Improvements in Toothed and other Gearing.
Year: 1892

page_text: Date of Application, 26th July, 1892
Complete Specification Left. 20th Apr., 1893-Accepted, 2nd June, 1893
PROVISIONAL SPECIFICATION.
Improvements in Toothed and other Gearing.
We AUGUSTE Descorfe and LEONIDAS ALEXANDRE DI GIORGIO both of
ille, France, Engineers, do hereby declare the nature of this invention to be as
ollows:-
This invention has reference to toothed gearing and also to other gearing of
ike nature such as worm or screw gearing, and it consists in constructing gearing
with teeth (or the corresponding parts in worm or screw gearing) the curve of
which is obtained from the primitive or pitch radius in the manner hereinafter
described, and the width of the teeth on the primitive or pitch circle being equal
With this construction
o the intervals or spaces between the teeth on such circle.
permanent contact is obtained between the teeth which have a rolling action, so
that all shock and consequent loss of work are avoided. The construction is chiefly
characterized by the appearance of the teeth formed of two curves meeting cach
other as in an ogive and having a very wide base and narrow summit so that the
metal or material always works in compression and never in tension. Further as
the teeth can be given a great height, which may reach two-thirds of the primitive
radius, and as their number can be as low as 6, multiple transmissions of motion
can be established while preserving practical dimensions of the teeth on small
diameters.
The proportions of the parts of our gearing are determined by the following
general formule which apply to all devices for transforming or transmitting motion,
whether spur gearing with external or internal teeth, racks, hevel gearing, worm
or screw gearing, wheels and chains or other apparatus in which teeth are employed.
Let R be the primitive or pitch radius;
p the pitch;
h the height of the teeth beyond the radius ;
the number of teeth (minimum 6);
7 the width of the body of the tooth on the primitive circle;
e the interval between the flanks of the teeth on the primitive circle;
R, the radius of the base of the teeth (internal radius);
R the radius of the summit of the teeth (external radius);
C the radius of the curve.
محوط الميام

page_text: From determined points a, b and h of the pinion taken successively as centres
describe three ares with the given radius of the curve; the intersecting points at n
and a will be the centres of the curve from which the curve hbd of the right
flank of the tooth and the curve ha c of the left flank are drawn.
Similarly the centres of the curves of the teeth of the wheel will be the points
of intersection " and n of three arcs described with the given curve radius from
the centres a¹ h¹ b'.
Under the same conditions of distance of the centres and of relation between the
primitive radii we can arrange spur gearing having three times the number or any
other desired number of teeth as will be well understood.
In order to construct a wheel with internal teeth the same general formulæ are
followed but the teeth are set out in the reverse sense.
The teeth can be made compound by dividing into two the thickness of the
teeth of the same wheel so as to form two juxtaposed half wheels, the teeth of
the one half being placed opposite the middle of the space between the teeth of
the other; or the teeth can be made oblique in such a manner that one of the
faces projects over and covers half the space between the teeth of the other, or
this obliquity can be made double and in contrary directions so as to form a V.
In constructing a rack and its wheel or pinion we proceed as follows: On the
vertical line oh (see Figure 2) representing the height h of the teeth of one of our
wheels draw three horizontal lines ab, cd and ef tangential respectively to the
interior, primitive and exterior circles of the wheel; on the primitive or pitch
line ed of the rack take ki=1= of the wheel; then from the points h and i as
centres describe two arcs with a curve radius C equal to / 2 p; the point of
intersection will be the centre from which is drawn with the radius C the
curve his forming the profile of the right flank of the rack tooth. In the same
way the profile of the left flank hkt is obtained as well as the profiles of the
=

page_text: following teeth with an interval on the pitch line ed according to the general
formulæ equal to
ij &c.
=
In constructing bevel gearing according to our invention we follow the rules
adopted for ordinary bevel gearing, that is to say,-being given two wheels of the
radius R and R' (see Figure 3) the axes of which form an angle a, the exterior
profile of the teeth should be what would be given to spur wheels of the radius »
and the teeth thus forming cones having this profile as a base and the point A
for the summit. By drawing from the point C a line at right angles to the
generatrix common to the two base cones the radii and v¹ are obtained by the
ملبسها لسعد
With these data, establish on the are of 322° the profile of the 8 teeth proposed
as we have said for spur gearing and apply this to the exterior surface of the cone
of radius R.
Proceed in the same manner to obtain the profile on the arc of 322° of radius vo
which should be applied to the interior surface of the supplementary cone of
radius

