U.S. patent application number 10/577165 was filed with the patent office on 2007-04-12 for cam drive mechanism.
Invention is credited to Emmanouel Pattakos, John Pattakos, Manousos Pattakos.
Application Number | 20070079790 10/577165 |
Document ID | / |
Family ID | 37910076 |
Filed Date | 2007-04-12 |
United States Patent
Application |
20070079790 |
Kind Code |
A1 |
Pattakos; John ; et
al. |
April 12, 2007 |
Cam drive mechanism
Abstract
For the conversion of a reciprocatory into a rotary motion or
vice versa, a reciprocating member is acting upon at least one cam
of a driveshaft. Among the benefits and advantages resulting from
the choice of the cam profile, there is the possibility of a single
cylinder engine which is full balanced, with respect to forces and
moments, and a three-in-line which is balanced as perfectly as the
Wankel rotary, i.e. perfect balance not only as regards inertia
forces and inertia moments, but also as regards inertia torques. It
turns out that the form of the profile of the cam and the location
of its axis of rotation, relatively to the axis of the
reciprocation are substantially limitless.
Inventors: |
Pattakos; John; (Piraeus,
GR) ; Pattakos; Emmanouel; (Piraeus, GR) ;
Pattakos; Manousos; (Piraeus, GR) |
Correspondence
Address: |
Manousos Pattakoas
Lampraki 356
Nikea Piraeus
18452 GR
GR
|
Family ID: |
37910076 |
Appl. No.: |
10/577165 |
Filed: |
October 29, 2004 |
PCT Filed: |
October 29, 2004 |
PCT NO: |
PCT/GR04/00052 |
371 Date: |
April 26, 2006 |
Current U.S.
Class: |
123/197.1 |
Current CPC
Class: |
F01B 9/06 20130101; F16H
25/14 20130101; F02B 75/32 20130101; F01B 2009/065 20130101; F01B
2009/066 20130101 |
Class at
Publication: |
123/197.1 |
International
Class: |
F01B 9/06 20060101
F01B009/06 |
Foreign Application Data
Date |
Code |
Application Number |
Oct 29, 2003 |
GR |
20030100442 |
Claims
1. A motion converting mechanism comprising a reciprocating member
(1) and a rotating member (7); said reciprocating member (1)
comprising at least two roller cam followers (5) in substantially
constant distance from each other; said rotating member (7)
comprising a cam (9); for each rotation of the cam (9) only one
reciprocation of the reciprocating member (1) takes place;
characterized in that: the centers of the roller cam followers
follow curves, relative to the cam, having an eccentricity E(f)
which is related to the displacement Y(f) of the reciprocating
member (1) substantially by the formula: E(f+f1)=square root
((a+Y(f)) 2+d 2), with f1=Arctan ((a+Y(f))/d), where f is the
rotation angle of the cam, d is half the distance between the axes
of reciprocation of the centers of the roller cam followers and a
is a constant; while Y(f)+Y(f+.pi.)=constant for any f; thereby the
same cam profile desmodromicly controls the reciprocation in both
directions.
2. A motion converting mechanism according claim 1, characterized
in that: the profile of said cam (9) is such that the reciprocation
of the reciprocating member (1) is substantially sinusoidal, versus
the rotation angle f of the rotating member (7).
3. A motion converting mechanism according claim 1, characterized
in that: the reciprocating member comprises at least one roller (4)
riding either on an immovable surface (16) or on a rotating
cooperating cam (11) and bearing thrust loads at low friction to
improve mechanical efficiency and reliability.
4. A motion converting mechanism comprising a reciprocating member,
at least two rotating external cams, not necessarily of the same
size or number of lobes, and at least a thrust wall; characterized
in that: the reciprocating member comprises a roller cam follower
assembly, trapped among the cams and the thrust wall.
5. A motion converting mechanism according claim 1, characterized
in that: the resulting side loads are substantially carried by the
rolling of rollers on angularly displaceable thrust walls in order
to provide variable compression ratio.
