A MODE OR MODES OF AND APPARATUS FOR FOLDING LONGITUDINALLY AND CHANGING THE PLANES OF MOTION OF TRAVELLING SHEETS OR WEBS, WHICH IMPROVEMENTS ARE PARTLY DAIYING
Year: 1870

page_text: LETTERS PATENT to Archibald Sandeman, of Tulloch, in the County
of Perth, North Britain, for the Invention of "A MODE OR MODES OF
AND APPARATUS FOR FOLDING LONGITUDINALLY AND CHANGING THE PLANES OF
MOTION OF TRAVELLING SHEETS OR WEBS, WHICH IMPROVEMENTS ARE PARTLY
DAIYING "
Sealed the 3rd March 1871, and dated the 19th December 1870.
PROVISIONAL SPECIFICATION left by the said Archibald Sandeman at
the Office of the Commissioners of Patents, with his Petition, on the
19th December 1870.
I, ARCHIBALD SANDEMAN, of Tulloch, in the County of Perth, North
" A MODE
Britain, do hereby declare the nature of my said Invention for
OR MODES OF AND APPARATUS FOR FOLDING LONGITUDINALLY AND CHANGING THE
PLANES OF MOTION OF TRAVELLING SHEETS OR WEBS, WHICH IMPROVEMENTS ARE
PARTLY APPLICABLE TO THE DRIVING BELTS OF SKEWED PULLIES," to be as
follows:-
:-
This Invention has for its chief object the folding longitudinally
(without twisting and whilst travelling lengthwise) of manufactured
A

page_text: fabrics or webs, which may consist, for example, of woven goods or of
a warp or collection of yarns only, and will be found more particularly
applicable when preparing, dressing, finishing, or otherwise treating
woven fabrics, whether by a dry or wet process, and also when making
them up or folding them for the market.
The said Invention further relates to the mere changing of the
direction or plane of motion laterally (without twisting) of a web or
piece of manufactured goods whilst travelling longitudinally, and will be
found advantageous in cases where it it required to dispose or arrange
several machines used, for example, in finishing processes in a given
confined space, as the goods can be directed in any desired direction
about the works without putting any twist into the said goods, and
without further impeding their onward travelling motion than by so
much as arises from drawing them over guiding surfaces or edges. The
same system of changing laterally the direction or plane of motion of
a travelling sheet or web is applicable to the proper guiding of an
endless driving belt whilst running over skewed driving pullies.
The essential feature of this Invention consists in so choosing the
surfaces or edges over which the sheet, web, or driving belt is to be
guided or directed, and in so arranging them with reference to the
desired planes of motion of the said sheet, web, or driving belt as that all
twisting, warping, wrenching, or bagging of the same shall be obviated.
The geometric principle on which the choice and the arrangement of
the guiding surfaces or edges are based is, that there are surfaces without
number into the shape of which a pliable inextensible sheet (such as a
piece of paper) in the form of a rectangle may be folded or bent without
twisting or crumpling, so as to have one edge in one plane and the edge
opposite in another plane. Under this general principle is included the
particular one, general enough however for the case, when the guiding
surface or surfaces are made up of two plane parts, viz., a straight line
ending in two straight lines not in one plane at points equidistant from
the perpendicular to both is such that the perpendiculars drawn from
any point therein to the two make up together always the same length,
and these perpendiculars and like perpendiculars drawn from any other
point in the same ending straight line intercept between them equal
lengths of the two straight lines. The guiding surfaces or edges before
referred to may consist of rods, rollers, edges or plane or other surfaces,
and as an illustration of one mode of applying the same for the purpose