page_text: These data allow of drawing as we have above stated the profile of the 16 teeth
on the arc of 161° which will be applied to the exterior conical surface of the
wheel of radius R. The profile of the teeth to be applied to the interior auxiliary
conical surface of the wheel of radius c will likewise be determined by intro-
ducing the value of = 0·070384 into the general formulæ which will give
In
teeth thus obtained by the general formulæ correspond exactly with those of the
conical sections of the teeth range on the length of the common generatrix in
all given conditions.
For a worm wheel and endless worn or screw we give the wheel teeth a profile
the same as for spur gearing and we hollow out in the space between them helicoidal
curves with a given angle and we make a worm or screw with a corresponding
inclination by giving to its threads the profile which is homologous with the wheel
teeth. We thus obtain an effect the same as that obtained by spur gearing
constructed according to our invention.
As regards chains and chain wheels, a chain that gears with two wheels should
be considered as a spur pinion common to these two wheels. The form of the teeth
The length of the
should be the same as that of the spur wheels but inverse.
links of the chain between two axes or pivots is equal to the chord that connects
the axes of the teeth taken on the pitch circle of the pinion if we adopt for the
form of the teeth on the links that appertaining to a pinion. The upper and lower
curves of the links conform to the arcs of the inner and outer circles between the
axes of two teeth of the pinion. Under these conditions the arcs of the inner
circle between the axes of two teeth of the wheel should conform to the inner ares
of the pinion.
T2] ahán 26th day of July 1892.
J. C. MEWBURN,
55 & 56, Chancery Lane, London, Chartered Patent Agent.

page_text: COMPLETE SPECIFICATION.
Improvements in Toothed and other Gearing.
We AUGUSTE DESGOFFE and LEONIDAS ALEXANDRE DI GIORGIO both of
63 Rue de Lens, Lille France, Engineers do hereby declare the nature of this
invention and in what manner the same is to be performed, to be particularly
described and ascertained in and by the following statement:-
This invention has reference to toothed gearing and also to other gearing of like
nature such as worm or screw gearing, and it consists in constructing gearing with
teeth (or the corresponding parts in worm or screw gearing) the curve of which is
obtained from the primitive or pitch radius in the manner hereinafter described, and
the width of the teeth on the primitive or pitch circle being equal to the intervals
or spaces between the teeth on such circle. With this construction a permanent
contact is obtained between the teeth as they have a rolling action, so that all
shock and consequent loss of work are avoided. The construction is chiefly
characterized by the appearance of the teeth formed of two curves meeting cach
other as in an ogive and having a very wide base and narrow summit so that the
metal or material always works in compression and never in tension. Further as
the teeth can be given a great height which may reach two-thirds of the primitive
radius, and as their number can be as low as 6, transmissions of motion can be
established while preserving practical dimensions of the teeth on small diameters.
The proportions of the parts of our gearing are determined by the following
general formula which apply to all devices for transformning or transmitting motion,
whether spur gearing with external or internal teeth, racks, bevel gearing, worm or
screw gearing, wheels and chains, or other apparatus in which teeth are employed.
Let R be the primitive or pitch radius,
P the pitch,
the height of the teeth beyond the radius,
n the number of teeth (minimum 6),
I the width of the body of the tooth on the primitive circle,
e the interval between the flanks of the teeth on the primitive circle,
R, the radius of the base of the teeth (internal radius),
R. the radius of the summit of the teeth (external radius),
Cthe radius of the curve.
I

