IMPROVEMENTS IN GEARING FOR INCREASING OR DECREASING ROTARY SPEED
Year: 1855

page_text: LETTERS PATENT to Henry Laxton, of the Firm of William and Henry
Laxton, of 19, Arundel Street, Strand, London, Patent Agent, for the
Invention of "IMPROVEMENTS IN GEARING FOR INCREASING OR DECREASING
ROTARY SPEED."-A communication.
Sealed the 29th April 1856, and dated the 1st November 1855.
PROVISIONAL SPECIFICATION left by the said Henry Laxton at the
Office of the Commissioners of Patents, with his Petition, on the 1st
November 1855.
1, HENRY LAXTON, of the Firm of William and Henry Laxton, of 19,
Arundel Street, Strand, London, Patent Agent, do hereby declare the nature
of the said Invention for "IMPROVEMENTS IN GEARING FOR INCREASING OR
DECREASING ROTARY SPEED" to be as follows:-
The Invention consists in an arrangement of wheels, or their equivalents,
for transmitting rotary motion at an increased or decreased speed, applicable
for all kinds of machinery where multiplying gearing is required, whereby a
great difference of speed and great strength may be obtained with small
wheels. For this purpose two internal spur or level gears, or their equivalents;
are employed; two of the wheels, viz., one of each gear, are placed on a
common fixed axis (by axis is meant a line representing the geometrical axis
FD 827

page_text: DESCRIPTION OF THE DRAWINGS.
Figure I. shows a diagram which will serve to illustrate the principal of
this
gear,
, and in which the full drawn circles a and b represent the pitch lines
of two internal wheels hung upon the common axis e, so that each is indepen-
dent from the other; and the dotted circles c and d, the pitch lines of two
external wheels, both fastened together and placed upon the common axis f,
e gearing into a, and dintob. Suppose that both the axese and be stationary
and the wheels revolving on them, as in common wheel gearings, then, accord-
ing to the well-known mechanical principles of the revolving lever, the
proportion of the angular motion of the wheel a to that of b will be expressed
by the following geometrical ratio :-
(angular motion of a): (angular motion of b) :: (b, c): (a, d);
the letters a, b, c, d, representing the diameters or numbers of teeth of the
repective wheels; making, for example, a=11; b=10; c=10; and d=9
then we obtain,―
(angular motion of a): (angular motion of 6) (10 × 10) (11 x 9
= 10099;
3
that is to say, when a makes 100 revolutions, will make 99, or when a makes
1 revolution, will make ; consequently after a has made one full revolu-
tion, 6 will have made rbo part of a revolution less than a, and the mutual
position of b to a will have changed as much from its original position; it will,
therefore, require a hundred revolutions of a in order that the wheels may
come again into their first position, and the wheel b will then have made one
revolution in relation to a.
It must next be supposed that the axis f of the wheels c, d, is moving in the
red circle around the fixed axis e, the pitch lines being constantly in contact