page_text: of folding or doubling along its centre a piece of goods whilst travelling
longitudinally one of such surfaces may consist of a triangular plane
having two equal sides and placed with its base horizontal and its apex
at a height above the level of the base equal to half the base. Over the
base of this triangle the goods pass and are drawn along towards and over
the apex which coincides exactly with the centre line of the sheet or web
to be folded, the two sides of the web passing over the two sides of the
triangle and being united in a perpendicular plane at the apex by passing
between vertical rollers or rails. So that if before passing over the base
the web were moving horizontally (which it might be made to do by
passing it under a horizontal rail or roller) the web's halves on opposite
sides of the centre line would have their planes of motion changed
through 90 degrees in opposite directions. On leaving these rollers or
rails the fabric will be found accurately folded along its centre, and may
then have its plane of motion restored again to the horizontal by passing
over the inclined side of a right-angled triangle placed as the half of the
first triangle on one side of the perpendicular from the apex to the base
is placed, but on the opposite side of the vertical rollers or rails and with
apex looking the contrary way, and being then drawn along that right-
angled triangle's plane, and taken thence under a horizontal rail or
roller.
Another example wherein it is desired to fold a piece of goods into
three folds longitudinally whilst it is travelling lengthwise and without
imparting any twist thereto, consists in first passing the web over the
base of a triangle cut from a rectangular plate by two straight cuts
running from the ends of one edge to a point in the edge opposite at one-
third of the edge's length from one end and two-thirds from the other
with this point (which is the apex of the triangle) in the exact line of
fold. One-third of the width of fabric will then pass over the shorter
side, and two-thirds over the longer side of the triangle, the two portions
uniting or meeting together in a double form by passing first along right-
angled triangles, the same as the triangular parts cut off at the corners
from the rectangular plate, but placed parallel to and very near the
positions those parts would take were they turned round the straight
cuts, as on hinges, until the one-third edge and the two-thirds edge
came into one line, ending at the apex, and then over and between the
parallel guides corresponding to the one-third and two-thirds edges.
Thus the two-thirds of the web's breadth is shifted through an angle (of
about 19 degrees) equal to one of the acute angles of a right-angled
A 2

page_text: triangle, having one of the sides bounding that angle thrice the other, and
. the remaining one-third is shifted in the contrary direction through an
angle (of about 160 degrees) supplementary to the former. After this the
folded fabric passes over the base of another triangle of equal sides, like
the triangle in the first example, with the two-thirds breadth next the
triangle, and the one-third breadth overlapping what is at once this two-
thirds half and the web's middle third, so that the centre line of the
two-thirds breadth of web or the selvage of the overlapping thirds runs
exactly over the apex, and the web's single and doubled parts pass over
the sides of triangle along two triangles that are equal and similar to the
halves whereinto the triangle is cut by the perpendicular from the apex
to the base, and are placed with the sides equal to the triangles, equal
sides lying side by side with and very near to these sides, and the sides
equal to half the base lying side by side of and very near to one another.
with the apex very nearly between them at one end of each until at last
the web passes out between these side by side, folded in three equal
length long leaves, with its outer thirds laid back Z wise upon the
opposite sides or faces of its middle third.
The same principle of surfaces or edges so guiding running webs as to
make them cross at right angles, and pass twistlessly from the one to the
other of two straight lines not in one plane applies readily to the driving
belts of pullies whose axes are not parallel. Thus, for instance, taking
in the unparallel axes of two circular cylinders two points at great
enough equal distances from the straight line that cuts both axis at
right angles, and drawing through those points a plane parallel to that
straight line, and then drawing in this plane the two straight lines, each
touched on one side by the ellipses, wherein the cylinders cut the plane
and any two straight lines parallel to the least diameters of those
ellipses to cut each of the touched straight lines between its points of
contact, pairs of planes drawn through these parallel straight lines
perpendicular severally to the axes cut off from the cylinders portions
about which as pullies of equal breadths, an endless belt of an equal
breadth may be put so as to pass off from one pulley on to the other at
those generating straight lines of the cylindric surfaces, wherein are the
contacts with one of the touched straight lines, and pass twistlessly from
the one to the other of those generating straight lines, over this touched
straight line along planes stretching from those to this as a common termi-
nating edge, and to pass from the latter pulley back again twistlessly to
the first along planes related in like manner to the other contacts, over

