RELATED APPLICATIONS

This application claims the benefit of the October 13, 2018 priority date of U.S. Provisional Application 62/745,347 the contents of which are herein incorporated by reference.

BACKGROUND

Packages are widely used for shipping goods. To enable more efficient use of resources, the package should be no larger than necessary to safely accommodate the goods to be shipped. Since goods come in many sizes, it is Useful to al so have packages that come in many sizes.

A typical package used to hold or ship product is a cardboard box or a padded bag. To make a box, a commercially available custom box size making machine begins by taking cardboard from a Z-fotd stack. It then makes appropriate cuts in the cardboard and either also folds it to make the box or presents the cut flat cardboard to then be folded into a box by a person or other machine. Such machines are quite large, particularly because of the need to accommodate the stacks of Z-folded cardboard and feeding mechanisms. Additionally, the cutting process results in wasted cardboard.

The cardboard that forms the raw material for such a machine is made on a large machine that outputs a continuous sheet of cardboard that is then periodically creased on opposite sides that allows it to form a Z-fold stack. The stack has a large footprint since Cardboard is mostly air, and thus the stack takes up a significant portion of the floorspaee allocated to a custom box making operation. As cardboard’s surface area to volume ratio is low, the stack must be often replenished.

Padded mailing bags are also made using large expensive machines that make one size of bag from rolls of material (converter machines). Very large quantities of the same size bag can be made, but significant set-up time is required to change the size of the bag made. Hence padded bags are made and stacked into a box for shipment and then the padded bags, which themselves take up a large volume because they are also mostly air, must frequently be replenished at packing stations that use padded bags to pack and ship goods. SUMMARY

The present invention provides a way to create box or bag packages having customized dimensions with minimal or zero waste of material by using an innovative machine that does not require a large space for holding the material that is used to make the package.

In one aspect, the invention features an apparatus that forms a package from roll- based materials. For example, in one embodiment, the apparatus produces cardboard boxes. Yet, it does so without actually having to be provided with cardboard, but rather just paper sheet on rolls that is formed into cardboard as a first step in the machine, and then wound on an adjustable mandrel to form the desired size box. One roll provides paper for the outer layer of the cardboard, one roll provides paper to be corrugated and for the center region, and one roll provides paper for the inner layer.

In another embodiment, the apparatus produces padded (cushion-lined) bags, again from just flat sheet material on rolls that is formed into the outer skin of the bag with an internal cushion layer. The outer layer can be paper and the cushion layer can be corrugated. Alternatively, the outer layer can be plastic (or paper) and the inner layer bubble wrap made from flat bubble wrap material on a roll that is inflated, sealed and combined with the outer layer material.

The apparatus thus does not require the actual substrate that is used to make the package. Instead, it accepts substrate precursors. The apparatus converts the substrate precursors into a“substrate strip” herein referred to just as the“substrate” or the“strip.” For a brief interval after having been formed, the strip remains flexible. Before the adhesive that bonds the sheets together to form the strip has time to become frilly solidified, it is helically (spiral) wound around a rotating adjustable size mandrel to form a tube of any desired cross section and length (depth of container). The size and shape of the mandrel define the cross section of the package, such as a rectangular (including square) box when die mandrel has four posts, a hexagon when the mandrel has two posts, or a bag when the mandrel has two posts. The length of the spiral defines the depth of the package and also provides the material to fold over to form the end flaps to close the package. In a preferred embodiment, the mandrel’s size is adjustable so that the cross section (footprint) of the package can be adjusted. Alternatively, the mandrel can be swapped out for another size mandrel having the desired cross section.

Among the embodiments with an adjustable mandrel are those in which the mandrel has N position-programmable comer posts around which the strip can be wound. When N equals four, this will produce a package having four sides. The lengths of the sides will depend on the distances between the comer posts. In other embodiments, there will be different numbers of comer posts to be used for packages that have different numbers of sides.

At the end of the winding process, when the package has reached the correct depth, the strip that has been fed onto the mandrel is cut to free the wound structure. The aids of the wound package structure will ultimately be folded inwards to form the package’s top and bottom, and just creases can be used, or slits along the wound structure's end comers to a desired depth can be made to enable easier inward folding to form flaps that can be used to close the box.

Since the package is formed from winding a strip around a mandrel, the aid result is a rectangular helix that extends along an axis. This axis is normal to a transverse plane.

Meanwhile, the edges at each end of the rectangular helix define proximal and distal end planes. These end planes and the transverse plane are not parallel. However, by choosing an extent to which these planes are not parallel, it is possible to reduce and virtually eliminate waste associated with trimming to form end flaps. Contrast this to a conventional box where die end flaps that are used to close die box are open, their edges define end planes that are parallel to die transverse plane.