page_text: or by giving rotary motion to E, the axis fis carried around e, and the
wheel B will make to part of a revolution for every revolution of E. In
this case the wheel B and the quick speed shaft E will both turn in the
same direction, but they may be also made to revolve in opposite directions by
giving other proportions to the diameters or numbers of teeth to the wheels;
the general rule is, that when the product of B, C, is greater than the product
A, D, both B and E will revolve in equal directions, and vice versa.
It has been represented above that both the wheels on the axis E are
internal, and both the wheels on F as external; but they may also be so
arranged that the wheels on the fixed axis E are external, and those on
the revolving axis F internal, or also that an internal and an external wheel
is placed on each axis.
Figure 4 shows the longitudinal section of a modification of the Invention,
in which the axis fis placed in an inclined position to the fixed axis e, so that
both meet at a point e¹. Now, as in all wheel gearings where the axes are
inclined to each other, the teeth must represent part of a cone which has its
apex in the point where the axes meet, A is a stationary internal bevel wheel;
B is another internal bevel wheel, fastened to shaft G, which is capable to
revolve; C and D are two external bevel wheels, cast in one piece, C gearing
into A, and D into B. The surfaces of the wheels are drawn to the point el.
F is a shaft, to which the double wheel C, D, is fastened, being supplied on
one side with a spherical end, that rests into a corresponding socket in the
centre of G, at the point e¹, where both axes meet. The other end of F
bears losely into the eye of the crank I, that is fastened to the quick speed
shaft E.
The mutual action of these wheels is the same as described above for
Figure 1, but the inclined position of the axes gives certain advantages to this
arrangement. Thus, in Figure 1 the difference between the diameters of A
and C must be equal to the difference of diameters between Band D, as the
distance of the axes f, e, from each other is equal for both pairs. In Figure 4
each pair may have another difference between their diameters, in accordance
to the distance of the axes from each other at that point where the pairs
placed on them, which must be equal to one half of the differences of their
diameters; the greater is this difference the further must they be place from
the point el; and, on the contrary, the nearer they are to an equal diameter the
nearer they must be placed to e¹. One pair of wheels may now be employed
with equal diameters or numbers of teeth, by placing them on the axes, so that
they gear at that point where the axes meet, and the distance between them

page_text: is equal to nothing. Such an arrangement is shown in Figure 5. The increase
of speed is here due only to the pair A, C, while B, D, serve only for the pur-
pose of transmitting the rotary motion G to F and C, in such a manner that
the other end of F is free to make that circular motion around the axis e..
It may here be observed that the formula given in Figure 1 can also be
applied for this case; but as here the work of b and d is equal, they may be
left out entirely on both sides of the proportion without changing the result.
When the diameters of the wheels of one pair are equal, as in the last-described
case, their action will be equal to that of an universal joint, and the latter may
therefore then be substituted for the same as an equivalent.
The construction of the gear may be modified in an almost infinite number
of ways, depending on the circumstances under which it is to be employed and
the duty it has to perform.
SPECIFICATION in pursuance of the conditions of the Letters Patent, filed
by the said Henry Laxton in the Great Seal Patent Office on the
1st May 1856.
TO ALL TO WHOM THESE PRESENTS SHALL COME, I, HENRY
LAXTON, of the Firm of William and Henry Laxton, of 19, Arundel Street,
Strand, London, Patent Agent, send greeting.
WHEREAS Her Most Excellent Majesty Queen Victoria, by Her Letters
Patent, bearing date the First day of November, in the year of our Lord
One thousand eight hundred and fifty-five, in the nineteenth year of Her
reign, did, for Eerself, Her heirs and successors, give and grant unto me, the
said Henry Laxton, Her special licence that I, the said Henry Laxton, my
executors, administrators, and assigns, or such others as I, the said Henry
Laxton, my executors, administrators, and assigns, should at any time agree
with, and no others, from time to time and at all times thereafter during the
term therein expressed, should and lawfully might make, use, exercise, and
vend, within the United Kingdom of Great Britain and Ireland, the Channel
Islands, and Isle of Man, an Invention for "IMPROVEMENTS IN GEARING FOR
INCREASING OR DECREASING ROTARY SPEED," (a communication,) upon the con-
dition (amongst others) that I, the said Henry Laxton, my executors or
administrators, by an instrument in writing under my, or their, or one of
their hands and seals, should particularly describe and ascertain the nature