page_text: the other straight line touched by the ellipses as a common terminating
edge of these last-mentioned planes. Should the belt be stretched tight
enough straight guiding edges placed at the straight lines touched by
the ellipses may serve alone without guiding planes terminating in these
straight lines to keep the portions of belt lying between those edges and
the pullies nearly enough in planes. There is no account here taken of
the bulge given to pullies at their middle, which itself puts a slight
twist in belts. Moreover even when straight edged guides only are used
the greater pull of the belt across the guide on the side toward which the
motion is than on the other tends to throw the belt off the pulley, and
guides put on beside the other guides in order to counteract this tendency
give a twist to the belt.
SPECIFICATION in pursuance of the conditions of the Letters Patent,
filed by the said Archibald Sandeman in the Great Seal Patent
Office on the 17th June 1871.
TO ALL TO WHOM THESE PRESENTS SHALL COME, I, ARCHIBALD
SANDEMAN, of Tulloch, in the County of Perth, North Britain, send
greeting.
WHEREAS Her most Excellent Majesty Queen Victoria, by Her
Letters Patent, bearing date the Nineteenth day of December, in the
year of our Lord One thousand eight hundred and seventy, in the thirty-
fourth year of Her reign, did, for Herself, Her heirs and successors, give
and grant unto me, the said Archibald Sandeman, Her special license
that I, the said Archibald Sandeman, my executors, administrators, and
assigns, or such others as I, the said Archibald Sandeman, my exccutors,
administrators, or 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 "A MODE OR MODES OF
AND APPARATUS FOR FOLDING LONGITUDINALLY AND CHANGING THE PLANES OF
MOTION OF TRAVELLING SHEETS OR WEBS, WHICH IMPROVEMENTS ARE PARTLY
APPLICABLE TO THE DRIVING BELTS OF SKEWED PULLEYS," upon the condition
(amongst others) that I, the said Archibald Sandeman, my executors
or administrators, by an instrument in writing under my hand and

page_text: and seal, should particularly describe and ascertain the nature 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 Archibald Sandeman, do hereby
declare the nature of my said Invention, and in what manner the same
is to be performed, to be particularly described and ascertained in and
by the following statement, reference being had to the accompanying
Drawings, and to the letters and figures marked thereon (that is to
say) :-
My said Invention has for its chief object the folding longitudinally
(without twisting and whilst travelling lengthwise) of manufactured
fabrics or webs which may consist, for example, of woven goods, or of
a warp or collection of yarns only, and will be found more particularly
applicable when preparing, dressing, finishing or otherwise treating
woven fabrics, whether by a dry or wet process, and also when making
them up or folding them for the market.
The said Invention further relates to the mere changing of the
direction or plane of motion laterally (without twisting) of a web or
piece of manufactured goods whilst travelling longitudinally, and will
be found advantageous in cases where it is required to dispose or
arrange several machines used, for example, in finishing processes in a
given confined space, as the goods can be directed in any desired
direction about the works without putting any twist into the said goods,
and without further impeding their onward travelling motion than by
so much as arises from drawing them over guiding surfaces or edges.
The same system of changing laterally the direction or plane of motion
of a travelling sheet or web is applicable to the proper guiding of an
endless driving belt whilst running over skewed driving pulleys.
The essential feature of this Invention consists in so choosing the sur-
faces or edges over which the sheet, web, or driving belt is to be guided
or directed, and in so arranging them with reference to the desired
planes of motion of the said sheet, web, or driving belt, as that all
twisting, warping, wrenching, or bagging of the same shall be obviated.
The geometric principle on which the choice and the arrangement of the
guiding surfaces or edges are based is that there are surfaces without
number, into the shape of which a pliable inextensible sheet (such as a

page_text: piece of paper) in the form of a rectangle may be folded or bent without
twisting or crumpling, so as to have one edge in one plane and the edge
opposite in another plane. Under this general principle is included the
particular one, general enough however for the case when the guiding
surface or surfaces are made up of two plane parts, videlicet, a straight
line ending in two straight lines not in one plane at points equidistant
from the perpendicular to both is such that perpendiculars drawn from
any point therein to the two make up together always the same
length, and these perpendiculars and like perpendiculars drawn from any
other point in the same ending straight line intercept between them
equal lengths of the two straight lines. The guiding surfaces or edges
before referred to may consist of rods, rollers, edges, or plane or other
surfaces, and as an illustration of one mode of applying the same for
the purpose of folding or doubling along its centre a piece of goods
whilst travelling longitudinally, one of such surfaces may consist of a
triangular plane, having two equal sides, and placed with its base
horizontal, and its apex at a height above the level of the base equal
to half the base. Over the base of this triangle the goods pass and are
drawn along towards and over the apex, which coincide exactly with
the centre line of the sheet or web to be folded, the two sides of the
web passing over the two sides of the triangle, and being united in a
perpendicular plane at the apex by passing between vertical rollers or
rails, so that if before passing over the base the web were moving
horizontally (which it might be made to do by passing it under a
horizontal rail or roller) the two halves of the web on opposite sides
of the centre line would have their planes of motion changed through
ninety degrees in opposite directions. On leaving these rollers or rails
the fabric will be found accurately folded along its centre, and may then
have its plane of motion restored again to the horizontal by passing over
the longest side of a right-angled triangle (placed like either of the
halves into which the first triangle would be cut by a perpendicular
from the apex to the base, but on the opposite side of the vertical
rollers or rails, and with apex looking the contrary or somewhat con-
trary way), and then along the plane of that triangle and over the
horizontal side.
Another example wherein it is desired to fold a piece of goods into
three folds longitudinally whilst it is travelling lengthwise, and without
imparting any twist thereto, consists in first passing the web over the