In some embodiments, the apparatus includes a feeder on which are mounted rolls of substrate precursors and a converter that converts the precursors into the substrate from which the package is made. One embodiment features three spools loaded with of paper to form first, second, and third layers of cardboard. The paper from the first roll forms the miter layer (skin) of the cardboard. This is the layer that is exposed to the environment. 'The paper from die third roller fomis the inner finer layer of the cardboard. This is the layer that faces the goods being shipped. The paper from the second roll passes through a flute maker and ultimately forms the fluting (corrugation) layer that separates the inner and outer layers and provides strength to the box’s sides.

In some embodiments, adhesive applicators apply adhesive to the underside of the first layer and the top side of the third layer. All three layers’ adhesive joints are fresh and hence compliant during the process of being wrapped around the comer posts during the winding process, bat fully cure soon thereafter in time tor the box to be loaded with goods to be shipped.

During the winding process, there will exist an angle between the mandrel’s axis of rotation and the line that the three layers traverse on their way to the mandrel. This angle, which will be referred to herein as a“wrap angle," governs the pitch of the winding. It is therefore useful for the feeder angle to be computer controlled to be able to rotate (yaw) with respect to the rotation axis of the mandrel so as to adjust this wrap angle to the desired position.

To carry out the winding process, it is useful to have relative motion between the feeder and the mandrel along the mandrel’s rotation axis. Accordingly, some embodiments feature a conveyor to axially move the package towards an end of the mandrel as the spiral winding process forms die package. Other embodiments have die feeder move along a linear axis parallel to the mandrel’s winding axis.

Embodiments further include those that add folding features (scores, creases, slits on end panels) to the ends of the package as it moves along the mandrel or as the completed package leaves the mandrel. These folding features enable the ends of die package to be folded over so that the package can be closed. Examples of such folding features include slits or scores. These can be formed mechanically or with a laser. Other examples include a creased set of facets in which one or more creases are disposed to guide the folding process.

In the preferred embodiment, the ends of die substrate (its precursors) are simply cut square (perpendicular to its length) so as to leave what will become, when the end flaps are folded down io close die box, a small overlappi ng triangle at the ends of the helically wound structure that can become part of the end-flap told and this totally eliminates waste So the machine does not have to deal with waste. What would have been waste instead becomes pan of the box, thus increasing its strength «id packing resilience. This greatly simplifies the machine’s design, as no mechanism for angled cuts or dealing with waste is needed. However, it does require a special angled end fold, which at first thought would seem not possible. Nevertheless, as shown herein, such a fold is indeed possible. Moreover, such a fold leads to a unique and interesting box end that is also very structurally sound.

Embodiments also include those in which there more than three precursors and those in which there are fewer than three precursors for making die substrate just prior to the winding process. For example, some embodiments feature only two roils of paper with paper from the first roll providing an outer layer and the paper from the second roll passing through a flute maker to form a fluted inner layer which can be of a common undulating (sinusoidal like) or honeycomb type structure.“Honeycomber” devices in the paper industry convert paper to a honeycomb structure for laminating between flat sheets to form an alternative form of cardboard which is then cut into desired flat shapes. In these embodiments, an adhesive applicator applies adhesive to an underside of the outer layer. The two layers then join to each other to form a substrate strip while being wound on the mandrel. This can be used to form a light duty box, or the resulting structure is one that is easily pressed flat to form a bag.

Although a substrate derived from paper is ubiquitous, there also exist substrates made of plastic film, or bubble wrap. Other examples include adhesive tape, such as gaffer’s tape. In such cases, the adhesive applicator can be dispensed with. When just two layers are used, such as forming a bubble wrap lined bag, the precursor materials can also be coated on one side with contact adhesive (contact cement) which only adheres to itself on contact This further greatly simplifies the machine design because it eliminates the need for an adhesive appl icator. Furthermore, if plastic substrate materials are used (e.g., PE film), heat bonding and sealing can be used totally eliminating the need for adhesives. Eliminating adhesives and just having“pure” plastic also greatly increases the recyclability of the bags.

