Balancing of Reciprocating Masses - Why & How is C Introduced?

[R Power]

Hi
I was reading balancing of reciprocating masses and read about balancing of force along the line of stroke for a simple reciprocating piston. The force particlualry primary force along the line of stroke was mw^2r cosA. Now this is supposed to be a cosine component of a mass m attached at the e0nd of crank or connecting rod. So a mass B is attached opposite to crank such that it's centrifugal force counteacts the supposed mass's centrifugal force(such that
m w^2 r1 cosA= B w^2 r2 cosA). Then it was written that by this method we get unbalanced force prependicular to the stroke because the new mass B attached also has sine component which is prependicular to the line stroke. Thus the above method just shifts the primary unbalanced force from parallel to prependicular line of stroke. Upto this it's ok. But then it was written that, So it is preferred to take

m r1 = C B r2 where C<1 is the factor that introduces partial balancing along the line of stroke

This is what i didn't understand. Why and how C is introduced?

 

[Filip Larsen]

If I understand your question correctly, I would say it sounds like the constant is introduced to model a partially (instead of fully) cancellation of the stroke-wise force so that the maximum magnitude of the overall unbalancing force is less than it would be if it was either completely stroke-wise or completely transverse. That is, instead of having an unbalancing force that varies from zero to maximum twice on each rotation you can choose to have a smaller forces that varies between some "negative" and positive value.