Figure shows an engine valve driven by an overhead camshaft. The rocker arm pivots about the fixed point O and the inertia of the arm about this point is Ir. The valve mass is mv and the spring mass is ms; its spring constant is ks. Let fc denote the force exerted on the rocker arm by the camshaft. Assuming that θ(t) and its time derivatives are known (from the cam profile and the cam speed), derive a dynamic model that can be used to solve for the cam force fc(t) (This information is needed to predict the amount of wear on the cam surface.)

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Cam Camshaft Rocker arm Valve spring k2 Mi I. Valve Im し2