page_text: of the said Invention, and in what manner the same was to be performed, and
cause the same to be filed in the Great Seal Patent Office within six calendar
months next and immediately after the date of the said Letters Patent.
NOW KNOW YE, that I, the said Henry Laxton, do hereby declare the
nature of my said Invention, and in what manner the same is to be per-
formed, to be particularly described and ascertained in and by the following
statement:-
This Invention consists in an arrangement of wheels, or their equivalents, for
transmitting rotary motion at an increased or decreased speed, applicable for
all kinds of machinery where multiplying gearing is required, whereby a great
difference of speed and great strength may be obtained with small wheels. For
this purpose we employ two internal spur or bevil gears, or their equivalents,
and place two of the wheels, viz, one of each gear, on a common fixed axis,
(by axis we mean a line representing the geometrical axis of the wheels,) and
the other two wheels gearing into them on a common axis within the circum-
frames of the first wheels, which is capable of revolving around the said fixed
axis. One of the wheels on the fixed axis we make stationary, and the
other revolving, which latter motion we use as the slower speed of the gear,
while the motion of the revolving axis around the fixed axis gives the quicker
speed, a crank or an equivalent to a crank being employed to transmit this
motion to the fixed axis.
In order that the improved arrangements of the wheels may be fully under-
stood and readily carried into effect, I have hereunto annexed a Sheet of
Drawings, the letters of reference marked thereon corresponding to the letters
herein.
DESCRIPTION OF THE DRAWINGS.
Fig. 1 shows a diagram which will serve to illustrate the principle of this
gear, and in which the full drawn circles a and b represent the pitch lines
of two internal wheels hung upon the common axis e, so that each is inde-
pendent of the other; and the dotted circles c and d, the pitch lines of two
external wheels, both fastened together and placed upon the common axis f
gearing into a, and d into b. Suppose that both the axese and fbe stationary
and the wheels revolving on them, as in common wheel gearings, then,
according to the well-known mechanical principles of the revolving lever, the
propertion of the angular motion of the wheel a to that of b will be expressed
by the following geometrical ratio :-
C
angular motion of a) (angular motion of
:
: : (b, c,): (a, d);
the letters a, b, c, d, representing the diameters or numbers of teeth of the

page_text: respective wheels; making, for example, a = 11; b=10;c=10; and d = 9;
then I obtain,
angular motion of a) (angular motion of b): (10 × 10): (11 × 9)
= 100 ÷ 99;
that is to say, when a makes 100 revolutions, 6 will make 99, or when a makes
I revolution, 6 will make fo; consequently, after a has made one full revolu-
tion, 6 will have made re part of a revolution less than a, and the mutual
position of b to a will have changed as much from its original position; it will
therefore require a hundred revolutions of a in order that the wheels may
come again into their first position, and the wheel b will then have made one
revolution in relation to a.
I will next suppose the axis f of the wheels c, d, to be moving in the red
circle around the fixed axis e, the pitch lines being constantly in contact with
each other; further, the wheel a to be now stationary, and 6 loose. The mutual
action of the pitch lines on each other will now be the same as before, and
consequently one revolution of the centre faround e will produce the same
change in the mutual position of b to a, as before did one revolution of the
wheel a; but as a is now stationary, this change of the mutual position will
be the only motion of b, while in the former case it was the difference between
the motion of a and6; consequently one revolution off around e will produce
Tu part of revolution in b, and 100 revolutions of f around e will give one
revolution to b.
This may be estimated for any other proportion of the diameters of the
wheels as follows:-Let R denote the number of revolutions of the axis f
around e; B, the number of revolutions of the wheel 6 on the fixed axis e; a,
the diameter or number of teeth of the fixed wheels; b, the same of the wheel
which is revolving on the fixed axis; c, the same of the wheel on the revolving
axis gearing into a; and d, the same of the wheel gearing into b; then,-
(b, c, a, d,) b, c, B R.
It may here be observed that any other of the pitch lines a, b, c, d, than
these assumed above may occupy the position of a or b when only the move-
ments of the other pitch lines are in the same relations to them, as described
above for c and d. I also do not confine myself to the employment of toothed
wheels, but desire it to be understood that any other equivalent being capable
of doing the same duty and to be employed in place of the toothed wheels may
be substituted for them. To transmit the rotary motion of the axis f around e,
to the axis e 1 employ a crank, or equivalent, which revolves on the axis e, and
has its eye connected to f.
Fig. 2 represents a front view, and Fig. 3 a longitudinal section, of a gear

