# Peaucellier-Lipkin Linkage Forces

**Classical Mechanics**Level 5

The lengths of the links are

\(OA=AB=BC=CD=DA=1\)

while \(P, O, E\) are co-linear, and \(PO=1\), \(OE=2\), and \(PE\bot EC\)

and \(PB=PD\)

Force \(F\) is applied tangentially at point \(A\) (perpendicular to \(OA\)), resulting in force \(F’\) along the line \(EC\) at point \(C\).

At angle \(\angle AOE=60°\), find the ratio of the forces \(\dfrac { F }{ F' } \) accurate to three decimal places. As this is an exercise in classical mechanics, use the **Conservation of Energy Law** to determine this ratio.

Note: A property of Peaucellier-Lipkin linkages is that points \(P, A, C\) are always co-linear.