Roger,
Many piston engines are not well balanced, it is a matter of the design.
Horizontally opposed engines are inherently balanced. As long as
the  components are close, the engine is smooth running. Inline
six's and the  derivative V-12's are also well balanced.
Inline fours suffer from a secondary shaking force. When the engine
  is at TDC
two pistons are at TDC and two are at BDC. The engine has a center
of gravity.
Now rotate the engine 90*. The center of gravity has changed. The
explanation
is that as the crank rotates, the conn rod and piston not only move
down the
bore, but the rod also moves to the side. Pythagorean theorm states
Asq'd +
Bsq'd = Csq'd. Now if the C is the rod length and B is 1/2 the
stoke  the math  will tell you the effective rod length at 90*. The
piston will be  lower in the  bore the 1/2 the stroke. Thus the
center of gravity wants to move  the engine  to keep the Cg in the
same spot.
V6 engines are a nasty mess of vibrations with rocking couples in
the mix.
They want to rock forward and back, and then side to side depending
on where
in the rotation the rod throws are. Early Buick V6's had very soft
engine
mounts to try to isolate the vibrations.
The rotor moving in the housing is sort of like an inline 6 crank.
When two
throws are at TDC the other four are at 120* and 240*. The two low
ones have a
higher mass combined, but that is closer to the rotational center.
Now the
rotor when at TDC has two apex seals that are vertically one over
the other.
If you measure from a line between them and another horizontally
to the  e-shaft center line and measure the distance it is less the the
rotor radius.
Thus you have a higher mass at a shorter radius. There is still
some  imbalance  that the balance weights take care of. Many piston
engines also have  balance  weights. Sm block Fords, 400 Chev, BB
Chevs to mention a few.
Dale Davies


Like an inline six? Hardly.
"When two throws are at TDC the other four are at 120* and 240*."
What do you mean by a "throw" ?
The two rotor has two eccentric 180 degrees out. The two rotors
exactly statically balance each other. Since there is an offset between
them they are dynamically out of balance. This is completely
canceled by the
counter weights. As you add more rotors the counter weights get
smaller and smaller.
Piston engine balance is a complex subject.
The rotary is very simple by comparison.
I recommend For those of you with an engineering degree or
equivalent Taylor's
series of books is the best there is. The bible of engine design.
The Internal Combustion Engine in Theory and Practice.
Volume 2: Combustion, Fuels, Materials, Design. Revised. Charles
Fayette Taylor. The MIT Press Cambridge Massachusetts, and London
England.
Engine Balance Chapter 8 page 240.
When I was at the Mazda factory the vibration test was a glass of
wine sitting
on the top of the engine when running on the dyno. No disturbance.
All engines coming off the assemble line were run on dynos.
Perry Mick's rotary is bolted solidly in his Long Ez airframe for
the last 16 years or so. No rubber bushings. One can hardly
feel the engine running.
Paul Lamar
--

This light written article talks about the various RPE configurations
and their balancing problems.
Rolf Pfeiffer

http://tinyurl.com/48e5sfm


Another good source on balance is V6 Performance  by Pat Ganahl. It does deal
primarily with V6 engines but does mention other engine designs and compares
the advantage and disadvantage of each. This is in the first chapter. You may
be able to find it at the library.

Dale Davies

Its on my list of recommended books.
http://www.rotaryeng.net/books10.html

" V-6 BUICK FORD & CHEVY 90 deg./60 deg. Performance. by Pat Ganahl
CARTECH 1988 ISBN 0-931472-13-X $18.95 I normally don't recommend
books of this genre as they do not have the detailed and factual
engineering information such as BSFC, stress and heat rejection
information necessary to successfully adapt and auto engine to
aircraft use. What this book does, in it's introduction and
crankshaft chapters, is discuss the myriad compromises that led to
the 90 degree V6 auto engine.

The real reason such a fundamentally mechanically unbalanced and
problematical design is used in cars is revealed. I.E. the properly
designed, high displacement, 60 degree V6 is too tall for modern car
styling and the 90 deg. V6 can be made on the same production line
as the V8. Consider this book one that should be read on why you
should not put a 90 degree V6 in your airplane. Besides, all V and
in-line engines are trying to jam their crankshafts out the bottom
of their blocks anyway. This is one of the reasons they are
inevitably heavier than opposed engines."

Paul Lamar