6. A motion converting mechanism comprising a reciprocating member
and a rotating camshaft; said camshaft comprising at least a first
external cam and a second external cam; said reciprocating member
comprising a first roller cam follower and a second roller cam
follower; said first roller cam follower rides on said first cam
with its center following a first centers curve relative to the
camshaft; said second cam follower rides on said second cam with
its center following a second centers curve relative to the
camshaft; characterized in that: the first cam and the second cam
are complementary in the sense that any line from the center of
rotation of the camshaft, intersects the first and the second
centers curves in a sequence of four points A, B, C and D with
AC=BD=constant and AB=CD.
7. A motion converting mechanism for desmodromic control of
reciprocating valves comprising: at least a cam having an eccentric
groove and at least a cam follower sliding along said eccentric
groove in substantially permanent contact to both sides of the
groove; characterized in that: the cam follower is substantially
longer than the width of the groove.
Description
[0001] This invention solves the known problem of the desmodromic,
or positive, control of a reciprocating member comprising a pair of
rollers riding on a uni-lobe cam.
[0002] By uni-lobe cam is meant a cam whose one rotation
corresponds to only one reciprocation of the reciprocating
member.
[0003] By desmodromic or positive control is meant that if the one
roller is in contact with the cam, the other roller is no more than
the running tolerance away from the cam.
[0004] In the art there are drive mechanisms using multi-lobe cams,
as in U.S. Pat. No. 4,545,336 patent or uni-lobe cams as in GB
891,490.
[0005] The uni-lobe is simpler, smaller for the same stroke and can
use counterweights, fixed on its shaft, for balancing inertia
loads.
[0006] It is possible for a cam mechanism to employ a second
camshaft to bear the thrust loads, or can bear the thrust loads on
walls, immovable or rotatable to provide variable compression.
[0007] The latter needs not a gearing of high strength/high
accuracy/small clearance to connect the cooperating camshafts, is
cheaper to make and compact.
[0008] The uni-lobe cam must control desmodromicly the
reciprocating member in both directions. Unless the necessary cam
profile can be defined as strictly as to provide the demanded
quality and accuracy of the reciprocation the control is
impossible, the cam cannot meet the contemporary demands.
[0009] As a roller rolls along a cam, it contacts the cam along the
cam profile but the center of the roller travels along its own path
which, being the trace of the center, can be called the centers
curve.
[0010] The centers curve derives from the cam profile and the
radius of the roller. Likewise, keeping the center of the roller on
the centers curve and moving it along its successive positions, the
roller defines the profiles of two cams, one external and one
internal. If the axis of a milling cutter follows the centers
curve, while removing material from a plate, it is machining the
two cams mentioned.
[0011] Any point on the centers curve derives the respective point
of the cam profile by drawing a line, of length equal to the radius
R of the roller, perpedicular to the centers curve at this point,
as FIG. 38 shows.
[0012] In GB 891,490 patent the control of the reciprocation is
provided by a uni-lobe cam whose geometry is described in Page 3,
lines 50 to 69, and in FIG. 5. In GB 891,490 the profile is defined
as the union of two concentric circular arcs and two connecting
curves such that the length of the line, defined by the contact
point of the top roller and the contact point of the bottom roller,
is constant. In the present invention only the distance between the
centers of the rollers is constant; the distance between the
contact points of the two rollers is substantially variable,
varying from a minimum length, equal to the distance of the centers
minus the sum of the radiuses of the two rollers, to a maximum
which, depending on the roller size, may become more than 10%
bigger than the minimum for reasonable size of roller. Also, in GB
891,490, although the two rollers ride on a common cam, it appears
that the top roller diameter is larger, probably because of its
heavier loads. In the present application the mathematical
derivation of the cam profile makes it clear that it is impossible
to control the piston desmodromicly with a common cam and rollers
of different diameter.