page_text: base of a triangle cut from a rectangular plate by two straight cuts
running from the ends of one edge to a point in the edge opposite at
one-third of the edges length from one end and two-thirds from the
other with this point (which is the apex of the triangle) in the exact
line of fold. One-third of the width of fabric will then pass over the
shorter side, and two-thirds over the longer side of the triangle, the
two portions uniting or meeting together in a doubled form by passing
first along right-angled triangles, the same as the triangular parts cut
off at the corners from the rectangular plate, but placed parallel to and
very near the positions those parts would take were they turned round
the straight cuts, as on hinges, until the one-third edge and the two-
thirds edge came into one line ending at the apex and then over and
between the parallel guides corresponding to the one-third and two-
thirds edges.
Thus the two-thirds of the web's breadth is shifted
through an angle (of about 70°) equal to one of the acute angles of a
right-angled triangle, having one of the sides bounding that angle thrice
the other, and the remaining one-third is shifted in the contrary direction
through an angle (of about 110°) supplementary to the former. After
this the folded fabric passes over the base of another triangle of equal
sides, like the triangle in the first example, with the two-thirds breadth
next the triangle, and the one-third breadth overlapping what is at
once this two-thirds's half and the web's middle third, so that the centre
line of the two-thirds breadth of web, or the selvage of the overlapping
third runs exactly over the apex, and the web's single and double parts
pass over the sides of the triangle along two triangles that are equal
and similar to the halves whereinto the triangle is cut by the per-
pendicular from the apex to the base, and are placed with the sides
equal to the triangle's equal sides lying side by side with and very near
to these sides, and the sides equal to half the base lying side by side of
and very near to one another, with the apex very nearly between them,
at one end of each, until at last the web passes out between these sides
folded in three equal length-long leaves with its outer thirds laid back
Z wise upon the opposite sides or faces of its middle third. The same
principle of surfaces or edges so guiding running webs as to make them
cross at right angles and pass twistlessly from the one to the other of
two straight lines, not in one plane, applies readily to the driving belts
of pulleys whose axes are not parallel. Thus, for instance, taking in
the unparalled axes of two cylinders two points at great enough equal

page_text: distances from the straight line that cuts both axes at right angles, and
drawing through those points a plane parallel to that straight line, and
then drawing in this plane the two straight lines, each touched on one
side by the ellipses, wherein the cylinders cut the plane, and any two
straight lines parallel to the least diameters of those ellipses to cut each
of the touched straight lines between its points of contact, pairs of planes
drawn through these parallel straight lines perpendicular severally to
the axes cut off from the cylinder's portions, about which as pulleys of
equal breadths an endless belt of an equal breadth may be put so as
to pass off from one pulley on to the other at those generating straight
lines of the cylindric surfaces, wherein are the contacts with one of the
touched straight lines, and pass twistlessly from the one to the other of
those generating straight lines over this touched straight line along
planes stretching from those to this as a common terminating edge, and
to pass from the latter pulley back again twistlessly to the first along
planes, related in like manner to the other contacts over the other
straight line touched by the ellipses as a common terminating edge of
these last-mentioned planes. Should the belt be stretched tight enough
straight guiding edges placed at the straight lines touched by the
ellipses may serve alone without guiding planes, terminating in these
straight lines to keep the portions of belt lying between those edges
and the pulleys nearly enough in planes. There is no account here
taken of the bulge given to pulleys at their middle, which itself puts a
slight twist in belts. Morcover even when straight-edged guides only
are used the greater pull of the belt across the guide on the side towards
which the motion is than on the other tends to throw the belt off the
pulley and guides put on beside the other guides, in order to counteract
this tendency give a twist to the belt. Instead too of each straight-
edged guide there may be used a small roller or pulley so placed as to
have its surface touched by the planes in which the belt would run
between the straight-edged guide and the pulleys, and this again twists
the belt.
+
And in order that my said Invention may be fully understood I shall
now proceed more particularly to describe the same, and for that purpose
shall refer to the several Figures on the annexed Sheets of Drawings,
the same letters of reference indicating corresponding parts in all the
corresponding Figures.

