Detailed Description
The present embodiment of footwear is shown in fig. 1-5 and is generally designated 10. In these embodiments, the improved article of footwear includes a sole construction configured to enhance engagement of the footwear with topographical features and provide improved traction.
Although the present embodiments are shown in the context of winter or waterproof footwear, they may be incorporated into any type or style of footwear, including show shoes, hiking shoes, off-road and off-road boots, hiking boots, work boots, all terrain shoes, barefoot running shoes, athletic shoes, traditional tennis shoes, walking shoes, multi-athletic shoes, casual shoes, dress shoes, or any other type of footwear or footwear component. In general, the shoe is well suited for wet or slippery surfaces, including those where the surface is flat or planar. For example, the shoes and protrusions described herein may cooperate to grip an underlying ground surface. This may provide reaction and dynamic friction to the sole assembly and footwear, thereby enabling the wearer to be confident in their walking, including on wet or otherwise slippery surfaces.
It should also be noted that directional terms, such as "vertical," "horizontal," "top," "bottom," "upper," "lower," "inner," "inward," "outer," and "outward," are used to facilitate describing the invention based on the orientation of the embodiments shown in the drawings. Furthermore, the terms "medial," "lateral," and "longitudinal" are used in a manner commonly used in connection with footwear. For example, when used to refer to a side of a shoe, the term "medial" refers to the medial side (i.e., the side facing the other shoe), and "lateral" refers to the lateral side. When used to refer to directions, the term "longitudinal direction" refers to a direction extending generally along the length of the footwear between the toe and heel portions, and the term "lateral direction" refers to a direction extending generally across the width of the footwear between the medial and lateral sides of the footwear. The use of directional terms should not be construed to limit the invention to any particular orientation. Further, as used herein, the term "arch region" (or arch or midfoot) generally refers to the portion of the footwear or sole assembly that corresponds with the arch or midfoot of the wearer's foot; the term "forefoot region" (or forefoot) generally refers to the portion of footwear forward of the arch region that corresponds with the forefoot of a wearer's foot (e.g., including the ball of the toe and the toe); and the term "heel region" (or heel) generally refers to the portion of the footwear behind the arch region that corresponds with the heel of the wearer's foot. Aforefoot region 22, an arch ormidfoot region 24, and aheel region 26 are generally identified in fig. 2. However, it should be understood that the depiction of these regions may vary depending on the configuration of the sole assembly and/or the footwear.
Referring to fig. 2, footwear 10 may incorporatesole assembly 14.Sole component 14 includes a lowermost surface or ground-contacting surface that may itself include a plurality of protrusions, patterns, pegs, stakes, and/or other features designed to enhance the frictional forces between footwear 10 and the underlying surface.Sole assembly 14 may include one or more various components, such as anoutsole 30, amidsole 16, and/or an insole or footbed (not shown). However, in some embodiments, more or fewer elements ofsole assembly 14 may be included. For example, some embodiments may exclude a footbed, while other embodiments may only include a footbed and an outsole.Sole component 14 may include EVA foam having a cushioned top portion and a more robust, wear resistant bottom portion. The components ofsole assembly 14 may individually and/or collectively provide a number of attributes to an article of footwear 10, such as support, rigidity, flexibility, stability, cushioning, comfort, reduced weight, and/or other attributes. In general,sole assembly 14 may form the bottommost portion of footwear 10, regardless of the components present.Sole assembly 14 includes a side-to-side width W and a heel-to-toe longitudinal length L, shown in fig. 3.
Footwear 10 may include a textile upper 12 and asole assembly 14. Upper 12 may be formed from various material elements that are joined together to cover at least a portion of a foot of a wearer. The material elements may be selected based on the intended use of the article of footwear 10, and may comprise, for example, synthetic textiles, mesh textiles, polymers, or leather. Upper 12 is generally configured so as not to interfere with the flexibility ofsole assembly 14 and may include a stretchable or elastic material element. For example, the material element may comprise lycra, neoprene or spandex. Upper 12 may include one or more closure elements, including, for example, laces or hook and loop fasteners. Upper 12 additionally includes an upper opening for receiving a foot of a wearer and a lower perimeter for attachment tosole assembly 14.
The footbed may be positioned within a void defined by the upper, and is generally non-stretchable and lightweight and is bonded to the upper to provide the void for receiving a foot of a wearer. The footbed may be constructed of a sheet of material (such as foam, EVA, PU, latex, gel, or other material) and provides cushioning due to its compressibility, and may also conform to the foot to provide comfort, support, and stability. The lower perimeter margin or edge of upper 12 may be stitched, bonded, or otherwise secured to the footbed around the perimeter of the footbed.Sole assembly 14 may be combined with any other type or style of upper construction (e.g., a Strobel construction) that may be suitably joined withoutsole 30. The bonding of the sole assembly/outsole to the upper may be accomplished using adhesives, cements, injection molding, cast molding, or any other technique for bonding the upper to the sole.
Themidsole 16 may be positioned below the footbed and may be constructed of a material having a generally lower density than the density of theoutsole 30; such as Ethylene Vinyl Acetate (EVA), Polyurethane (PU), latex, foam, gel, or other materials. In general, the density of themidsole 16 is such that it compresses relatively easily to provide cushioning to the foot (e.g., heel) of the wearer. The midsole material may have a hardness of, alternatively, about 30 Asker C to about 65 Asker C, further alternatively, about 42 Asker C to about 48 Asker C, and even further alternatively, about 45 Asker C or about 43 Asker C. In general, harder materials have higher wear resistance, but they are also less flexible. In contrast, softer materials have lower wear resistance, but are more flexible.