[0013] The constant breadth cam of US 0020043225 patent application
can control the system desmodromicly only if the diameter of the
rollers is equal to zero, for reasonable diameter of the rollers
the mechanism cannot be desmodromic.
[0014] Besides its main cam lobe, the engine of the U.S. Pat. No.
4,493,296, FIG. 22, needs a secondary groove-cam, i.e. internal
cam, and additional secondary rollers for the restoring of the
piston, while the opposed pistons move independently. If, as FIG.
20 of the present invention shows, the profile of the main cam is
properly derived then the groove and the secondary rollers are
unnecessary and the pairs of the opposed pistons can be united in a
single body reducing inertia loads and friction. The typical groove
cam used in U.S. Pat. No. 4,493,296 and many other patents of the
prior art, can be replaced by a pair of complementary external cams
on the same camshaft, as shown in FIGS. 47 to 49.
[0015] Compared to groove cams, the use of a camshaft comprising a
first external cam, to constrain the reciprocation at one
direction, and a second complementary external cam, to constrain
the reciprocation at the opposite direction, provides more robust
cams of reduced size, easier construction etc. In FIGS. 47 and 48
the secondary external cam is selected to be a circle, while in
FIG. 49 the general case is illustrated. The only requirement for
the centers curves E1 and E2 is AC=BD=constant, i.e. given the CP1
cam profile or the piston's position function Y(f), the radiuses R1
and R2 and the constant distance of their centers, the centers
curve E1 derives, then the E2 from the E1 and finally the
complementary cam profile CP2.
[0016] The version shown in FIGS. 19, 26 and 27 necessitates a
second camshaft but eliminates the second roller cam follower
assembly. As long as the top cam is free of combustion loads, its
size can be reduced in order to reduce the piston rod height and
mass.
[0017] In a preferred embodiment the motion converting mechanism of
FIG. 8 consists of a pair of counter-rotating shafts (7) and
(8).
[0018] The shaft (7) has double-disk cams (9) and (10) to allow
room for the cam (11) of the shaft (8).
[0019] The profile of the cams, i.e. the control surface of the
cams is made so that to derive a harmonic reciprocation for the
piston rod.
[0020] By the mathematical term harmonic it is meant a strictly
sinusoidal motion versus the time, i.e. versus the shaft-angle in
the case of a single-lobe cam and versus the shaft-angle times the
lobe-number for the cases of multi-lobe cams.
[0021] The balance of inertia forces and moments for such a
reciprocation is simple, even for a single cylinder or a twin, by
virtue of a couple of counterweight webs fixed on the shafts, but
only in case of single-lobe cams.
[0022] The additional merit of the three-in-line of the FIG. 8, as
compared to the single or twin, is that besides being perfectly
balanced with respect to inertia forces and moments, ie. the
rocking moments along the shaft, it is also fill balanced with
respect to the inertia torques, i.e. the twisting moments about the
shaft This feature makes it as perfectly balanced as the Wankel
rotary engine.
[0023] Higher order harmonic components can be added to or
subtracted from the single-lobe, kidney-shape, cam as shown in FIG.
2.
[0024] In the multi-lobe cams, of the prior art, the time for one
rotation of the multi-lobe cam is longer than the time for a
reciprocation of the reciprocating member, thus balance web on them
provide no good. Hence, if something makes them in the future
desirable, the balance of the engine will necessitate additional
counterweight shafts faster than the drive shaft.
[0025] Multi-lobe cams impact, as many times as the number of
lobes, stronger momentary torques from combustion and even worse
torque impacts from inertia, which means as many times stronger
impacts for the whole mechanism, gearing included.
[0026] FIG. 1 illustrates a way to derive a reciprocation by
forcing a pin or a pair of pins to ride on a cam, in this case to
produce a strictly sinusoidal reciprocation, called harmonic
reciprocation. As it is geometrically shown in FIG. 24, if the pin
is kept in permanent contact with the cam, and the center of the
pin can move along a line then, as the cam rotates about its axis
the pin will perform a harmonic reciprocation.
