In example Represent Binary Link Frame Tree, you modeled the frame tree of a binary link rigid body. In this example, you add to that frame tree the solid properties of the binary link: geometry, inertia, and color.

To model a binary link, you must use multiple Solid blocks.
Each Solid block represents an elementary portion of the binary link.
Rigid bodies that you model using multiple Solid blocks are called *compound
rigid bodies*. The compound rigid body technique reduces
a single complex task (modeling the entire binary link shape) into
several simple tasks (modeling the Main, Hole, and Peg sections of
the binary link).

To use the compound rigid body technique:

Divide shape into simple sections.

Dividing the shape simplifies the modeling task in more complex cases. You can divide the binary link into three simple sections: Main, Peg, and Hole, shown in the figure.

Represent each section using a Solid block.

Each section should be simple enough to model using a single Solid block. In the binary link example, you can represent sections Main and Hole using SimMechanics™ shape

`General Extrusion`

, and section peg with SimMechanics shape`Cylinder`

.Rigidly connect Solid blocks to rigid body frame tree.

Rigid connections ensure the different solid sections move as a single rigid body. Connect the Solid blocks to the binary link frame tree to apply the correct spatial relationships between the solid sections.

You model the binary link as a compound rigid body subsystem.
In this subsystem, three Solid blocks represent the basic solid sections
of the binary link. Each solid section has a shape and a local reference
frame that you connect to the binary link frame tree. Two SimMechanics shapes
are used: `General Extrusion`

and `Cylinder`

.

You can promote subsystem reusability by parameterizing solid
properties in terms of MATLAB^{®} variables. In this example, you
initialize the variables in a subsystem mask. You can then specify
their numerical values in the subsystem dialog box. The table provides
the dimensions needed to model the binary link solid sections. In
the previous example, Represent Binary Link Frame Tree, you used the first three dimensions
to specify the spatial relationships between the different binary
link frames.

Dimension | MATLAB Variable |
---|---|

Length | `L` |

Width | `W` |

Thickness | `T` |

Peg Radius | `R` |

SimMechanics shape `General Extrusion`

requires
you to specify a set of cross-section coordinates. This is a MATLAB matrix
with all the [X Y] coordinate pairs needed to draw the cross-section.
Straight line segments connect adjacent coordinate pairs.

Coordinate matrices must obey a set of rules. The most important rule is that the solid region must lie to the left of the line segment connecting adjacent coordinate pairs. For more information, see Revolution and General Extrusion Shapes. The figure shows the coordinates required to specify the cross-section shapes of solid sections Main and Hole.

At the MATLAB command prompt, enter

`smdoc_binary_link_frames`

. A SimMechanics model opens with the frame tree you modeled in the Represent Binary Link Frame Tree tutorial.Right click Binary Link and select

**Mask**>**Look Under Mask**.From the SimMechanics Body Elements library, drag three Solid blocks into the model.

Connect and name the blocks as shown in the figure.

In the Solid block dialog boxes, specify these parameters.

Parameter Hole Main Peg **Geometry**>**Shape**Select `General Extrusion`

.Select `General Extrusion`

.Select `Cylinder`

.**Geometry**>**Cross-section**Enter `HoleCS`

. Select units of`cm`

.Enter `MainCS`

. Select units of`cm`

.— **Geometry**>**Radius**— — Enter `R`

. Select units of`cm`

.**Geometry**>**Length**Enter `T`

. Select units of`cm`

.Enter `T`

. Select units of`cm`

.Enter `2*T`

. Select units of`cm`

.**Geometry**>**Density**Enter `Rho`

.Enter `Rho`

.Enter `Rho`

.**Graphic**>**Color**Enter `LinkRGB`

.Enter `LinkRGB`

.Enter `PegRGB`

.

In the subsystem mask, initialize the MATLAB variables you entered for the block parameters.

Select the subsystem block and press

**Ctrl+M**to create a subsystem mask.In the

**Parameters & Dialog**tab of the Mask Editor, drag four edit boxes into the**Parameters**group and specify these parameters. Then, click**OK**.Prompt Name `Peg Radius`

`R`

`Mass Density`

`Rho`

`Link Color [R G B]`

`LinkRGB`

`Peg Color [R G B]`

`PegRGB`

**Note:**The subsystem mask should contain three other parameters: L, W, and T. You specify those parameters in Represent Binary Link Frame Tree.In the

**Initialization**tab of the Mask Editor, define the extrusion cross-sections and press**OK**:% Cross-section of Main: Alpha = (-pi/2:0.01:pi/2)'; Beta = (pi/2:-0.01:-pi/2)'; PegCS = [L/2+W/2*cos(Alpha)... W/2*sin(Alpha)]; HoleCS = [-L/2 W/2; -L/2 + R*cos(Beta)... R*sin(Beta); -L/2 -W/2]; MainCS = [PegCS; HoleCS]; % Cross-section of Hole: Alpha = (pi/2:0.01:3*pi/2)'; Beta = (3*pi/2:-0.01:pi/2)'; HoleCS = [W/2*cos(Alpha) W/2*sin(Alpha); R*cos(Beta) R*sin(Beta)];

In the binary_link subsystem block dialog box, specify these parameters.

Parameter Value **Length**`30`

**Width**`2`

**Thickness**`0.8`

**Peg Radius**`0.4`

**Mass Density**`2700`

**Link Color [R G B]**`[0.25 0.4 0.7]`

**Peg Color [R G B]**`[1 0.6 0.25]`

Update the block diagram. You can do this by pressing **Ctrl+D**. Mechanics Explorer opens with a static
view of the binary link. To obtain the view shown in the figure, in
the Mechanics Explorer toolstrip select the isometric view button
.

To view a completed version of the binary link model, at the MATLAB command
prompt enter `smdoc_binary_link_a`

.

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