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.

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 $L \mathrm{e\_\_axis}$ and $\frac{L}{2} \mathrm{e\_\_axis}$ 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 $\mathrm{L\_\_add}\left[i\right] \mathrm{e\_\_axis}$. This is illustrated in the following figure.

Figure 2: Orientation of end frames and an additional frame with $\mathrm{L\_\_add} \=\left[\frac{L}{2}\right]$for a linkage along the x-axis

Linkage mass is calculated as

$m\=\mathrm{\ρ} L H W$

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

$\mathrm{I\_\_xx}\=\frac{1}{12} m\cdot \left(H{ }^2\+W{ }^2\right)$

$\mathrm{I\_\_yy}\=\frac{1}{12} m\cdot \left(W^{ 2}\+L^{ 2}\right)$

$\mathrm{I\_\_zz}\=\frac{1}{12} m\cdot \left(H^{ 2}\+L^{ 2}\right)$

The right-hand side of these equations will interchange if another axial unit vector is specified or the Rotate 90 degrees parameter is true.