In some embodiments, the apparatus is a computer-controlled package forming machine that controls the positions of the comer posts and the relative axial movement between the mandrel and the strip that is being fed by the feeder.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an isometric view of a package-forming machine;

FIG. 2 is an isometric view of a three-layer substrate strip that has been formed by the

package-forming machine of FIG. 1; FIG. 3 is an isometric view of a section of two adjacent strips of the type shown in FIG. 2 that have been connected at a lap joint;

FIG. 4 shows the lap joint of FIG. 3 In detail;

FIGS. 5 and 6 show an end of a package formed by the package-forming machine of FIG. 1 with slits to allow the ends to fold over with the end flaps open and partially folded closed;

FIG. 7 shows the package from FIGS. 5 and 6 with the end having been folded over and taped shut;

FIGS. 8 and 9 show a package formed by the package-forming machine of FIG. 1 in which scores at forty- five-degree angles have been formed to allow the ends to be folded over;

FIG. 10 shows the package of FIGS. 8 and 9 with the end having been folded over and taped shut;

FIG. 11 shows a computer model of a package having seven side panels that can be farmed by 1.75 rotations of the mandrel of the package-forming machine of FIG. 1. Where lines indicate triangles and quadrilaterals defined by scoring that will «table folding the end panels to close the box;

FIG. 12 shows the dimensions of the first panel of the package in FIG. 1 1 as it would be wrapped; FIG. 13 shows the second and sixth panels of the package in FIG. 11 With score lines and dark regions showing the triangles that would lay flat when the sides are folded in;

FIG. 14 shows the fourth and seventh panels of the package in FIG. 11 with score lines and dark regions showing the quadrilaterals panels bordering top and bottom edges that would lay flat when the sides are folded in; FtG. 15 shows the box of FIG. 11 where the very beginning and the very end of the material wound to form the box has been cut perpendicular to the length of material, and variables for dimensions of the box are provided. FIG. 16 shows a square footprint box with ends open, with labeled significant parameters, made from many wraps of strip;

FIG. 17 shows cells from a spreadsheet and the formulas for helping to design the box and control its manufacture in the package maker machine; and FIG. 18 shows the square footprint box of FIG. 16 with the ends folded closed to form the angled (with respect to the sides of the box) edge-to-edge closure line of the folded closed end flaps.

DETAILED DESCRIPTION

FIG. 1 shows a package-forming machine 1 for making packages out of a substrate. A typical package is a polyhedron that has been translated along an axis to form a“prism” (not limited here to a classic prism as thought of in optics, but rather as an N dimensional package). This axis will be referred to herein as the“translation axis."

In the discussion that follows, the polyhedron is a rectangle having a length and a width with the length exceeding the width. This defines a short side and a long side of the package. Die extent to which the rectangle is translated to form the“prism” will be referred to as the package's“depth." Although boxes for shipping are often made of cardboard, the term“box” as used herein is not limited by the material from which it has been made.

For convenience, it is useful to define a coordinate system in which the x-axis extends along the translation axis. The y-axis extends orthogonally from the x-axis in an upward direction as shown in the figure. These can both be seen in FIG. 1. A z-axis, which is not shown, extends in a direction appropriate to form a right-handed coordinate system. The direction along the x-axis will be referred to a§“axial directions. ^* ' Directions parallel to the y- axis will be referred to as“vertical.”

The package-forming machine l includes a supporting structure 11 that supports a mandrel 2Q having a mandrel axis 24 and a mandrel head 23. A drive, which would be located inside die mandrel head 23, rotates die mandrel 20 about the axial direction.

The mandrel head 23 has a rotating spindle 24 that holds four angularly position controlled anus 21a, 21b, 21c, 21d that are perpendicular to the mandrel longitudinal axis X. Only first and second arms 21a, 21b are visible in the figure. Extending from each arm 21a, 21b, 21c, 21d is a corresponding first, second, third, and fourth corner post 22a, 22b, 22c, 22d, each of which are linear position controllable along the lengths of the respective arms to which they are attached. A rectangle defined by these comer posts 22a, 22b, 22c, 22d thus defines a footprint of the resulting package. The first post 22a and the second post 22b are separated by a first distance. This same first distance separates the third post 22c and the fourth post 22d. This first distance will be the length of a side of the package. Similarly, the first post 22a and the fourth post 22d are separated by a second length. This second length also separates the second post 22b from the third post 22c. The second distance will be the length of a second side of the package. By adjusting the relative angles of the arms 21a, 21b, 21c, 21 d and the positions of the posts along the lengths of the arms, the shape of the rectangle that defines the cross section of the box can be defined. This is referred to as an R-Theta machine. If six arms and six posts are used, a hexagonal box could be wrapped. If just two arms, which would be fixed colinearly, and two position controllable posts are used, a bag could be formed. In some embodiments six sums can be provided and the posts can be removable so a single machine could be used to make bags or up three, four, five, or six sided boxes.

In operation, the mandrel head 23, the arms 21a, 21b, 21c, 21d, and tiie posts 22a, 22b, 22c, 22d rotate as a unit around the translation axis.

