SAG COMPENSATED CONTACT PIN

Construction Design & Examples

INTRODUCTION

Typically struts and leaf springs demonstrate a parasitic sag-movement when moving sideways.

 

In some cases this parasitic motion is unwanted. Then a rigid tip can be implemented on the elastic element. By designing the proper tip radius, the parasitic motion can be perfectly compensated resulting in a straight-line
guided motion.

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Formulas

The kinematic behavior is described by the following formulas for small values of u, \phi:

z_{tip}=(L_r+L_f)-\frac {2}{15} \bullet \frac {2L_f^3+20L_r^2L_f+10L_rL_f^2+15L_r^3}{(2L_r+L_f)^2} \bullet \phi ^2
\Delta z_{tip}=-\frac{2}{15} \bullet \frac {2L_f^3+20L_r^2L_f+10L_rL_f^2+15L_r^3}{(2L_r+L_f)^2} \bullet \phi^2
u_{tip}=\frac {2}{3} \bullet \frac{3L_rL_f+L_f^2+3L_r^2}{2L_r+L_f} \bullet \phi
L_p=\frac{u_{tip}}{\tan (\varphi )} \approx \frac{u_{tip}}{\phi }=\frac {2}{3} \bullet \frac{3L_rL_f+L_f^2+3L_r^2}{2L_r+L_f}

z_{eff}=(L_r+L_f)+[\frac{R_{tip}}{2} - \frac{2}{15} \bullet \frac {2L_f^3+20L_r^2L_f+10L_rL_f^2+15L_r^3}{(2L_r+L_f)^2}] \bullet \phi ^2
\Delta z_{eff}=[\frac{R_{tip}}{2}-\frac {2}{15} \bullet \frac {2L_f^3+20L_r^2L_f+10L_rL_f^2+15L_r^3}{(2L_r+L_f)^2}] \bullet \phi ^2

Special case 1: L_r=0 (cantilevered leaf spring / strut)

L_p=\frac {2}{3} \bullet L_f
\left\begin{matrix} \Delta z_{tip}=-\frac{4}{15}L_f \bullet \phi ^2 \\u_{tip}=\frac {2}{3}L_f \bullet \phi \end{matrix}\right\} {\Delta z_{tip}}=-\frac{3}{5} \frac{u_{tip}^2}{L_f}

Special case 2: \Delta z_{eff}=0

R_{tip}=\frac {4}{15} \bullet \frac{2L_f^3+20L_r^2L_f+10L_rL_f^2+15L_r^3}{(2L_r+L_f)^2}

Sag compensated contact pin

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