[0027] FIG. 2 depicts the necessary modification of the cam profile
in order to add or subtract some higher order Fourier components to
the displacement of the pin of the FIG. 1. Here a third order
sinusoidal has been added and has been subtracted respectively to
derive the other two profiles. The general way for the geometrical
derivation of the appropriate cam profile is outlined in FIG.
24.
[0028] FIG. 3 shows the way a single-lobe cam, which derives a
harmonic reciprocation, needs to be modified if a different motion
for the pin is, for some reason, more desirable than the harmonic
motion. In most of the drawings, however, the design keeps on for
cams deriving a harmonic reciprocation.
[0029] FIG. 4 does compare the true dimensions, for the same stroke
of the pin, of a three-lobe and a five-lobe cam, i.e. for identical
harmonic reciprocation amplitude, e.g. piston stroke. Also FIG. 4
does compare the dimensions of the three-lobe cam with the
dimensions of the single-lobe cam for the same stroke, again, to
make it clear that only with a single-lobe cam reasonable
dimensions are possible for specific stroke, either for the coaxial
cams of FIG. 5 or for simply parallel cams or for the rest ways,
here presented, deriving scissors-like action.
[0030] FIG. 5 shows one way to force the pin of FIG. 1 to keep
contact with the cam frontal surface, let it be called control
surface, by virtue of the cooperation of the cam of FIG. 1 with
another coaxial cam, the problem lies with the driving of the
second shaft, it takes at least five gears to accomplish the
differential.
[0031] FIG. 6 shows a second way to force the pin to ride on the
cam control surface of FIG. 1, i.e. by means of a second cam which
is simply parallel, but not coaxial, to the cam of FIG. 1.
[0032] FIG. 7 proves that the pattern of FIG. 6 easily apply to a
single piston.
[0033] FIG. 8 illustrates a three cylinder twin-shaft engine. The
cams are single-lobe and their counter-rotation takes place by
means of a pair of gears (13) and (14).
[0034] FIG. 9 is a cross section of the engine of FIG. 8 to reveal
a piston arrangement.
[0035] FIG. 10 is another cross section of the engine of FIG. 8 and
a disassembly, to show the piston rod with its rollers
[0036] FIG. 11 is a bottom view of the engine of FIG. 8 to show the
two cams as they cooperate, the one being formed as a double disk
to allow a gap for the other cam to pass through, in order to keep
them close to make the engine compact and the piston assembly
strong, and the balance webs on the two shafts.
[0037] FIG. 12 is a transparent view of the engine of FIG. 8 to
show the three pairs of cams and the position of the respective
pistons.
[0038] FIGS. 13, 14 and 15 depict a double-head piston
four-cylinder or H-4 arrangement.
[0039] FIG. 16 shows how a shuttle can be formed in a piston to
house the cam throughout its rotation, i.e. to connect the
reciprocating member with the rotating member desmodromicly,
thereby provide an engine consisting of merely two moving parts,
i.e. the rotating component and the reciprocating component
[0040] FIG. 17 shows the displacement of the piston of FIG. 16 as a
result of the rotation of the single-lobe cam of FIG. 16. The
single-lobe cam has full desmodromic control over the piston, i.e.
complete control without any involvement of additional restoring
means.
[0041] FIG. 18 shows another way to force the pin of FIG. 1 to keep
in contact with the control surface of the cam of FIG. 1, i.e. by
virtue of wall means, or rails, etc.
[0042] FIG. 19 shows the desmodromic control of a reciprocating
roller trapped between a pair of non concentric cams and a pair of
walls.
[0043] FIG. 20 shows the wall version for a double-head piston and
a X-type engine at right angle.
[0044] FIG. 21 shows the mechanism at 12 successive angles of shaft
rotation. The thrust rollers are coaxial to the rollers rolling on
the frontal surface of the rotating cam-lobe. There are walls, not
shown, where the thrust rollers roll on.