page_text: In order to make a lengthy piece of cloth or other like flexible sheet
after crossing untwistedly one of two fixed straight lines not in one
plane run on untwistedly so as to cross untwistedly the other, I proceed
as follows, viz. :-I run the cloth or sheet partly in the plane of a
triangle (ABC) (Figure 1) having two of its corners in one (A B.) of
the fixed straight lines (AB) (CD) and the third in the other line
(CD.) and partly in the plane of a triangle (BCD.) having for
corners B, C, and any point but C in (CD) across the common side
(BC) of those triangles. The cloth may be kept to the planes by
putting up as need be either a guy rod at (BC) or one or both of two
guy planes having a common edge in (BC) and stretching away there-
from in (ABC) (BCD). Planes ending severally in the straight
lines (A, B,) (C, D,) and each in a straight line drawn parallel to either
of those straight lines from a point in the other will do quite as well as
(ABC) (BCD). Instead of either each or both of the guy triangles
(ABC) (BCD) a surface may be used made up as a chain of plane
parts, as links whereof the end ones end severally in (A B) (B C) if
the surface be instead of (ABC) in (BC) (CD) if instead of (BCD)
and in (AB) (CD) if instead of both. And again, instead of each,
all, or any linked set of these parts a portion may be used of a curve
surface that can be rolled out flat. If the triangles (A BC) (BCD)
have the angles (CBA) (BCD) equal (and this happens when and
only when the ends B, C, of the guy line (BC) are equidistant from the
straight line that can be drawn cutting each of the straight lines (AB)
(CD) at right angles) a straight line fixed to the cloth and which
lay for an instant in (AB) will at any instant in the run from (AB)
across (BC) to (CD) be either in (A BC) parallel to (A B) in (BCD)
parallel to (CD) or at some line (EFG) made up of the straight
part (EF) in (ABC) parallel to (A B), and the straight part (FG)
in (BCD) parallel to (CD) and will at last lie for an instant in;
(CD). Then, too, the paths taken by points in the cloth from (A B)
to (CD) are all of the same length. If further (CA) (BD) be per-
pendicular severally to (AB), (CD) and a piece of cloth as taken
from the loom (of rectangular shape, that is, with the warp threads
along and the woof threads across when flattened out) be run in (A B C) :
(BCD) across (BC) so that the warp threads cross at right angles
(AB) then the warp threads cross at right angles (CD) cach warp
thread runs in an unchanging plane, either the same as or parallel to