FIG. I shows die package-forming machine built as a modular system of

subassemblies mounted to a frame 1 after having just begun to form a package using windings 7 formed from a“substrate” (“strip”) that is formed at a gathering head 44. As is apparent, only a first winding 7 has been laid down around the posts 22a, 22b, 22c, 22d. Each revolution of the mandrel 10 draws a further length of the strip and uses it lay down another winding 7.

To form the box, especially where the depth tif the box is larger than the width of the substrate, each winding must be displaced from the previous and thus it is required to provide movement in the axial direction. To achieve such axial movement, it is useful to provide conveyor mechanisms, such as a chains with sharp spiked protrusions (outward facing gripping protrusions) to grip the inner surface of the strip, that move along the posts 22a, 22b, 22c, 22d as indicated by the arrows in FIG. 1, thereby advancing the helix along the posts as the box is wound. Alternatively, there can be relative axial modem between the mandrel and the substrate forming apparatus, such as by mounting one on a linear motion mechanism which can be a modular purchased item that is readily interfaced to the system’s computer controller and it is comprised of a linear motion bearing(sX actuator, and position feedback device that provides relative axial motion between the feeder and die winder, either of which could be mounted to it.

The package- fonning machine 1 further includes a feeder 3 that carries out two functions: creating the substrate strip and then feeding the newly created strip towards the mandrel 10.

The feeder 3 creates the substrate strip using pre-eursor materials that are stored on first, second, and third pre-cursor material roll handlers 4a, 4b, 4c that hold rolls of precursor material and meter it out as needed, often using a servo motor to maintain tension. These sorts of roll handlers are commonly used in the field of converter machines. In the embodiment described herein, the precursor materials are paper that is used to make cardboard, such as Kraft paper. However, the principles described herein are useful for making similar composite materials, for example for making bubble wrap or paper sheets with bubble wrap integrated therewith.

First paper 4a' stored on the first roll 4a forms an inner layer of the strip. This is what that feces the goods being shipped. Second paper 4b' stored on the second roll 4b passes through a flute maker 14b to form a layer of fluting (corrugation) 4b". A typical flute maker 14b features a corrugated rolling machine or a corrugating machine that forms undulating shapes (sinusoidal like) or a honeycomb type structure on a material passing through it. It will thus be understood that herein“fluted” (and“fluting”) is defined to mean a“corrugated” or “honeycomb -like” structure that can be formed from a flat sheet that can be adhered between two flat sheets to make a strong laminated board-like structure. This fluting 4b" forms die air space that separates the inner and outer layers of the strip and provides the means by which the inner and outer layers of paper act as together as a laminate where the fluting transmits shear stresses between them. Third paper 4c' stored on the third roll 4x forms an outer layer. This is the layer that is exposed to the environment. The two layers and the fluting 4b” come together at the gathering head 44 to form the“substrate” (or strip). As shown in FIG. 2, this substrate is a multi-layer structure. The gathering head 44 would, at its output, also contain a substrate cutter that may cut the substrate’s end perpendicular to the long axis of the material to ensure no waste (FIG. 15). As the mandrel 10 rotates, the posts 22a, 22b, 22c, 22d take up the strip and form a winding 7 that wraps around the posts 22a, 22b, 22c, 22d. As it does so, the layers bond to each other. A robot or other similar mechanism (not shown) would place the end of the strip on a post at the beginning of the winding process: die end region of the inner layer of the strip would be pierced and held by the aforementioned spiked chain conveyers), it would thus be held so die helical winding process could begin.

At each revolution of the mandrel 10, the posts 22a, 22b, 22c, 22d draw another winding’s worth of the strip from the gathering head 44 and form another winding 7' next to the preceding winding 7. Each revolution of the mandrel 10 thus lays down one winding 7 and extends tins package along the translation axis by a fixed growth increment, although as die winding process occurs, die relative axial motion of the wound structure and the feeder is continually controlled. The value of the growth increment depends on the width of die strip, the extent to which strips overlap with each other, and a wrap angle at which the strip meets the mandrel 10. The feeder 3 rotates about a vertical yaw axis 5 so as to adjust this wrap angle. In some embodiments, a controller controls a motor, such as a stepper motor or a servo motor, that controls the wrap angle. For a non-square footprint box, this wrap angle will change between die short and long sides. The controller has been omitted from the figures for clarity. However, such controllers, which include computer numerical control systems, ate well known in the art of automated machinery, and can simultaneously control many different motion axes.

Upon completion of one revolution, the package will have extended along the translation axis by the width of one winding 7. To make the package extend further, the mandrel 10 begins a second revolution. This lays down a second winding T. The first and second windings 7, 7' are offset so that the second winding T is laid down adjacent to the first winding 7, as seen in FIG.3. Thus, at the completion of the mandrel’s second revolution, the package will have grown to extend along the axial direction by the width of two windings 7, 7'. This procedure continues, with each revolution of the mandrel 10 causing the package’s length to grow by a fixed amount.