[0045] FIG. 22 shows an in line three cylinder engine having a
single shaft with single-lobe cams, as well as the necessary
immovable walls and the various parts disassembled.
[0046] FIG. 23 shows a shaft with a cam lobe and a piston assembly,
with the piston at an offset from the axis of the shaft, as well as
immovable walls for taking the thrust loads.
[0047] FIGS. 24 and 25 show the geometrical construction of the cam
lobe profile.
[0048] FIG. 26 shows two counter rotating cam lobes and immovable
walls. The piston has a unique pin with rollers.
[0049] FIG. 27 is the mechanism of FIG. 26 with the cam lobes
rotating at the same direction.
[0050] FIG. 28 shows another realization of the mechanism with a
unique cam lobe, immovable walls and the piston assembly.
[0051] FIGS. 29 and 30 show a straight four balanced engine with a
single shaft.
[0052] FIG. 31 shows the contact angle between roller and cam lobe.
All curves are for the same stroke and for sinusoidal
reciprocation, i.e. harmonic. Increasing the size of the single
lobe cam, shown at bottom right, it results the basic curve shown
at top right, having weaker thrust loads and larger size. The three
lobe curve, of similar external size, imparts heavier thrust
loads.
[0053] FIGS. 32 to 37 show a desmodromic valve control system.
[0054] FIGS. 38 to 45 analyze the geometry of the mechanism.
[0055] FIG. 46 shows a mechanism similar to the one shown in FIGS.
28 to 30 with the difference that the piston has a connecting rod
and the thrust rollers roll along paths which are rotatable for a
few degrees about the main shaft, providing variable
compression.
[0056] FIGS. 47 to 49 show a mechanism based on a camshaft having
two different complementary external cams. Each reciprocating
roller cam follower rides on the external surface of its own
cam.
[0057] In the embodiment of FIG. 8 the two shafts counter-rotate by
virtue of the equal gears (13) and (14).
[0058] The cams on the shaft (7) are made as double disk cam (9)
and (10), to allow the cams (11) of the shaft (8) to pass through,
so that no twisting moment is imparted to the piston assembly.
[0059] The camlobes (9) and (10) of the shaft (7) and the camlobe
(11) of the shaft (8) rotate. The rollers (5), (6) and (4) on the
piston assembly (1) rolls along the periphery of the camlobes,
making the piston to reciprocate inside its cylinder. The proper
selection of the profiles of the camlobes and of the diameter and
arrangement of the rollers on the piston assembly, make the
mechanism full desmodromic, as all rollers are kept permanently in
contact to the camlobes.
[0060] Adjusting means, such as bolting, springs etc, known in the
art, may be added to the rod assembly to provide the desirable
clearances or preloading between the roller and the lobe.
[0061] Unlike a multi-lobe cam, the rotation of the single-lobe cam
is of the same order, i.e. frequency, as the reciprocation of the
piston, thereby the webs (12) on the counter-rotating shafts
suffice for the fill balance of the forces and moments and, as the
total kinetic energy of the three harmonically reciprocating
members remain constant all along a revolution, there is no inertia
torque altogether. The engine of FIG. 8 is as perfectly balanced as
a rotary engine, e.g. Wankel rotary engine. The counterweight (12)
are also to reduce the main bearing loads.
[0062] FIGS. 28, 29 and 30 illustrate an even simpler embodiment.
Here a single cam (9) in cooperation with a wall or rail (16), as a
second rolling surface, completes the scissors. The rail has the
advantage of been easily adjustable.
[0063] The even firing, straight four engine of FIG. 29 has a
single, one piece, shaft with a single-lobe cam for each cylinder.
The engine is perfectly balanced as regards inertia forces and
inertia moments. The rods connecting the upper part of the piston
assembly to the lower part of the piston assembly could be just
wires, as they are loaded with only tension loads.