page_text: the plane through one of the perpendiculars (CA) (BD) parallel to
the other with any points path from (A B) to (CD) equal to (CA) or
(BD) and each woof thread is in a plane which, though changing, is
yet at any instant either the same as or parallel to the plane through one
of the straight lines (A B) (CD) parallel to the other. A means is
thus afforded for sluing or shifting round in a cross plane as if turned
about a length-long axis without twisting a sheet moving lengthwise.
The amount of sluing is the angle between (A B) (Figure 1) and
(CD) or between (BA) and (DC). The breadth of the sheet must
be not greater than (BA) or (CD), the distance between either end B
or C of the guy line (BC) and the foot A or D of the perpendicular
(CA) or (BD) drawn from the other end to the slue line wherein is
the first end. This distance, however, may always be made great enough
for the breadth by taking the ends of the guy line far enough from the
perpendicular distance of the slue lines. If (PQ) (Figure 2) be the
perpendicular distance of the (AB) and (CD) straight lines with P
in the first, and Q in the other, P is on the same side of B as A, and Q
on the same side of C as D; P is between B and A, at A, or beyond A,
and likewise Q between C and D, at D or beyond D, according as the
angle between (PB) and (Q C) is greater than, equal to, or less than
a right angle, and a sheet run from (AB) across (BC) to (CD) is
slued through the angle between (PB) and CQ that is, an angle
supplementary to the angle between (P B) and (QC). If now a point
B' be taken in the (A B) straight line, so that B' and B may be equi-
distant from but on opposite sides of P, and B', C, be joined by a straight
line (BC) and a perpendicular (B'D') be drawn from B¹ to the
(CD) straight line, (B₁ C) makes equal angles (P B'C), (QCB') with
(B' P) (CQ); P is on the A side of B¹ and Q on the D¹ side of
C; D and D are either at or equidistant from and on opposite sides
of Q, and a sheet run right across (A B') in the triangle (A B¹C)
across (BC) and in the triangle (B'CD¹) runs right across (CD¹)
and is slued through the angle between (P B¹) and (CQ) or the equal
angle between (PB) and (QC). Hence, and since the triangles
(ABC) (A B¹ C) make up as parts the whole triangle (B B¹ C) a
sheet run right across (BA B¹) throughout the whole breadth in, the
triangle (BBC) and with the part on the B side of (A C) in the triangle
(BCD) and the part on the line B¹ side in the triangle (B¹C D¹)
has the part crossing (A B) slued one way through the angle between
(AB) and (CD) and the part crossing (A B') slued the contrary

page_text: way through the supplementary angle between (AB¹) and (CD¹) so
that the two parts run together right across the straight line (CQ) and
at the very same portion of that straight line throughout the portion
common to (CD) and (CD¹). The points D and D' are the same
when and only when each is at Q, and then A is at P (Figure 3) (PQ)
is (AD) and a sheet run in (BB¹C) (Figure 3) with its middle
length line along (A C) and its halves on opposite sides of that line
severally in (BCD) (BCD) has these halves slued contrary ways.
through right angles and brought together at (CD) so as to cross at
right angles the very same portion ending at C of (CD). Here, there-
fore, is a way twistlessly to fold together along a middle length line,
double length long, or crisp in half breadth leaves, a sheet moving
lengthwise. If the doubled sheet be taken off by nipping rollers pro-
jected on the plane (BB¹ D) into (KH), (K H¹) (Figure 4) the part
near C of the triangle (B B¹ C) may be changed into a nose fitting into
the rollers cut from a cylindric surface, and having a projection (H, K, H¹)
on the plane of (BBD) if H, H', be the points where (BD), (B¹ D)
severally touch the rollers when these are placed symmetrically close
up to the triangles (BCD) (BCD). Then if C be projected on the
plane of (BBD) into a new C, and this C be joined to K and a new
(CD) be drawn at right angles to (CK) equal to the old (CD) and
(HL), (KM) be drawn parallel to this (CD) to meet in (LM)
severally a parallel (LDM) drawn to (CK) through D on fitting the
new (CD) to the old (CD) and bringing (DL) into the line (DA)
(KH) becomes the projection on the plane (ACD) of the nose,
(K, M) the line along which the rollers nip, and (H, L) the projection
on the plane (ACD) of the straight lines along which the rollers
touch the triangles (BCD) (BCD). Then, too, the nipping rollers
between these straight lines and (KM) take the place of those parts
of the guy triangles (BCD) (BCD), which lie between the same
straight lines and (CD).
If a sheet were doubled through two-thirds of its breadth (see Figures 5
and 5) beginning at one edge, then by lapping together the doubled
third and the single third like the half breadthis in two-leaved crisping
a three-leaved crisp is made. The doubling through two-thirds may be
donc as in doubling a sheet of one-third greater breadth, and those parts
of the guy triangles may be cut off where the outside fourth of this
broader sheet would come. Or it may be done by taking (A B',) or

