We are designing a small internal combustion engine for research purpose $($smooth load$).$ The engine will use a double$-$strand chain drive to drive the camshaft via crankshaft. The small sprocket is mounted on the crankshaft while the large sprocket is mounted on the camshaft. The camshaft must rotate at one half $(1/2)$ crankshaft speed to ensure correct valve timing $($for research purpose, a sprocket which is smaller than $17$ teeth can be used, and you may custom build large sprocket if necessary to maintian the timing$).$ The center distance is $10"\backslash$pm $0\mathrm{.}25".$ The crankshaft turns at $4200$ rpm$,$ and the camshaft power requirement is $4$ HP$.$ Design the chain drive. Minimize the sizes of the sprockets. Include the recommended lubrication method and angle of wrap of the chain around the crankshaft sprocket.