[0064] Replacing the second shaft (8) of FIG. 8 with a wall, as
shown in FIG. 22, the result is one shaft and one gearing less but
also one first order balance shaft lacking. Now the perfectly
balanced three-in-line of FIG. 8 is no longer perfect unless an
extra balance shaft is added for the elimination of the rocking
moments along the shaft, but with respect to inertia forces and
inertia twisting moments, i.e. torques, it remains balanced. A
correct clearance between the thrust rollers and the wall, permits
the use of the same thrust rollers to roll along the left wall
surface as long as the thrust load is to the left direction, and to
the right wall when the thrust load is to the right direction. As
the direction of the thrust load changes at top and bottom of the
reciprocation, where the thrust rollers stop rotating, the
transition from the one side wall to the other is smooth and
friction free.
[0065] As shown from FIG. 31, the thrust loads resulting from the
mechanism are significantly stronger compared to the thrust loads
of the conventional crank-rod mechanism. In order to make the
mechanism efficient and reliable, these strong thrust loads must be
carried without losing excessive energy in friction. The secondary
rotating cam lobe geared to the primary cam lobes, or the immovable
wall surfaces, allows to bear the thrust loads with rollers rolling
on them.
[0066] FIG. 24 shows the way to create a cam lobe profile, given
the amplitude of the sinusoidal, i.e. harmonic, reciprocation. The
basic curve, upper left, has an eccentricity described as:
E(f)=a+r*sin(f).
[0067] A roller having its center on the periphery of the basic
curve moves around the curve. Taking a circular disk, like the one
shown in upped middle, and subtracting the roller as it rotates
around the basic curve periphery, it results the upper right curve
and finally the low middle curve. Holding two rollers, like the one
used to subtract material from the circular disk, in a distance 2*a
from center to center, shown in low middle, and permitting them to
move only perpendicularly, the rotation of the cam lobe causes a
harmonic reciprocation, along perpendicular axis, of the two
rollers assembly, keeping both of them in permanent contact to the
cam lobe. In the low right side is shown a groove made in similar
way. Using a pair of counter rotating grooves, coaxial or parallel,
it can result a reciprocation free from thrust loads.
[0068] If the desirable reciprocation is not harmonic, the formula
becomes:
[0069] E(f)=a+Y(f), where Y(f) is the desirable displacement along
the perpendicular axis, relatively to the rotation angle of the cam
lobe.
[0070] In FIG. 25 the center of rotation of the cam lobe is offset
from the axis of reciprocation of the rollers. For harmonic
reciprocation the eccentricity of the basic curve, left, becomes:
E(f+f1)=square root((a+r*sin(f)) 2+d 2), with
f1=Arctan((a+r*sin(f))/d), where d is the offset.
[0071] Moving a roller, while keeping its center on the basic
curve, it results the cam lobe profile, shown at the middle. 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 in the right side, with a piston assembly keeping all
rollers. Again 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((a+Y(f))/d).
[0072] The above geometrical method apply in the same way for multi
lobe cams, for instance two lobe, three lobe etc.
[0073] As in the prior art, the space beneath the piston remains
available for a second chamber which may serve as a compressor for
supercharging etc.
[0074] In the following it will be proved that the disclosed
solution of the problem of desmodromic or positive control of a
reciprocating piston comprising a pair of roller cam followers, by
a single cam surface rotating once per reciprocation, is not just
one solution but the only possible solution, i.e. it is sufficient
and necessary.
[0075] In the general case, as shown in FIG. 39, a uni-lobe cam
profile CP rotates about a center O, with f being the rotation
angle. One roller cam follower of radius R1 reciprocates with the
piston and moves along an axis XI. Another roller cam follower of
radius R2 reciprocates with the piston and moves along an axis X2
parallel to X1. The piston is controlled desmodromicly by the cam
with the roller cam follower R1 at one direction, and with the
roller cam follower R2 at the opposite direction. E1 is the centers
curve of R1 roller while E2 is the centers curve of R2 roller.
