Table 1 Calculation of the minimum tension condition and the required tension using the maximum pen tip force from the literature

Axial

\( {\mathrm{T}}_{\mathrm{axial}}\ge \frac{{\mathrm{F}}_{\mathrm{axial}}}{\upmu \left(2+\mathrm{Cos}{\varnothing}_1+\mathrm{Cos}{\varnothing}_2+\mathrm{Sin}{\varnothing}_1+\mathrm{Sin}{\varnothing}_2\right)}\kern0.6em (8) \)

0.302–0.679

Pitch

\( {\mathrm{T}}_{\mathrm{pitch}}\ge \frac{\left({\mathrm{L}}_1+{\mathrm{L}}_2\right){\mathrm{F}}_{\mathrm{pitch}}}{{\upmu \mathrm{L}}_2\left(2+\mathrm{Cos}{\varnothing}_1+\mathrm{Cos}{\varnothing}_2\right)-\left(\mathrm{Sin}{\varnothing}_1+\mathrm{Sin}{\varnothing}_2\right)\left({\mathrm{L}}_2-0.5\mathrm{d}\right)}\kern0.85em (9) \)

3.285–7.390

Yaw (left)

\( {\mathrm{T}}_{\mathrm{yaw}\_\mathrm{left}}\ge \frac{2{\mathrm{L}}_1\ {\mathrm{F}}_{{\mathrm{yaw}}_{\mathrm{left}}}}{\mathrm{d}\left(2+\mathrm{Cos}{\varnothing}_1+\mathrm{Cos}{\varnothing}_2\right)}\kern0.85em (10) \)

3.7994