 Linkage - MapleSim Help  Description The Linkage 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, total mass, and moments of inertia are calculated for this rigid body. Linkage visualization is a cuboid with rounded ends and holes. This visualization is preferred for mechanism. Connections

 Name Description Modelica ID $\mathrm{frame__a}$ Frame on one end of the linkage axis frame_a $\mathrm{frame__b}$ Frame on the other end of the linkage axis frame_b $\mathrm{frame__c}\left[n\right]$ An array of additional frames on the linkage 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 $L$ $1$ $m$ Linkage length L W 0.1 m Linkage width W $H$ 0.2 m Linkage height H Select density Steel 7860 (kg/m^3) - Select a predefined material density selectDensity $\mathrm{ρ}$ 1000 $\frac{\mathrm{kg}}{{m}^{3}}$ Linkage 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[:] 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 - Disk color in the 3-D playback color Equations Linkage 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). The two end holes are always along the width axis.  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 linkage 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 linkage along the x-axis   Linkage mass is calculated as where the linkage material density, ρ, is 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 in 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.  Four-Bar Linkage Figure 4 shows the layout of a MapleSim model that uses three Linkage components with revolute joints to simulate a four-bar linkage. Note how employing Linkage components facilitates modeling and provides a realistic 3-D playback, shown in Figure 5. Use of 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 Linkage, 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 Linkage component to connect the crank to the slider. Using MachineElement components facilitates modeling complex multibody systems by taking care of mass and moment 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