The depth of the package is thus controlled by the number of revolutions of the mandrel 10, the width of the strip, and the wrap angle. The length mid width of the package are controlled by the positions of the comer posts 22a, 22b, 22c, 22d. These can be adjusted to make different size packages, either manually or, more conveniently, by using a computer- controlled stepper or servo motor to reposition them. This allows the apparatus to be conveniently modified to accommodate different packages. The comer posts 22a, 22b, 22c, 22d also include conveyors or linear-motion mechanisms that move the forming package towards the end of the mandrel 10 as it grows with each winding 7. As the package comes off the mandrel 10, a cutting device forms slits or scores to permit the ends of the package to function as flaps that fold over to close the ends. A suitable cutting device is a mechanical cutter, such as a rotating knife, or a laser.

In a preferred embodiment, the second roll 4b carries a strip of second paper 4b' that is narrower than either the strip of first paper 4b' or the strip of third paper 4c'. As a result it is possible to construct a strip in which there exist overhangs on either side, as shown in FIG.

2. These overhangs extend along the axial direction both towards and away from the mandrel head 23 and enable forming a lap joint between wraps as shown in FIG. 3.

In a second embodiment the four comer posts 22a, 22b, 22c, and 22d are located on X-Y (cartesian) linear motion position controlled axes. These posts’ positions would be moved to form the comers of a rectangle that is formed by changing their relative X-Y positions by moving linear motion axes mounted to the faceplate 24 .

The supporting structure also contains a feeder structure 3 that is on a position- controlled yaw axis 5 that is computer angle-controlled with respect to the rotation axis of the mandrel in order to form the wrap angle of the structure. The feeder holds three rolls of paper 4c, 4b, and 4a where paper from the first roll 4c forms the outer layer, the paper 4b’ from the second roll 4b passes through a corrugator 14b to form corrugated paper 4b” and the paper 4a’ from the third roll 4a forms the inner layer, where adhesive is applied to the underside of the first layer 4c’ from applicator 6b and the topside of the third layer 4a ^* by applicator 6a and all three layers of paper come together at a gathering head (e.g., between rollers 44) to form a laminate 7 where successive wraps are then bonded by the action of wrapping over die mandrel’s comer posts. The layers are brought together with an offset as shown in Fig. lb and to form different size packages the positions of ihe comers of the mandrel are computer controlled and they have at their outer comers conveyor devices to axially move the package structure as it is forming by being spirally wound towards the end of the mandrel; «id then the package end is slit of scored mechanically or with a laser as it moves along or comes off the mandrel so the ends can be folded over to close the ends of the package. As the three strips 4a’, 4b”, and 4c’ are brought together between the rollers 44 and wrap onto foe mandrel posts at an angle as the mandrel rotates, they are offset such that foe top sheet 4c’ overhangs the corrugated sheet 4b” to foe left as shown in FIGS. 2-4, and the bottom sheet 4a’ overhangs the corrugated sheet 4b” to the right as shown in FIGS. 2-4. This means that for the rolls of material 4c, 4b, and 4a, the roll 4b is narrower than the roll 4c and foe roll 4a by the overhang amount. As shown in FIGS. 3 and 4, foe overhang allow subsequent wraps to overlap and form foe double-sided lap joint with the adhesive previously applied.

In another embodiment, adhesive wbuid not he applied, rather an adhesive backed tape, such as gaffer's tape, which is easy to peel, coukl be used for the first and third rolls of material, where the adhesive on one side of the material on the first and third rolls is used to bond the fluted center to the outer layers and then the exposed overhanging portions 47’ and 47 dial are used to form the lap joint as shown in FIG. 3 can adhere to the corresponding surfaces (e.g., 47 with its adhesive on the inside adheres to the outside of layer 4a’). Stronger adhesives and plant-based recyclable adhesives can also be used for the tape. For extremely strong and water-resistant boxes, fiber-reinforced paper (tape) could be used. Even clear plastic tape could be used and in place of the corrugated material, a clear bubble wrap used, so contents placed inside the package could be protected and still visible. The advantage of using tape is that a machine that does not need an adhesive applicator would operate more cleanly and be less likely to have reliability issues. Note the adhesive backed tape could also be heated at the point of wrapping so as to make the strip more pliable.