page_text: The curve of the teeth is obtained as follows (see Figure 1 of the accompanying
drawings):-
:-
From determined points a band of the pinion taken successively as centres
describe three arcs with the given radius of the curve; the intersecting points at n
and will be the centres of the curve from which the curve hd of the right flank
of the tooth and the curve hac of the left flank are drawn.
Similarly the centres of the curves of the teeth of the wheel will be the points
of intersection and ¹¹ of three arcs described with the given curve radius from
the centres a² h¹b'.
Under the same conditions of distance of the centres and of relation between
the primitive radii we can arrange spur gearing having any other desired number
of teeth as will be well understood.
For three times the number of teeth, which we will take as an example
(see Figure 2) we shall have.
In order to construct a wheel with internal teeth the same general formulæ are
followed, but the teeth are set out in the reverse sense (see Figure 3).
The teeth can be made compound by dividing into two the thickness of the teeth
of the same wheel so as to form two juxtaposed half wheels, the teeth of the one
half being placed opposite the middle of the space between the teeth of the other
(see Figure 4); or the teeth can be made oblique in such manner that one of the
faces projects over and covers half the space between the teeth of the other
(see Figure 5) or this obliquity can be made double and in contrary directions so
as to form a V (see Figure 6).
In constructing a rack and its wheel or pinion we proceed as follows:-On the
vertical line o (see Figure 7) representing the height of the teeth of one of our
wheels draw three horizontal lines ab cd and ef tangential respectively to the
interior, primitive and exterior circles of the wheel; on the primitive or pitch
line cd of the rack take ki = 1 = of the wheel; then from the points h and i as
centres describe two arcs with a curve radius C equal to h = 2p the point of
intersection n will be the centre from which is drawn with the radius C the
curve his forming the profile of the right flank of the rack tooth. In the same
way the profile of the left flank kt is obtained as well as the profiles of the
following teeth with an interval on the pitch line cd according to the general
formulæ equal to = ij &c.
In constructing bevel gearing according to our invention we follow the rules
adopted for ordinary bevel gearing, that is to say, being given two wheels of the
radius R and R¹ (see Figure 8) the axes of which form an angle a, the exterior
profile of the teeth should be what would be given to spur wheels of the radius v
and the teeth thus forming cones having this profile as a base and the point A
for the summit. By drawing from the point C a line at right angles to the
generatrix common to the two base cones the radii and are obtained by the
usual formulæ :-

page_text: With these data establish on the arc of 322° the profile of the 8 teeth proposed
as we have said for spur gearing and apply this to the exterior surface of the cone
of radius R.
Proceed in the same manner to obtain the profile on the arc of 322° of radius v
which should be applied to the interior surface of the supplementary cone of
radius vo
If for example the thickness of the teeth a parallel to the common
מז
generatie
11 1
תו
4 × 0.017596

page_text: These data allow of drawing as we have above stated the profile of the 16 teeth
on the arc of 161° which will be applied to the exterior conical surface of the
wheel of radius R. The profile of the teeth to be applied to the interior
auxiliary conical surface of the wheel of radius will likewise be determined
m
by introducing the value of v¹ = 0.070384 into the general formule which will
of teeth thus obtained by the general formulæ correspond exactly with those of the
conical sections of the teeth range on the length of the common generatrix in all
given conditions.
For a worm wheel and endless worm or screw we give the wheel teeth a profile
the same
as for spur gearing and we hollow out in the space between them
helicoidal curves with a given angle, and we make a worm or screw with a corre-
sponding inclination by giving to its threads the profile which is homologous with
the wheel teeth. We thus obtain an effect the same as that obtained by spur
gearing constructed according to our invention.
As regards chains and, chain wheels, a chain that gears with two wheels should
be considered as a spur pinion common to these two wheels. The form of the teeth
should be the same as that of the spur wheels but inverse. The length of the links
of the chain between two axes or pivots is equal to the chord that connects the axes
of the teeth taken on the pitch circle of the pinion if we adopt for the form of
the teeth on the links, that appertaining to a pinion. The upper and lower curves
of the links conform to the arcs of the inner and outer circles between the axes of
two teeth of the pinion. Under these conditions the arcs of the inner circle
between the axes of two teeth of the wheel should conform to the inner ares of the
pinion. Figure 10 illustrates a chain and chain wheels with teeth constructed in
accordance with our invention.
Having now particularly described and ascertained the nature of our said inven-
tion and in what manner the same is to be performed we declare that what we
claim is
The construction of the teeth (or corresponding parts) of toothed (or other)
gearing with flanks having a special curve obtained in the manner set forth from
the primitive or pitch radius, the width of the teeth on the primitive or pitch circle
being equal to the width of the intervals between the teeth on such circle, and the
relative proportions of the parts of the gearing being determined by the application
of the general formulæ hereinbefore given.
Dated this 20th day of Anvil 1893
J. C. MEWBURN,
55 & 56, Chancery Lane, London, Chartered Patent Agent.