The Disk component models a homogeneous disk-like rigid body along a given axis with a predefined density. Based on the properties, i.e., axial unit vector, radius, and density, the center of mass, total mass, and moments of inertia are calculated for this rigid body. Although Disk and Cylinder components share similarities, Disk is preferred when length/thickness is insignificant compared to radius.
Center of disk
An array of additional frames on the circular cross section containing the center of mass
Axial unit vector
Disk inner radius
Steel 7860 (kg/m^3)
Select a predefined material density
Disk user-defined material density
Use additional frames
True means additional frames can be added
Each value defines the radial distance of an additional frame to frame_a
Each value defines the angle of rotation of an additional frame around the axial vector
True means the disk geometry is visible in the 3-D playback
True means the geometry is transparent in the 3-D playback
Disk color in the 3-D playback
The arrays R__add and θ__add should have the same length. Each additional frame is defined by rotating frame_a around the axial vector an angle θ__add i and then translating along the reference axis by L__add i. The reference axis is the next local axis after the e_axis (e.g., if e_axis is y, the reference axis is z). Figure 1 illustrates this process.
Figure 1: The axial unit vector (e_axis) for this disk is [0,1,0]. Additional frame was added by defining L__add = R2,R and θ__add =45,180 deg. Both of these frames lie on the plane defined by the normal vector of e_axis and passing through the center of mass.
Disk mass is calculated as
m=ρ π⋅R2−R__i2 T
where the disk material density, ρ, can be defined using the "Select density" parameter. This parameter lets the user either enter a value or select among predefined material densities.
Figure 2: Different options for the "Select density" parameter
Assuming the default direction of 1,0,0 for the e_axis, the moments of inertia expressed from the center of mass frame (frame_a) are
I__yy=112 m⋅3R2+R__i2+T 2
The right-hand side of these equations will interchange if another axial unit vector is specified.
Figure 3 shows the layout of a model that uses a spherical joint, a Cylinder, and a Disk to simulate the precession of a spinning top. A snapshot of the 3-D playback is shown in Figure 4. This example also shows how the Cylinder and Disk components differ in modeling different rigid body geometries.
Figure 3: Model layout
Figure 4: 3-D playback snapshot
In this example, a Disk and three Cylinder components are connected with revolute and prismatic joints, as shown in Figure 5, to model a slider-crank mechanism. This model is similar to the one discussed in the Cylinder help page with the difference of using a Disk with an additional frame as the crank rather than a cylindrical rod.
Using Disk and Cylinder components facilitates modeling by automatically calculating mass and moments of inertia and also results in realistic visualization in the 3-D playback window, as shown in Figure 6.
Figure 5: Model layout
Figure 6: 3-D playback snapshot
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