Solid block and generate a new subsystem, e.g., by pressing Ctrl+G.

### Define Solid Properties

1. Select the Subsystem block and create a subsystem mask, e.g., by pressing Ctrl+M.

2. In the Parameters & Dialog tab of the Mask Editor, drag five Edit boxes into the Parameters group and specify these parameters.

PromptName
`Base Radius``R`
`Cone Height``H`
`Wall Thickness``T`
`Density``Rho`
`Color``RGB`

3. In the Initialization tab of the Mask Editor, define the cross-section coordinates and assign them to the MATLAB variable `CS`:

```Alpha = atan(R/H); CS = [0 0; R H; R-T/cos(Alpha) H; 0 T/sin(Alpha)];```

4. In the Subsystem block dialog box, specify the numerical values of the solid properties. The table shows some values that you can enter.

ParameterEnter
Base Radius`1`
Cone Height`2`
Wall Thickness`0.1`
Density`2700`
Color`[0.85 0.45 0]`

### Visualize Solid Model

You can now visualize the cone solid. To do this, look under the Subsystem mask—e.g., by selecting the Subsystem block and pressing Ctrl+U—and open the Solid block dialog box. The solid visualization pane shows the solid that you modeled.

Parameterizing the solid dimensions in terms of MATLAB variables enables you to modify the solid shape without having to redefine its cross-section coordinates. You can change the solid size and proportions simply by changing their values in the Subsystem block dialog box. The figure shows some examples.