# Spring TYPE12 - Pulley (/PROP/SPR_PUL)

Spring TYPE12 is used to model a pulley. When used in a seat belt model, it is defined with three nodes.

Node 2 is located at the pulley, and a deformable rope is joining the three nodes (Figure 1). The spring mass is distributed on the three nodes with ¼ at node 1 and node 3 and ½ at node 2.

A Coulomb friction can be applied at node 2, taking into account the angle between the two strands. Without friction, forces are computed as:(1)
$|{F}_{1}|=|{F}_{2}|=K\delta$
With,
$\delta$
Total rope elongation
$K$
Stiffness
If the Coulomb friction is used, forces are computed as:(2)
${F}_{fr}=\mathrm{min}\left\{|\text{Δ}F|,\mathrm{max}\left[0,\left(|{F}_{1}|+|{F}_{2}|\right)\cdot \mathrm{tanh}\left(\frac{\beta \cdot \mu }{2}\right)\right]\right\}\cdot sig\left(\text{Δ}F\right)$
Where,
$\mu ={\mathrm{f}}_{fr}\left(\frac{\text{Δ}F}{Xscale_F}\right)\cdot Yscale_F$
$\beta$
${\mathrm{f}}_{fr}$
$\text{Δ}F=|{F}_{1}-{F}_{2}|$
$\text{Δ}F={F}_{1}-{F}_{2}$
${\delta }_{1}$ is the elongation of strand 1-2 and ${\delta }_{2}$ of strand 2-3.