Box

Rigid cuboid with box visualization

 Description The Box component models a homogeneous rigid body along a given axial vector with a rectangular cross section. Based on the properties, i.e., axial unit vector, length, height, width, and density, the center of mass, mass, and moments of inertia are calculated for this rigid body. Box visualization is a simple cuboid.

Connections

 Name Description Modelica ID $\mathrm{frame__a}$ Frame on one end of the box axis frame_a $\mathrm{frame__b}$ Frame on the other end of the box axis frame_b $\mathrm{frame__c}\left[n\right]$ An array of additional frames on the box axis frame_c[n]

Parameters

 Name Default Units Description Modelica ID $\mathrm{e__axis}$ $\left[1,0,0\right]$ Axial unit vector e_axis Rotate 90 degrees $\mathrm{false}$ True means the cross section is rotated 90 degrees rotate90 $L$ $1$ $m$ Box length L W 0.1 m Box width W $H$ 0.2 m Box height H $\mathrm{W__i}$ 0.1 m Inner box width Wi $\mathrm{H__i}$ 0.2 m Inner box height Hi Select density Steel 7860 (kg/m^3) Select a predefined material density selectDensity $\mathrm{ρ}$ 1000 $\frac{\mathrm{kg}}{{m}^{3}}$ Box user-defined material density customDensity Use additional frames false True means additional frames can be added addFrames $\mathrm{L__add}$ $\left[\frac{L}{2}\right]$ m Each value defines the offset of an additional frame w.r.t. frame_a along the axial vector. L_add[:] Use initial conditions false True means parameters for specifying initial conditions for frame_a are enabled. Refer to: Rigid Body useICs Show visualization true True means the disk geometry is visible in the 3-D playback visualization Transparent false True means the geometry is transparent in the 3-D playback transparent Color Box color in the 3-D playback color

 Equations Box length (L) is always along the specified axial unit vector (e_axis). Unit vectors for width (W) and height (H) are defined according to Figure 1. The sequence depends on whether or not the Rotate 90 degrees option is checked (true).      Figure 1: Order of L, W, and H follows above diagrams. Rotate 90 degrees option is unchecked (false) for the left sequence and checked (true) for the right one.   Note that the rotate 90 degrees option just rotates the box cross section. Regardless of this option, the orientation of the end frames and additional frames remains the same. Translation vectors of  and  w.r.t. frame_a defines the frame_b and the center of mass frame respectively. Moreover, each additional frame is defined by translating from frame_a along the vector . This is illustrated in the following figure. Figure 2: Orientation of end frames and an additional frame with for a box along the x-axis   Box mass is calculated as   where the box 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 3: Different options for the "Select density" parameter   Assuming the default direction of $\left[1,0,0\right]$ for the e_axis and that the Rotate 90 degrees option is unchecked (false), the moments of inertia expressed from the center of mass frame (frame_a) are The right-hand side of these equations will interchange if another axial unit vector is specified or the Rotate 90 degrees parameter is true.

Examples

 Four-Bar Linkage Figure 4 shows the layout of a MapleSim model which uses three Box components with revolute joints to simulate a four-bar linkage. Note how employing Box components facilitates the modeling and provides a realistic 3-D playback, shown in Figure 5. Using this component also decreases the burden on the user by automatically calculating the mass and moments of inertia. Figure 4: Model layout   Figure 5: 3-D playback snapshot
 Slider-Crank Mechanism In this example, a Box, a Disk, and two Cylinder components are connected with revolute and prismatic joints, as shown in Figure 6, to model a slider-crank mechanism. This model is similar to the one discussed in the Cylinder and Disk help pages with the difference of using a Box to connect the crank to the slider. Using Machine Element components facilitates modeling complex multibody systems by taking care of mass and moments of inertia calculations and also decreases the total number of components. A snapshot of the 3-D playback window is shown in Figure 7. Figure 6: Model layout   Figure 7: 3-D playback snapshot