Hypocycloidal Engine

A conventional four-stroke spark-ignition reciprocating engine employs 
a simple cranking mechanism with a crank pin that revolves in a circle, 
causing the pistons to undergo a periodic motion consisting of four 
"strokes" of equal lengths.  These four strokes are

  (1) Intake:      A mixture of air and fuel is drawn into the 
                   cylinder as the piston moves from top center 
                   to bottom center.
  (2) Compression: The mixture is compressed as the piston moves 
                   back from bottom center to top center.
  (3) Expansion:   A spark near top center causes the mixture
                   to combust, raising the pressure and temperature.
                   The resulting gas expands as the piston moves
                   from top to bottom center.
  (4) Exhaust:     The products of combustion are expelled from the
                   cylinder as the piston returns from bottom to
                   top center, at which point it begins the cycle
                   again.

The basic cranking mechanism and the corresponding pressure/volume
diagram illustrating the four-stroke spark-ignition engine are shown
in the figure below:


 
The simplicity of the conventional cranking has many beneficial
effects, such as ease of construction, durability, low mechanical
complexity, and so on.  However, one disadvantage  of the conventional
mechanism is that the compression ratio of the cycle, i.e., the ratio 
of the volumes of the fuel-air mixture at the beginning and end of 
the compression stroke, is necessarily equal to the expansion ratio, 
i.e., the ratio of volumes of the fuel-air mixture at the beginning 
and end of the expansion stroke.  This is a disadvantage because the
compression ratio of a spark-ignition engine with modern fuels can
usually not be greater than about 9:1, and typically must be even
less to avoid "knock", which is the spontaneous detonation of the
mixture rather than the intended controlled burning initiated by
the spark.  Knock is very destructive to an engine, and must be
avoided.  

Unfortunately, this implies (with the conventional cranking
mechanism) that the expansion ratio is also limited to about 9:1.
At high power this is typically somewhat wasteful, because after
the gas has expanded through a ratio of 9:1 it is still at a 
significantly elevated pressure and capable of doing more useful 
work, but since the piston has reached bottom center we have no
choice but to open the valves and allow the gas to "blow down",
after which the remaining products of combustion are exhausted by 
the exhaust stroke.

Typically (at high power) the gas inside the cylinder at the time
when the exhaust valves are opened is more than 1.9 times the
atmospheric pressure, so we get "choked" sonic flow at the valves,
which creates extremely high sound levels.  This is why automobile
engines are equipped with mufflers on the exhaust.  If the muffler 
of an an internal combustion engine is removed and the engine is 
run at high power, it is incredibly loud.  This noise is an indication
of the energy that is being wasted.

Another disadvantage of the conventional cranking mechanism is due
to the fact that extremely high forces are applied to the piston
during the "power stroke" (i.e., the expansion stroke), when the
high-pressure products of combustion force the piston downward,
and during this motion the link rod between the piston and the
crankpin is deflected sideways because the crankpin moves horizontally
as well as vertically (as it moves around in a simple circle).  At
the mid point of the expansion cycle the link rod is at its maximum
angle relative to the axis of the cylinder, which results in extremely
high side loads and friction between the piston and the cylinder.

Both of these disadvantages of the conventional cranking mechanism
can be alleviated by adopting a somewhat more complex cranking
mechanism, so that the path of the crankpin is hypocycloidal instead
of circular.  A schematic of the hypocycloidal cranking mechanism
is shown below.

         

The outer green circle represents a fixed gear with teeth on the
internal circumference, and this engages the external teeth of a gear 
wheel of 2/3 the diameter represented by the next smaller green 
circle.  The center of this inner gear is connected to the crankshaft,
and follows the path indicated by the red circle.  The actual crankpin
is offset from the center of the internal gear by 1/3 of the length
of the primary crank link.  The hypocycloidal path of the crankpin is 
indicated by the blue curve in the figure above.

Since the path of the crankpin has three-way symmetry, it is possible
to locate cylinders along three radial axes, as indicated by the red 
radial lines in the figure.  The wrist pins and link rods connecting
them to the crankpin are shown in purple.  Notice that the absolute
rotation of the internal gear is in the opposite direction and at 
1/2 the speed as the main crankshaft.  The thermodynamic cycle of
the hypocycloidal engine is illustrated in the PV diagram below:

         

The improved efficiency of the engine is due largely to the elongated
expansion stroke, which is made possible without increasing the 
compression ratio beyond the "knock" limit by means of the hypocloidal
cranking mechanism.  (Of course, similar cycles can be produced by
offsetting the usual valve timing, but this results in greatly 
increased pumping losses, which offset the cycle gains.)

If your browser supports Java applets, you can see an animated view 
of the kinematics of the hypocycloidal engine.

To maximize the benefits of the hypocycloidal design, it would be
possible to mount the external (outer) gear in a collar that enabled
it's orientation to be adjusted slightly.  This would allow for
variations in the in-cylinder compression and expansion ratios, and
could be used in conjunction with external turbo-charging to optimize
the cycle over a wide range of power outputs.  Throughout this range
the full expansion of the products of combustion would provide high
thermodynamic efficiency by not "throwing away" gas that is still at
fairly high pressure.  In addition, this arrangement provides reduced 
exhaust noise levels which would allow operation with less pressure 
drop across a muffler.

In addition, notice that the power (expansion) stroke, during which 
the greatest force is applied to the piston and link rod, occurs
when the crankpin is on the "inner" loop of the hypocycloidal path,
so that the deflection of the link rod is less than for a conventional
cranking mechanism, resulting in reduced side loads, friction, and
losses on the piston and cylinder walls.