Part D : Sling Finger Analysis

Fig. (D.1)

At the moment the sling finger is a simple steel rod attatched to the very tip of the beam by under an angle δ with respect to the beam's length axis. At steel ring is attached to the end of the rope from the pumpkin which exerts a force onto the finger with components Pp and Np. Both of these components are determined during each time step of the numerical analysis until the ring slides off the finger. For each time step we express this force by components along the finger's axis and perpendicular to it.

\begin{align*} N_s &= N_p \cos\delta + P_p \sin\delta \\ P_s &= P_p \cos\delta - N_p \sin\delta \end{align*}

We apply the law of dry friction which leads us to the condition that the ring will NOT slide of the finger while :

\begin{equation*} \mu_s P_s > N_s \end{equation*}

Provided that Ns is positive. Feel free to follow the columns labeled Ps and Ns of the table provide by the simulation.

This analysis is probably not complete because rope and the ring at its end are exposed to centripedal acceleration.

Trebuchet HomePage Trebuchet-Math/Physics Background Part A : Dynamics of counter-weight
Part B : Dynamics of pumpkin Part C : Dynamics of Beam Part D : Sling Finger Analysis
Part E : Stress Analysis Part F : A few Notes on Programming Aspects

Zig Herzog;
Last revised: xx