FIG. 3 shows a small portion of adjacent first and second windings 7 while FIG. 4 shows a cross section of the portion in FIG. 3 along the translation axis. Between the first winding 7 and the second strip 7’ is thus formed a double-sided lap joint 77. An application of adhesive on the overhanging surfaces creates a durable bond between adjacent windings 7, 7\ In an alternative embodiment, tape (e.g., gaffer’s tape) bonds the adjacent windings 7, 7’. Other embodiments use fiber-reinforced tape to bond adjacent windings 7, 7\ This is particularly useful where strong packages with some water-resistance are desired. Yet other embodiments rely on clear tape. A particularly useful embodiment is one in which the second roll 4b stores bubble wrap precursor sheet, which is inflated by an infiater that takes foe place of the corrugator to form the sealed bubble chambers as it comes off the roll, instead of the second paper 4b ^* . Once the number of windings 7 is sufficient, the winding process completes. Ibis results in a rectangular tube having a proximal section, a distal section, and a central section between the proximal and distal sections. The length of the central section is equal to the desired depth of the package. The proximal and distal sections will be used as flaps to close off the proximal and distal ends of the package. Because the windings 7 define a spiral, the proximal and distal sections do not have a well-defined length.

A distal section features four sides that meet and form four edges. To permit the distal section to fold, it is necessary to convert these four sides into four end flaps on each Mid of the box. This is carried out by manipulating the substrate in the vicinity of the edges so that die four sides will fold along a preferred folding line.

FIG.5 shows a distal section of a package 70 in which first, second, third, and fourth sides of the distal section have been converted into corresponding first, second, third, and fourth flaps 70a, 70b, 70c, 70d by cutting corresponding first, second, third, and fourth slits 71a, 71b, 71c, 7!d along tire translation direction at each edge along which two sides intersect. As shown in FIG. 5, the first, second, third, and fourth flaps 70a, 70b, 70c, 70d have distal edges that define four lines.

The first and third flaps 70a, 70c told around parallel first and third folding axes on opposite sides of the package. These two flaps 70a, 70c are along the rectangle’s length. As such, they define a long pair. Similarly, the second and fourth flaps 70b, 70d fold around parallel second and fourth folding axes on opposite sides of the package. These two flaps are along the rectangle’s width. As such, they define a short pair. Hie process of closing of the package includes two folding steps: folding die flaps 70b, 70d in the short pair followed by folding the flaps 70a, 70c in the long pair over the short pair.

FIG. 6 shows the distal section after completion of the first folding step. The angle of the wrap can be plainly seen, it is apparent here that for this size box that a gap exists between the two flaps 70b, 70d of the short pair and that this gap extends across the package’s width. It is also apparent that die length of this gap is longer than the package’s width. The extent to which the gap’s length exceeds the package’s width depends on the wrap angle, which in turn is controlled by swiveling the feed 3. Indeed, this gap will change depending on the size of the box, but is indicative of the fact that the final folding over of flaps 70a and 70c are to be on the long side of the box which as shown in Fig. 2c where they are fully folded over, they yield a closed diagonal seam, indicated by dashed line 72 on the bottom of the box which is then taped over. That the angled ends of the open box can close to form a tightly sealed end, albeit with a diagonal seam, is an unexpected result that means the material that forms the box can be almost entirely used, or as discussed below in accordance with FIG. 15, entirely used.

FIG. 7 shows the distal section after completion of the second folding step. It is apparent that there exists a diagonal seam 72 that is longer than the length of the rectangle. The extent to which the seam’s length exceeds the package's length depends on the wrap angle, which in turn is controlled by swiveling the feed 3 in response to die width of the strip used to form the box. This seam 72 is then taped over to seal the end of the package.

Of particular interest is the observation that the short pair, when folded, results in a gap whereas the long pair, when folded results in a seam 72. This means that the package can be sealed with no angled cuts to the strip and hence no waste. This is something that no other box making machine can accomplish and is of significant advantage, because managing waste, no matter how minimal, is very difficult in a high- volume production environment

FIGS. 8-10 show the same principle in connection with a distal end in which the slits 7 la, 71b, 71c, 71d of FIGS. 5-7 have been replaced by score lines 71a’, 71b’, 71c’, 7ld’.

Here box 70’ where scores 7la\ 71b’, 71c’, and 71d’ have been formed at the comers to allow the end flaps 70a', 70b’, 70c’, and 70d’ to fold over. The end flaps 70b’ and 70d’ are first folded inwards in die same way that when a Christmas present in a box is wrapped and the wrapping paper forms a tube that overhangs the box, diagonal creases (here scores) are formed, that as they continue to be bent inwards, the flaps 70a’ and 70c’ remain planar and start tilting as they fold inwards. As before there will be a gap between the edges of sides 70b’ and 70d’ depending on the size of the box, but is indicative of the feet that the final folding over of flaps 70a’ and 70c’ are again to be on the long side of the box which as shown in Fig. 3c where they are felly folded over, they once again yield a diagonal seam, indicated by dashed line 72’ on the bottom of the box which is then taped over. Once again this is an unexpected result that means the material that forms die box can be almost entirely used, or as discussed below in accordance with FIG. 15, entirely used.

