A "first order" cam activates "desmodromically" a reciprocating piston, without crankshaft, without connecting rods.
Case with a single shaft:
Case with two counter-rotating shafts:
The "Grecoi3" (three cylinder in line, even firing) is perfectly balanced, as perfectly as the Wankel rotary engine.
The "Grecoi3" is much better balanced than any six (straight or boxer or Vee or �).
It is also better balanced than any eight cylinder engine.
Compact and light compared to competitors. For instance, the GrecoU6 (six cylinder in U, even firing) is not longer than the conventional three in line, it is as balanced as the conventional V-12, it is only a little wider than the conventional three in line and it uses a unique (single piece) cylinder head.
What makes the difference is the geometry of the cam profile.
Unlike a multi-lobe cam, the rotation of the single-lobe cam is of the same order (frequency) as the reciprocation of the piston, thereby the webs on the counter-rotating shafts can (depending on cam profile) fully balance the forces and the moments.
As the total kinetic energy of the three harmonically reciprocating pistons of the "Greco3" remains absolutely constant, all along a revolution, there is no inertia torque altogether, making the engine as perfectly balanced as the rotary engine of Felix Wankel (somewhat better than best V-12).
Click any of the above images to download the relative windows exe controllable animation
The "Grecoi4" (straight four, even firing) uses a unique, "single piece" shaft with a single-lobe cam for each cylinder.
The "Grecoi4" is perfectly balanced as regards forces and moments. It is as balanced as the high quality conventional straight four (SAAB, BMW, Mercedes, Opel etc) which use a pair of additional double speed, counter-rotating balancing shafts, i.e. a total of three shafts and the associated "gearings". The "Greco4" comprises only one shaft rotating at normal speed, i.e. one shaft altogether and no gearings at all.
The "rods" connecting the upper part to the lower part of the piston assembly, could be just wires, as they are loaded with only tension loads.
Cam Lobe geometry
The "basic curve", top left, has an eccentricity described as:
E(f)=a + r*sin(f).
A roller having its center on the periphery of the basic curve moves around the curve. Taking a circular disk, like the one shown at top right, and subtracting the roller as it rotates around the basic curve periphery, it results the bottom right curve and finally the bottom middle curve or the actual cam lobe profile. Holding two rollers, like the one used to subtract material from the circular disk, in a distance 2*a from center to center (shown at bottom middle) and permitting them to move only vertically, the rotation of the cam lobe causes a harmonic reciprocation along vertical axis of the two rollers assembly, keeping both of them in permanent contact to the cam lobe.
If the desirable reciprocation is not a harmonic one, the formula becomes:
E(f)=a + Y(f), where Y(f) is the desirable displacement along vertical axis relatively to the rotation angle of the cam lobe.
If the center of rotation of the cam lobe is offset from the axis of reciprocation of the rollers, the eccentricity of the basic curve shown at top left below (for harmonic reciprocation) becomes:
E(f+f1)=square root ((a + r * sin(f))^2 +d^2), with
where d is the offset.
Keeping the center of a roller on the periphery of the basic curve and moving it around the basic curve, it results the cam lobe profile, shown at bottom left. In this case the two rollers are in constant distance from each other and reciprocate harmonically as the cam lobe rotates, but they are horizontally offset at 2*d. Two "offset" counter rotating cam lobes are shown at the right side, with a piston assembly keeping all rollers.
If the harmonic reciprocation is not the desirable one, the formula becomes :
E(f+f1)=square root ((a + Y(f))^2 +d^2), with f1=Arctan (Y(f)/d).
The above geometrical method applies in the same way for multi lobe cams, for instance two lobe, three lobe etc.