page_text: (C D') (Figure 5") twice (A B) or (CD) and
then if (A B B')
(CDD') (PQ) were severally projected on a plane at right angles to
(PQ) into (a, b, b¹) (c, d, d') (p 1) (Figure 6) the angle between
(PB) (Figure 5*) and (CQ) is determined by the triangle (a q c)
(Figure 6) having the side (q, c) thrice the side (q, a.) In thus twist-
lessly sliung and crisping endless other lines than straight lines, and
endless other surfaces than triangles or planes may be used as guys or
guiding edges and surfaces. The sheet may be run backward as well
as forward, or the sheet's motion is reversible, and so to every case of
twistless sluing or crisping there is a counter case of twistless unsluing
or uncrisping.
The system of twistless sheet sluing by guys is applicable to the
running of a belt twistlessly about two cylindric pulleys whose axes
are not parallel. If through a point straight lines be drawn parallel to
the axes (A B) (DC) (see Figures 7 and 8) and two straight lines
(at right angles to one another) be drawn, each halving two vertical
opposites of the four angles under which those straight lines cut one
another, a plane (XY) cutting at right angles either halver so cuts
any two straight lines drawn parallel severally to the axes (AB) (DC)
that the portions of them on the side of the plane whereon they either
cut or are least distant from one another make equal angles with the
straight line joining the cutting points. Thus two straight lines (S. S,)
(T. T,) drawn each touching on one side the two ellipses (like shaped
and like lying) wherein the cylindrical pulley surfaces (run out if need
be) cut, this plane (X, Y,) may be used as guys across which to run a
belt to or from those straight lines in the pulley surfaces that (run out
if need be) cut the plane (X Y,) at the several touching points. Any
two straight lines (U. U,) (V. V,) drawn in the plane (XY) each at
right angles to the axes (A. B.) (D. C,) and each so as to cut each
toucher between its touching points may be taken as where the planes
of the belt's edges in leaving the plane (XY,) for one pulley cut
severally the planes of the same edges in leaving the plane (X Y,) for
the other pulley. Although it is not every plane cutting at right angles
a halver that has touchers each cuttable between the touching points
by two straight lines each at right angles to the axes (A. B.) (D. C)
yet there are many planes of the kind having touchers so cuttable.
Indeed by taking the plane of the touchers far enough from where the
straight lines of the axes either cut or are least distant from one another

page_text: a belt of any breadth may be run twistlessly on the pulleys. If a plane
be taken cutting at right angles the other halver, and therefore at right
angles to the former plane, everything is the same as before, but that on
keeping the shaft of either axis turning round the same way as before
the other shaft turns round the contrary way to what it did.
Having shown the geometrical principles on which my improvements
are based I shall now describe examples of some of the practical
applications of the said principles.
Figures 9 and 10 represent respectively in sectional elevation and
plan, an arrangement of apparatus constructed on the geometrical
principles herein-before set forth for "crisping," that is, folding or
doubling a piece of goods longitudinally along its centre during its
traverse. The red lines in all my Figures and Diagrams represent the
goods which are being either slued or folded longitudinally. In Figures 9
and 10 A is a cloth roller or beam on which is wound the piece of
goods to be folded; B is a guide roller; C, a triangular plane inclined
upwards from its base to its apex at a; D, D, are a pair of vertical
nipping or pressing rollers acting also as guys or guides; E is a second
triangular inclined plane which is exactly equal to one-half either of the
first plane C itself, if divided centrally from its apex to its base, or of
another which might take C's place; F is another horizontal guide roller,
and G is a roller or beam on which the longitudinally folded or doubled
cloth is or may be wound. The cloth when being folded is drawn in the
direction of the arrows over the two triangular surfaces by turning the
roller or beam G, or otherwise drawing forward the cloth, and as it
proceeds up the incline C the selvages pass over the opposite sides (ab)
and (a c) of the triangle C, which sides thus constitute inclined guy
lines or edges, over which the edges of the cloth pass in a vertical plane
whilst the centre line of the cloth coincides with and passes over the
apex a which forms the line of fold. The two halves or folds meet
together at the rollers D D and the cloth passes between them in its
doubled state. The doubled cloth then proceeds over the inclined guy
line or edge (a¹ 6¹) of the second inclined angular surface E, the folded
edge proceeding onwards parallel to the side (a' c') of the triangle E,
and after passing under the guide roller F may be finally wound in its
doubled form upon the roller or beam G. Of course by reversing the
direction of traverse of the goods a longitudinally folded piece of cloth
may be unfolded by this apparatus.