page_text: constructed according to this Invention. A is a stationary internal wheel; B
is another internal wheel, fastened to the shaft G, which is capable of revolving
on its own axis; C and D are two external toothed wheels, which are fastened
together, or may be cast in one piece; they turn loosely on the crank pin F
of the crank I, that is connected or forms part with the quick speed shaft E,
that revolves on the fixed axis e. The number of the teeth of each wheel is
as follows: A = 11; B=10; C = 10; D = 9, which corresponds with the
numbers assumed above for the diameters of the pitch lines in Fig. 1. And
all that has been explained above for these pitch lines will now also be
applicable for the wheels; that is, by giving rotary motion to B, the axis F
of the wheels C, D, will revolve one hundred times around the axis E for
every revolution made by B, which motion is transmitted by the crank I
to the quick speed shaft E; or by giving rotary motion to E, the axis F
is carried around E, and the wheel B will make rv part of a revolution for
every revolution of E. In this case the wheel B and the quick speed shaft E
will both turn in the same direction, but they may be also made to revolve
in opposite directions by giving other proportions to the diameters or numbers
of teeth to the wheels; the general rule is, that when the product of B, C,
is greater than the product A, D, both B and E will revolve in equal directious,
and vice versa.
It has been represented above that both the wheels on the axis E are internal,
and both the wheels on F are external; but they may also be so arranged
that the wheels on the fixed axis E are external, and those on the revolving
axis F internal, or also that an internal and an external wheel is placed
on each axis.
A modification of this latter arrangement is shown in Fig. 4, which is a
front view; and Fig. 5, which is a longitudinal section of the same; here the
stationary wheel A is an interual, and the wheel B on the same axis au
external wheel. The wheels C, D, are here represented by a single wheel,
having pins or staves in place of common teeth, which, acting as internal and
external teeth at the same time, will represent on one side the wheel C by
gearing into A, and on the other side the wheel D by gearing into B. The
general formula for the proportion of speed B.R, given above, is also applicable
in this case, by setting for both c and d the number of the staves.
Figs. 6 and 7 show another modification of this gear as I apply it for
mechanists' geared lathes. Fig. 6 is a cross section through the red lines z, z, in
Fig. 7, showing the front side of the wheels; and Fig. 7, a longitudinal section
of the same. It will be seen, that here the wheels C, D, are of less than half
the diameters of A and B, giving space for the main spindle G. to pass through.

page_text: This arrangementadmits the application of two or more pairs of the wheels C,D,
which will increase the strength and improve the action of the gear. A is the
stationary wheel, fastened to the spindle head P; B is the slow speed wheel,
being internal and fastened to the spindle G; E is the pulley, turning loosely
on the spindle; it is supplied with a flange Ecast to it, into which rests the end
of each of the stud pins F, F; the other ends of the pins rest into the pulley
itself, so that they will revolve with the pulley; as also the wheels C,D,C,D¹,
which turn loosely on the stud pins, each pair being fastened together.
It will be seen that the only difference between this arrangement and that
of Fig. 1 consists in the proportions of the sizes of the wheels and the employ-
ment of a second pair of C, D, which, however, is not to be introduced into
the formula for the calculation of the difference of speed. The gear may be
thrown out of action by pushing the wheels C, D, C, D', against the pulley,
so that the wheels C, C', are disconnected from A, and establishing at the
same time a connection between the flange E' and the wheel Bin any suitable
manner.
Fig. 8 shows the longitudinal section of another modification of the Inven-
tion, in which the axis fis placed iu au inclined position to the fixed axis e, so
that both meet at a point e'. Now, as in all wheel gearing where the axes are
inclined to each other the teeth must represent part of a cone which has its
apex in the point where the axes meet, A is a stationary internal bevel wheel;
B is another internal bevel wheel, fastened to shaft G, which is capable of
revolving; Cand D are two external bevel wheels, cast in one piece, C gearing
into A, and D into B. The surfaces of the wheels are drawn to the point e¹.
F is a shaft, to which the double wheel C, D, is fastened, being supplied on
one side with a spherical end, that rests into a corresponding socket in the
centre of G at the point e', where both axes meet. The other end of F bears
loosely into the eye of the crank I, that is fastened to the quick speed shaft E.
The mutual action of these wheels is the same as described above for Fig. 1,
but the inclined position of the axes gives certain advantages to this arrange-
ment; thus,in Fig. 1 the difference between the diameters of a and c must be
equal to the difference of diameters between 6 and d, as the distance of the
axes f, e, from each other is equal for both pairs. In Fig. 8 each pair may
have another difference between their diameters, in accordance to the distance
of the axes from each other at that point where the pair is placed on them,
which must be equal to one half of the differences of their diameters; the
greater is this difference the further must they be placed from the point e';
and, on the contrary, the nearer they are to an equal diameter the nearer they