[0076] There are only six cases.
[0077] 1.sup.st case: X1 and X2 coincide, R1=R2, O on the
coinciding axes.
[0078] 2.sup.nd case: X1 and X2 are not coinciding, R1 equal to
R2.
[0079] 3.sup.rd case: X1 and X2 coincide, R1=R2, O outside
coinciding axes.
[0080] 4.sup.th case: X1 and X2 coincide, R1 not equal R2, O
outside coinciding axes.
[0081] 5.sup.th case: X1 and X2 coincide, R1 not equal R2, O on the
coinciding axes.
[0082] 6.sup.th case: X1 and X2 are not coinciding, R1 and R2 are
not equal.
[0083] Case 1, FIG. 24. For any given piston's position function
Y(f), provided that Y(f)+Y(f+.pi.)=constant for every f, there
exist a cam profile CP that provides the specific piston motion. To
get the CP, the first step is to derive from the Y(f) the relevant
centers curve E of eccentricity E(f)=a+Y(f), where a is a constant.
Then, the cam profile CP derives from the centers curve E as an
offset, by R, curve, as shown in FIGS. 38 and 24. The constant a
can increase if deficiencies, i.e. cutaways, on the final cam
profile occur.
[0084] Case 2, FIG. 40. When the piston is at TDC, the center of R1
is at A1 and the center of R2 is at A2. So the A1 is a point of
maximum eccentricity for the centers curve, while the A2 is a point
of minimum eccentricity. The circle with center O and radius OA2
intersects the X1, at the side of A1, at a point B1 which is
necessarily a BDC for the piston. The circle with center O and
radius OA1 intersects the X2, at the side of A2, at a point B2. Due
to desmodromic control the lengths of A1B1 and A2B2 must be equal.
So the two triangles OA1B1 and OA2B2 are equal, having all their
sides equal. So the O is necessarily in equal distances from X1 and
X2 axes, as shown in FIG. 25. For any given piston's position
function Y(f), provided that Y(f)-Y(f+.pi.)=constant for any f,
there exist a cam profile CP that provides the specific piston
motion. To get the CP, the first step is to derive from the Y(f)
the relevant centers curve E of eccentricity E(f+f1)=square
root((a+r*sin(f)) 2+d 2), with
[0085] f1=Arctan ((a+r*sin(f))/d), and the a being a constant.
Then, the cam profile CP derives from the centers curve E as an
offset by R curve, as shown in FIG. 38. The constant a can be
increased, if necessary, to correct deficiencies on the final cam
profile.
[0086] Case 3, FIG. 41. The offset position of the cam leads to a
series of maximum eccentricity points having minimum eccentricity
points between them. When the piston is at TDC, the center of R1 is
at A1 and the center of R2 is at B1. A circle with center O and
radius OA1 intersects the reciprocation axis, at the side of B1, at
a point A2. The angle between OA1 and OB1 is .phi., with
.phi.<.pi.. For each point of minimum eccentricity on the cam
surface, there are two maximums at +.phi. and -.phi. angles, and
for each point of maximum eccentricity on the cam surface there are
two minimums at +.phi. and -.phi., giving infinite maximums and
minimums for random .phi. as shown in FIG. 42. In the best case
there is a series of a maximum, a minimum, a second maximum and a
second minimum at .pi./2 angle from each other. This means that the
cam profile, if it exists, cannot be a uni-lobe cam profile.
[0087] Case 4, FIG. 43. When the piston is at TDC, the center of R1
is at A1 and the center of R2 is at B1. When the piston is at BDC
the center of R1 is at A2 and the center of R2 is at B2. The angle
between OA1 and OB1 is .phi.1 and the angle between OA2 and OB2 is
.phi.2 with .phi.1<.pi. and .phi.2<.pi.. For each maximum on
the cam there are two minimums at angle -.phi.1 and +.phi.2, and
for each minimum on the cam there are two maximums at angles
-.phi.2 and +.phi.1. As in case 3 this necessarily leads to
multi-lobe cams, so there is no uni-lobe cam for such a case.