page_text: Figures 11, 12, and 13, illustrate in vertical section, front elevation, and
plan respectively, an arrangement of apparatus constructed on the
geometrical principles herein-before set forth and demonstrated by
diagrams for the purpose of folding a piece of goods longitudinally
during its traverse in a triple fold in lieu of (as in the apparatus
Figures 9 and 10,) in a double fold only. The cloth or piece goods to
be folded (shewn by the red lines,) passes over or is wound off the roller
or beam A carried by the framing or standards B and is guided down-
wards over the edge or guy (CE) which forms the base of the right
angled triangle (C. D. E). The cloth in passing over the inclined guide
edge (D. E) receives its first slue or lateral change of direction, (but
without any twist in the cloth itself.) From this inclined edge or guy
(DE) the cloth in its full breadth but in an altered plane passes under
the guy F and thence over the two inclined guys or edges (G.H) and
(H. I) the apex H of the triangle (G. H. I) coinciding with the line
of the first longitudinal fold. Now as this fold must be situate at one-
third the width of the cloth from one edge thereof, it follows that the
apex H should be also one-third nearer one side of the triangle than the
other, the side or guy or guiding edge (H. I) being consequently longer
than the side or guiding edge (G. H.) as will be seen on referring to the
plan (Figure 13.) The cloth as it passes over the apex H receives its
first longitudinal fold, one-third of its breadth being folded over on to
the other two-thirds. In this partially folded state the cloth passes
under the guiding edge K, and thence over the two inclined edges
(LM) and (L. N) the apex L of which is situate exactly opposite the
centre of the base, as shewn clearly in Figure 11, and coincides with
the line of the next fold to be made and with the selvage of the portion
previously folded over. After passing the apex L and under the guide
edge O the cloth will be found to have received its second longitudinal
fold, which completes the operation of continuously folding a piece of
goods during its traverse in a triple ply or fold zig-zag fashion or after
the form of the letter Z, the folded goods may then be drawn away to
any convenient place to be wound on a roller or otherwise treated.
The blue lines shew the supports for the guiding edges.
From the two arrangements of folding apparatus herein-before
described and illustrated by Figures 9 and 10, 11, 12, and 13 it will be

page_text: fold in a piece of goods whilst travelling longitudinally is a pair of
angularly disposed guiding surfaces meeting in a point, over which
edges and point of junction or apex the goods must be caused to
travel.
Figures 14 and 15 represent respectively in elevation and plan the
practical application of the geometrical principle herein-before demon-
strated for accurately arranging the guiding surfaces for driving belts.
intended to transmit motion from one pulley set at an acute or obtuse
angle to another pulley. Supposing A to be the driving pulley which
is required to transmit motion by means of the belt B to the pulley C
mounted on a shaft at an angle to that of the driving shaft, then it will
be necessary to pass the two halves of the belt over two angularly
disposed guy or guiding surfaces D. D, which in this case may be anti-
friction rollers. The particular angle at which the guiding rollers D. D,
are placed will of course depend on the angle between the two shafts of
the pulleys A and C, and will be determined by the rule herein-before
laid down and demonstrated by the diagrams, Figures 7 and 8.
Having now described and particularly ascertained the nature of my
said Invention, and the manner in which the same is or may be used or
carried into effect, I would observe in conclusion that what I consider to
be novel and original, and therefore claim as the Invention secured to me
by the herein-before in part recited Letters Patent is,-
First. The so arranging and combining together any desired number
of guiding surfaces or edges as that a web or piece of goods or a driving
belt shall be enabled to travel over them in different planes of motion
without twisting, warping, wrenching, or bagging of the same, sub-
stantially as and for the various or other equivalent purposes herein-
before described.
Second. The folding of fabrics or piece goods longitudinally by causing
them to travel longitudinally over angularly disposed guiding edges
uniting in a point, which point coincides with the line of fold to be
made, substantially as herein-before described.
Third. The combination of any desired number of angularly disposed
guiding edges, and the varying of the relative positions of their points
or apieces so as to fold piece goods whilst travelling over them in two,
three, or more folds as herein-before described.

page_text: Fourth. The application of the guiding edges arranged and disposed
in the manner herein-before set forth to the guiding of belting for
transmitting power or motion at an angle substantially as herein-before
described.
In witness whereof, I, the said Archibald Sandeman, have to this
my Specification set my hand and seal, this Fourteenth day of
June One thousand eight hundred and seventy-one.
ARCHIBALD SANDEMAN. (L.S.)