The Double Acting Cylinder component models a double-acting translational actuator. It transforms energy between the pneumatic and translational domains.

Optional end cushions restrict the stroke length of the piston. The length and volume parameters are shown in the following figure.

$$\begin{gathered} {\mathrm{mflow}}_a\=\mathrm{VolumeA} \cdot \frac{\ⅆ}{\ⅆt}\left(\mathrm{\ρ\_\_a}\right) \+ \frac{\ⅆ}{\ⅆt}\left(\mathrm{VolumeA}\right)\cdot \mathrm{\ρ\_\_a} \\ {\mathrm{mflow}}_b\=\mathrm{VolumeB} \cdot \frac{\ⅆ}{\ⅆt}\left(\mathrm{\ρ\_\_b}\right) \+ \frac{\ⅆ}{\ⅆt}\left(\mathrm{VolumeB}\right)\cdot \mathrm{\ρ\_\_b} \end{gathered}$$

$\mathrm{Volume\_\_A} \= V_A^{ 0} \+ A_a^f\cdot \min \left(\max \left(\mathrm{s\_\_rel} \, 0\right)\, \mathrm{L\_\_h}-\mathrm{L\_\_p}\right)$

$\mathrm{Volume\_\_B} \= V_B^{ 0} \+ A_b^f\cdot \min \left(\max \left(\mathrm{L\_\_h}-\mathrm{L\_\_p} -\mathrm{s\_\_rel} \, 0\right)\, \mathrm{L\_\_h}-\mathrm{L\_\_p}\right)$

$s_{\mathrm{rel}}\=s_b-s_a{v}_{\mathrm{rel}}\=\frac{\mathrm{d}{s}_{\mathrm{rel}}}{\mathrm{d}t}$

$f_a\=-f_b\=\{\begin{array}{cc}f\+f_{e_1}\+f_{e_2}& \mathrm{Use\; end\; cushions}\\ f& \mathrm{otherwise}\end{array}$

$f\=A_a\cdot \left(p_a-\mathrm{p\_\_atm}\right)-A_b\cdot \left(p_b-\mathrm{p\_\_atm}\right)-d \cdot v_{\mathrm{rel}}$

$f_{e_1}\=\{\begin{array}{cc}0& 0\le f_{c_1}\+f_{d_1}\\ f_{c_1}\+\max \left(f_{c_1}\,f_{d_1}\right)& \mathrm{otherwise}\end{array}{f}_{e_2}\=\{\begin{array}{cc}0& f_{c_2}\+f_{d_2}\le 0\\ f_{c_2}\+\min \left(f_{c_2}\,f_{d_2}\right)& \mathrm{otherwise}\end{array}$

$f_{c_1}\&equals;\{\begin{array}{cc}-k_c\left(s_{\mathrm{rel}}-L_{\max }\right)& L_{\max }<s_{\mathrm{rel}}\\ 0& \mathrm{otherwise}\end{array}{f}_{c_2}\&equals;\{\begin{array}{cc}-k_c\left(s_{\mathrm{rel}}-L_{\min }\right)& s_{\mathrm{rel}}<L_{\min }\\ 0& \mathrm{otherwise}\end{array}$

$f_{d_1}\&equals;\{\begin{array}{cc}-c_c{v}_{\mathrm{rel}}& L_{\max }<s_{\mathrm{rel}}\\ 0& \mathrm{otherwise}\end{array}{f}_{d_2}\&equals;\{\begin{array}{cc}-c_c{v}_{\mathrm{rel}}& s_{\mathrm{rel}}<L_{\min }\\ 0& \mathrm{otherwise}\end{array}$