[0088] Case 5, FIG. 44. The E1 centers curve is the offset by R1 of
the cam profile CP and the E2 centers curve is the offset by R2 of
the CP. So between E1 and E2 there is a band of constant
perpendicular, to the curves, width R1-R2. A random line from the O
intersects the E1 at A and B points, it also intersects the E2 at C
and D points. The constant distance between the centers of R1 and
R2 gives AD=CB, and so AC and DB must be equal. Rotating the AB
line for an infinite angle df, the A comes to A1, the B to B1 and
so on. AD is constant so ALD1=AD, so AA2-D2D1, with A2 being the
point on OA with OA2-OA1, and D2 being the point on OB with
OD2=OD1. But A1A2=d0A1 and D1D2=df*0D1. And because
tan(A2AA1)=A1A2/AA2 and tan(D2DD1)=D1D2/DD2, so
tan(A2AA1)/tan(D2DD1)=OA1/OD1, so the angle at the longer
eccentricity is bigger. But (R1-R2)=AC*sin(A2AA1)=BD*sin(D2DD1),
due to the constant perpendicular width between E1 and E2, and
AC=BD, so the angles A2AA1 and D2DD1 are equal. Not possible.
[0089] Case 6, FIG. 45. A1 is the center of R1 at TDC and A2 is the
center of the R2 at TDC. B1 is the center of R1 at BDC and B2 is
the center of R2 at BDC. Either the .phi.1 is not equal .pi. or the
.phi.2 is not equal .pi., the cam has multiple lobes, so a uni-lobe
cam cannot exist, as in cases 3 and 4. If both .phi.1 and .phi.2
are equal to it, because of the equal lengths of the A1B1 and A2B2,
the O is at equal distances from X1 and X2, which gives OA1=OB2.
But OA1=OC1+R1, and OB2-OD2+R2, with OC1=OD2, because A1 and B2
correspond to maximum eccentricity on the cam lobe. So it is
necessary R1=R2. So for not concentric axes the only solution to
achieving the desmodromic control is to have roller cam followers
of equal radius.
[0090] Decreasing until zero the offset d of case 2, it results the
case 1, with d=0 and f1=.pi./2. So the problem of the positive or
desmodromic control of a reciprocating piston, having a pair of
roller cam followers, by one only uni-lobe cam surface is solved,
the solution provided is the only possible while the only
limitation is the piston's position function Y(f) to obey in the
rule Y(f)+Y(f+.pi.)=constant. The practical application of the
method is clear: in the general case, given the piston's position
function Y(f) the centers curve E(f) is calculated according the
formulas given and then the center of the cutting tool of a milling
machine follows the specified centers curve creating the cam.
[0091] If the roller, as it moves contacting the cam lobe, is held
parallel to itself, then instead of die rolling, a sliding takes
place. However, only a small part of the periphery of the roller
comes in contact to the cam and the rest periphery of the roller,
being free, is not necessary. By machining a pair of cams, one
external and one internal, as FIG. 32 to 37 show, and holding
between them a slim cam follower resulting as the section or the
subtraction of the two rollers used initially to configure the two
cams, according the geometrical method provided, a desmodromic
mechanism of small dimensions, reduced inertia, broad contact
surfaces, of fewer components and free of springs, capable of
controlling the motion of a reciprocating valve, is provided. FIG.
34 shows seven successive positions of the cam follower sliding
along the groove. FIG. 36 and 37 show the application on a pair of
valves. The two cam followers are formed at the two sides of a flat
valve holder, whose thrusting surface is not shown.
[0092] The present invention is, of course, in no way restricted to
the specific disclosure of the specification and drawings, but also
encompasses any modifications within the scope of the appended
claims.
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