FIGS. 11-14 show a computer model with details of a box that can be formed, where there are 7 side panels created by 1.75 rotations of the mandrel, and the footprint of the box is 7” x 6” to achieve the closing properties illustrated in FIGS. 5-10 for a particular case in which the package has a length of seven inches and width of six inches is made using a five inch wide strip in which the fluting 4b" is 4.5 inches wide, resulting in a half inch overlap between strips. The depth of the finished package in the illustrated example will come to 3.224 inches. Also shown are the representative dimensions of the features along the edges for the 6” x 7” box.

Each quarter turn of the mandrel 10 lays down one a section of strip used for one side panel of the package. FIG. 11 shows the package after seven such quarter turns so that Seven side panels have been formed. The five-inch strip can be seen in FIG. 4B after having been lain down with a wrap angle of 12.02 degrees. Hie vertical projection of the strip is therefore the product of the strip’s width and the secant of die wrap angle, which in this case is 5.112 inches.

FIGS. 13 and 14 shows where score lines are placed on two sides of the package for the configuration shown in FIGS. 11-12 to correctly close the end flaps.

In the case of a rectangular helix, to assure a constant overlap to reliably form the lap joint 77 in FIGS. 3 and 4 as the strip makes its way around the different posts 22a, 22b, 22c, 22d, it is useful to axially shift the strip by a quarter of the winding’s vertical projection, which in this example is 5.112 inches. This will ensure that four quarter-turns of the mandrel 10 will shift the strip by the extent of the winding’s vertical (axial) projection.

For a given configuration, there exists an angular shift rate, which is the derivative of the extent that windings 7 shift along the translation axis as a function of the angular position of the mandrel 10. Ideally, angular shift rate should be constant. This will ensure that the extent of the shift remains the same as the strip proceeds one post 22a, 22b, 22c, 22d to the next 22b, 22c, 22d, 22a. Thus, upon reaching the second post 22b, the strip should have shifted by 25% of the vertical projection; upon reaching the third post 22c, the strip should have shifted by 50% of the vertical projection; and upon reaching the fourth post 22d, the strip should have shifted by 75% of the vertical projection so that by the time the first post 22a comes around again, the shift by one vertical projection will have been completed.

However, as a result of having a rectangular (not square) footprint, the distances between the posts 22b, 22c, 22d, 22a are not all the same. Therefore, to achieve a constant angular shift rate, it is useful to vary the wrap angle as the different posts 22b, 22c, 22d, 22a go by the gathering head 44. It is for this reason, that a controller causes the feeder 3 to rotate about a vertical yaw axis Y perpendicular to die longitudinal (translation)axis of the box (and mandrel). In the particular examples described herein, the controller yaws the feeder 3 between a 12.02-degree angle when laying the strip down on the short side and 10.35-degree angle when laying the strip down on the long side. The box is thus effectively wound in a segmented spiral-like manner (a sequence of angled straight lines around a longitudinal axis).

In the illustrated example, the net height of the package is 3.224 inches. In this case, this is also equal to the box-depth growth increment tor the illustrated geometry. In general, the growth increment will depend on die strip's width and how many times the mandrel 10 rotates. For a package with a small footprint, the growth increment is large, which means that die package's depth cannot be adjusted with high resolution. In such cases, where die footprint of the package is comparable to the strip’s width, the growth increment will be on the order of a quarter of the strip’s width. Thus, to finely control the package’s depth, it is desirable to use narrow strips. In cases where the footprint is larger, it is easier to adjust the package’s depth with finer resolution without running the risk of the first end flap 70a being too long.

FIG. 15 shows die box of FIG. 10 where the very beginning and the very end of the material wound to form the box 70 have been cut perpendicular to the length of material. This leaves small triangles 170a and 170b of material hanging over the sides of the box prior to folding the ends to close the box. This material can become part of the end flap ibid, thereby totally eliminating waste so the machine does not have to deal with waste that would occur if the end had to be cut at an angle because the next box might be a different size and require a different angle cut. This triangle of material thus becomes part of the box, increasing its strength and packing resilience. While these small triangles have the advantage of totally eliminating waste and providing some added measure of strength, they will require a small slit 170s in the edge of the side that makes the first wrap at this comer. This means that a substrate cutter at the exit of the gathering head 44 would cut the substrate's end

perpendicular to the long axis of the material to ensure no waste This also greatly simplifies the machine design and operation.