page_text: must be placed to e¹. One pair of wheels may be now employed with equal
diameters or numbers of teeth, by placing them on the axes so that they gear
at that point where the axes meet, and the distance between them is equal to
nothing. Such an arrangement is shown in Fig. 9. The increase of speed is
due only to the pair A, C, while B, D, serve only for the purpose of trans-
mitting the rotary motion of G to F and C, in such a manner that the other
end of F is free to make that circular motion around the axis e.
It may here be observed that the formula given in Fig. 1 can also be applied
to this case; but as here the work of B and D is equal, they may be left out
entirely on both sides of the proportion without changing the result. When
the diameters of the wheels of one pair are equal, as in the last-described case,
their action will be equal to that of an universal joint, and the latter may
therefore then be substituted for the same as an equivalent. Fig. 10 shows a
section, and Fig. 11 a frout view, of such a joint, which, however, can be
changed into many other forms. B and D are two similar parts, one being
fastened to Gand the other to F,each having two pins fastened into them, which
in proper bearing on the ring K, by which the parts B and Dare connected,
the whole forming an universal joint, the action of which will be in some cases
more smooth and noiseless than wheels. The great advantages of this gear
are, that but few teeth and consequently small wheels are required to obtain a
great difference of speed; that by giving the same number of teeth as in the
other gears the action will be more smooth, frictionless, and noiseless; on
account of more teeth being in gear at the same time, the motion will be
transmitted in the same line with the driving shaft; and, lastly, the gear will
occupy less space, and is more compact. The construction of the gear may be
modified in an almost infinite number of ways, depending on the circumstances
under which it is employed and the duty it has to perform.
Having now described the nature of the said Invention, and shown several
of its modifications, I wish it to be understood that I do not confine myself to
the precise details and arrangements of the parts shown and described, so long
as the peculiar nature of the Invention is retained, as these must vary for
every other kind of machines to which the gear is applied; but what I claim
as my Invention is, the combination in any manner, substantially as herein
described, for the purpose of increasing or decreasing rotary speed, of two
internal or beval gears, or such equivalent thereof, as herein specified; two of
the wheels, viz, one of each gear having a common fixed axis e, and the
others a common axis f, revolving around the said fixed axis e, and one of the
wheels on the fixed axis e being stationary and the other revolving with slower

page_text: speed of the gear, while the revolution of the axis f around e is applied, by
means of a crank or equivalent, to a crank as the quicker speed, herein set
forth.
In witness whereof, I, the said Henry Laxton, have hereunto set
my hand and seal, this First day of May, in the year of our Lord
One thousand eight hundred and fifty-six.
Witness,
RICHARD SILVESTER,
1st May 1856.
HENRY LAXTON. (L.S.)