Irving's suggestion (going from the '0 deg' crankshaft to a 76 deg one) yielded .......
only about 21% reduction in peak vibrating force at primary (engine rpm) frequency
and (broadly) eliminated ........
vibrating forces at secondary (twice engine rpm) frequency (but these were anyway only a quarter of the primaries)
variations in crankshaft torque due to inertia of rods & pistons
(so ? - these are trivial compared to torques from power strokes - firing 284 deg then 436 deg would demand more flywheel for town speeds)
the modern take on this (started in the Yamaha Tenere) is the 90 deg crankshaft ......
if without counterbalance shafting this would reduce peak primary vibrating force by about 28.5% (and secondary by about 90%)
on the basis as above, the flywheel would need increasing (but in the interests of high-rpm shifting presumably doesn't get it)
but the modern way is to add counterbalance shafting
the 90 deg crank means less 28.5% less of this is needed with a further benefit as single shafting gets closer to the (impossible) ideal positioning
given that Triumph make 0 deg and 90 deg crankshaft versions of one machine an interesting comparison might be possible
of course parallel twins of 650cc and less all use the 180 deg crankshaft ......
(on its own this would give perfect primary force balance but a smallish moment 'couple' imbalance)
but it's combined with a couple counterbalance shaft to cancel primary moment 'couple' imbalance (TX500-style, Suzuki's takeup c.1978 widespread)
not surpising as the ride-to-work 250s now do 13000 rpm
essentially the of vibration signature a 4 cylinder engine of similar size. secondaries remaining untreated except in the largest 4 cylinder machines
regarding the now-traditional 180 deg without counterbalance shafting .....
135-150 deg would maybe offer a better compromise between uneven firing, and primary vs secondary imbalance
(though elastomer engine mounts are rather good where the designer doesn't decide to use the power unit structurally}
the simplest 180 deg crankshaft would be shaped such that it has mass balance but it's own moment imbalance when rotating
adding to the unbalanced couple from rods&pistons at tdc and bdct but Honda of course included crankshaft counterweighting of this
if this was over 100% counterweighting it would have reduced tdc and bdc moment 'couple' vibration at the cost of some vibration midstroke
https://images.cmsnl.com/img/products/c ... 1_137a.jpg
but these current 180 deg twins having a (primary) couple counterbalance shaft (which works by having its own couple imbalance of course) ....
have the crankshaft also (primary) couple imbalanced (by overweighting) thus
http://world.honda.com/CBR500R-CB500F-C ... age02.html
such that .....
at tdc&bdc couple balance shaft's p couple imbalance adds to crankshaft's p couple imbalance to cancel exactly the p couple imbalance from pistons&rods
around midstroke the the balance shaft's couple imbalance cancels the crankshaft's couple imbalance (as they are in opposite rotation)
and the piston& rod primary couple imbalance is around nil
job done !
and we should remember that the valve reciprocation also produces vibrating effects though this is usually ignored as inevitable