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Model Pivot Mount

Model Overview

In this example, you model a simple pivot mount. This mount is a compound rigid body with a hexagonal shape and a protruding cylindrical peg. You represent the hexagonal shape using solid shape Regular Extrusion. You then offset the protruding peg from the hexagonal shape using a Rigid Transform block. In later examples, you use this mount to support mechanical linkages like the double pendulum and the four bar system.

Modeling Approach

To model the pivot mount, you use two Solid blocks. Because the pivot mount has a hexagonal shape, you can model it using the Regular Extrusion shape. To represent the cylindrical peg, you use the Cylinder shape.

Each shape has a reference frame with origin at the geometry center. To offset the cylindrical peg with respect to the hexagonal mount, you apply a rigid transform between the two reference frames. You do this using the Rigid Transform block.

The Z axes of the two reference frames align with the cylindrical and extrusion axes of the peg and mount, respectively. Assuming the two solids both have thickness T, the rigid transform between the two reference frames is a translation T along the common Z axis.

In later examples, you connect the pivot mount to a binary link using a revolute joint. One example is a double pendulum that moves due to gravity. In this example, it helps to rotate the Z axis of the mount so that it is orthogonal to the world frame Z axis. This task, which involves a Rigid Transform block, makes the pivot rotation axis orthogonal to the gravity vector, [0 0 -9.81] m/s^2.

Build Model

  1. Drag these blocks into a new model.

    BlockLibraryQuantity
    SolidSimMechanics > Second Generation > Body Elements2
    Rigid TransformSimMechanics > Second Generation > Frames and Transforms2
    Reference FrameSimMechanics > Second Generation > Frames and Transforms1
    Solver ConfigurationSimscape > Utilities1

  2. Connect and name the blocks as shown in the figure.

      Note:   Include the disconnected frame line. This line becomes important when you generate a subsystem for the pivot mount. To add this line, right-click on the solid frame line and drag to the right.

  3. In the Hexagon block dialog box, specify these parameters.

    ParameterValue
    Geometry > ShapeSelect Regular Extrusion.
    Geometry > Number of SidesEnter 6.
    Geometry > Outer RadiusEnter HexagonR. Select units of cm.
    Geometry > LengthEnter T. Select units of cm.
    Inertia > DensityEnter Rho.
    Graphic > ColorEnter HexagonRGB.

  4. In the Peg block dialog box, specify these parameters.

    ParameterValue
    Geometry > ShapeSelect Cylinder
    Geometry > RadiusEnter PegR. Select units of cm.
    Geometry > LengthEnter 2*T.
    Inertia > DensityEnter Rho.
    Graphic > ColorEnter PegRGB.

  5. In the To Peg block dialog box, specify these parameters.

    ParameterValue
    Translation > MethodSelect Standard Axis.
    Translation > AxisSelect +Z.
    Translation > OffsetEnter 3/2*T. Select units of cm.

  6. In the To World block dialog box, specify these parameters.

    ParameterValue
    Rotation > MethodSelect Standard Axis.
    Rotation > AxisSelect –Y.
    Rotation > AngleEnter 90.

Generate Subsystem

You can now generate a subsystem to encapsulate the pivot mount block diagram. The subsystem mask provides a convenient place to initialize the MATLAB® variables that you defined the block parameters with. To generate the subsystem:

  1. Select all the blocks excluding Solver Configuration.

  2. Press Ctrl+G to enclose the blocks in a subsystem. Name the subsystem block Pivot Mount.

  3. Select the Pivot Mount block and create a subsystem mask, e.g., by pressing Ctrl+M.

  4. In the Parameters & Dialog tab of the Mask Editor, drag six edit boxes into the Parameters group and specify their properties. Click OK.

    PromptName
    Hexagon Outer RadiusHexagonR
    Hexagon ThicknessT
    Mass DensityRho
    Hexagon ColorHexagonRGB
    Peg RadiusPegR
    Peg ColorPegRGB

  5. In the Pivot Mount block dialog box, specify these parameters.

    ParameterValue
    Hexagon Outer Radius (m):4
    Hexagon Thickness (m):0.8
    Mass Density (kg/m^3):2700
    Hexagon Color [R G B]:[0.25 0.4 0.7]
    Peg Radius (m):0.4
    Peg Color [R G B]:[1 0.6 0.25]

Visualize Model

Update the block diagram. You can do this by pressing Ctrl+D. Mechanics Explorer opens with a 3-D static display of the pivot mount rigid body.

Open Reference Model

To view a completed version of the pivot mount model, at the MATLAB command prompt enter smdoc_pivot_mount.

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