As shown in FIG. 15, the total length of the strip of material of width w to form the box 70 is L ' which is shown by the dashed line which as is traced around the box has seven segments. L is the top edge length shown (ibur free edge segments, none of which are parallel to a crass section plane orthogonal to the longitudinal (translation)axis of the box), which it will be noted none. The perimeter P of the box 70 of height c when ends are folded shut as a function of its dimensions a and b is:

For a square box, the following analysis applies.

The helix angle 0 (which is then the angle between each top edge and the cross- section plane, is given by

The diagonal width of the strip, w’ is aligned with the vertical edge of the box and is given by:

The top-edge length L of a square box is given by:

Using trigonometric identities, it can be shown thus that:

The total length of die strip needed to form a box is the product of L and die number of wraps, which need not be an integer.

Given the width w of the snip of material used to form die box, and the dimension b of the box such that the ends will fold closed with the flaps meeting along a line (which can be an angled closure line as shown in FIG. 10), the achievable height c of a square-footprint box is found from FIG.15 by:

For a box having a rectangular footprint, the angle 8 will change with the relative side length according to the constraints:

The above constraints lead to 45-degree told lines for the end panels (e.g., FIG. 13) that meet in the middle of the edge, which is also an important result.

The above analysis is focused on the case where a minimum-size box is made from a maximaliy-wide strip of material. Of course these equations can be manipulated to select the desired dependent and independent variables. When a strip is narrow in relation to the box dimensions, the end of the strip is still kept perpendicular (square cut) to the length of the strip and the end folds still form in a simitar manna with the folded flaps forming an angled seam across the ends of the box. Once again, there is literally zero waste that needs to be generated and clean closed ends of the box are achieved, just with the unique angled seam made possible by the present invention.

FIG. 16 shows a square footprint box 70S, with labeled significant parameters, made from many wraps of strip of width w, with a width along the longitudinal axis of the box of w’ as before described. Flaps 74a and 74b will fold down and then be covered by end forming flaps 73a and 73b that form a diagonal seam across the «ad with edges 71a and 7ib. FIG. 17 shows cells from a spreadsheet and the formulas for helping to design the box 70S and control its manufacture in the package maker machine. Here the size of the box is L x L x D _p *. Being a square box, the wrap angle Q is ihe same for each comer. Note ihe dimension “L” corresponds io the dimension“a” previously discussed. FIG. 18 shows the box 70S with end flaps closed where the edge 71a of flap 73a meets edge 71b of flap 73b meet io form the angled top seam 71 (across which then for example a strip of tape would be placed to seal the end). The lapjoint between strips is indicated for example by 77. The dimension L _b , is the total length of the long side of the top flap. This box is constructed by having slits cut in the edges such as indicated by the dotted lines in the comm with dimensions d», C$> Cr, C3. Similar analysis is done for a non-square footprint box, and the end flaps will also close forming a diagonal seam across the end. The small triangular appearance zones 171a and 171b are analogous to 170a and 170b in FIG. 15, and are actually a result of the right angle cut on tire strip. These enable there to literally be zero waste in forming die box, and they would fold over the sides of the box at final closure.

For an embodiment that is made just to create bags, die system can be greatly simplified where there are only two posts on die mandrel where the distance between posts is controlled. This mechanism will not require two degree of freedom control of each post the way a box winder does, and now a simple rack and pinion system can be used for example to control the distance between the posts. The same material-forming and method is used for bags as described previously for boxes, but die ends of the bag have two sides, not tour, and slitting is not needed, only folding over die end features to form end flaps that fold over onto the middle section to close the bag’s ends.

As with the box, the proximal and distal sections’ free edges are each not parallel to die cross section and thus when the ends are folded over, they will form a seam with the bag that is not perpendicular to the longitudinal axis of die bag. This means there is no waste generated and the extra bag thickness in the region of the folded-over ends increases padding for tire product shipped inside the bag.

In some cases depending on the strip size this will result in two layers of material being folded over, but in the case of a bag made with integral bubbles, this just results in extra padding at the end of the bag. Alternatively, the bag can be heat-sealed along a diagonal (ends of bag are not square) to form a rhombus-like shaped bag, or if waste is tolerated, the bag can be heat-sealed square at the ends and cut off from the infeed strip. This will leave an angled end on die strip that would need to be trimmed for making the next bag be the same as the previous.

The bag formed by this embodiment would have a length along the mandrel’s posts’ longitudinal axis and a slim rectangular cross section that lies in a plane that is orthogonal to the longitudinal axis, where the cross section has a defined width by die spacing between the posts and the post diameter and a thickness of twice the bag material when the bag is pressed fiat.