Outsole 30 may be joined to upper 12 and disposed belowmidsole 16.Outsole 30 includes anupper surface 32 and alowermost surface 34.Outsole 30 may include a plurality of projections and/or patterns extending downward, as described below. The protrusions and patterns may be arranged as desired and need not be arranged in a repeating pattern. The protrusions and patterns may comprise one or more geometric shapes.Outsole 30 may be constructed of one or more materials, such as, for example, natural or synthetic rubber, thermoplastic polyurethane elastomer (TPU), nylon, polymer blends, abrasion resistant polymers, elastomers, and/or other materials. Other materials may be used (such as fiber reinforced polymers) which may include epoxy, polyethylene or thermoset reinforced with carbon, glass and/or aramid fibers to achieve enhanced protection. The outsole material may have the following hardness: alternatively from about 40 Shore A to about 70 Shore A, and further alternatively from about 68 Shore A to about 72 Shore A.
As shown in fig. 2, thesole assembly 14 may include one or more firstgripping compartments 40, the firstgripping compartments 40 having a firstcentral axis 42 and afirst actuator projection 44, thefirst actuator projection 44 being generally aligned with the firstcentral axis 42 and optionally centered on the firstcentral axis 42. The firstgripping pod 40 may be interspersed between the treads and other protrusions, and may be integrally formed with theoutsole 30.Outsole 30 may have a preselected thickness selected to provide the desired flexibility between various projections, patterns, regions, and/or portions of outsole 20. Theactuator protrusion 44 may be constructed of a material having a selected hardness and static coefficient of friction.
Referring to fig. 2 through 4, thefirst actuator protrusion 44 may include: an actuator raisedground contact surface 46 defining aperimeter 48; and an actuator projectionouter wall 50 extending upwardly from the actuator projectionground contacting surface 46. While thefirst actuator protrusion 44 is shown as being oval in shape, it is understood that the protrusion may comprise one or more geometric shapes. The height of theactuator protrusion 44 may vary depending on how much grip is desired. Further, the actuator protrusionground contact surface 46 generally transitions to an actuator protrusionouter wall 50 at theperimeter 48, and may include a chamfer, fillet, or the like at this interface or transition.
As shown in fig. 3-8, the firstgripping pod 40 may include at least onefirst tab ring 52 that surrounds or encircles thefirst actuator tab 44 and is disposed radially outward from the actuator tabouter wall 50. Thefirst tab ring 52 can include a tab ringinner edge 54 and a tab ringinner wall 56 that generally face the actuator tabouter wall 50. The lowermost surface of the first raisedring 52 defines a raised ringground contact surface 58. The lug ringinner edge 54 is defined at the intersection of a lug ringinner wall 56 and a lug ringground contact surface 58. The tab ringinner edge 54 extends around the perimeter of thefirst tab ring 52, and when the tab ringinner edge 54 is shown as being a substantially right angle corner, the tab ringinner edge 54 can contain a rounded or chamfered corner (both of which can be considered herein as a corner) as well as a true right angle corner where the two surfaces intersect at 90 ° to each other. Thefirst tab ring 52 may follow the shape of theactuator tab 44, which generally surrounds the actuator tabouter wall 50. Alternatively, theprojection ring 52 may be disposed around all or a portion of theactuator projection 44.
Theactuator protrusion 44 may be "taller" than theprotrusion ring 52. When the sole assembly is placed on a surface, such as a horizontal surface, the actuator raisedground contact surface 46 extends a first distance D1 below the raised ringground contact surface 58. In other words, the first distance D1 may be and may comprise at least 1 mm. In one example, theactuator protrusion 44 may be higher than the adjacent protrusion ringground contact surface 58 by a distance D1. The distance may optionally be at least 1.0mm, further optionally 1.0mm to 5.0 mm inclusive, further optionally 1.0mm to 8.0 mm inclusive, and yet further optionally 1.0mm to 12.0 mm inclusive. Additionally, the tabinner edge 54 and the actuator tabouter wall 50 are separated by a distance D3.
The distance D3 may alternatively be at least 1.0mm, further alternatively 1.0mm to 5.0 mm inclusive, further alternatively 1.0mm to 8.0 mm inclusive, and yet further alternatively 1.0mm to 12.0 mm inclusive. The firstgripping capsule 40 may include afirst collapse chamber 60. Thefirst collapse chamber 60 may be a substantially open space defined in thesole assembly 14 and disposed above thefirst actuator tab 44 and thefirst tab ring 52. The collapsingchamber 60 may have a substantially similar perimeter shape as thefirst actuator tab 44 and thefirst tab ring 52, however, other shapes are also contemplated. Optionally, a liner, such as asoft material 62, may be contained within the collapsingchamber 60 for purposes to be discussed below. Thematerial 62 may be a material having a density that is generally less than the density of the outsole 20; such as Ethylene Vinyl Acetate (EVA), Polyurethane (PU), latex, gel, or other materials. In general, the density of the material 62 may be such that it is relatively easily compressed.Material 62 may be sized and shaped to leave a gap between itslower surface 62A andupper surface 32 ofoutsole 30. The gap may optionally be 0.1 mm to 10 mm inclusive, further optionally 1 mm to 6 mm inclusive.
Referring to fig. 3-4, agroove 64 may be defined between thefirst actuator protrusion 44 and the surroundingfirst protrusion ring 52. Thegroove 64 may extend upward toward themidsole 16 and may follow the perimeter shape of the actuator protrusionouter wall 50. Thegroove 64 surrounding thefirst actuator lug 44 provides partial flexibility to theoutsole 30 so that theactuator lug 44 may more easily move upward toward the collapsingchamber 60, as described below. The depth of thegroove 64 may be selected to modify the amount of movement of the raisedring 52 toward theactuator protrusion 44 and/or each other. Thebase 64A or the uppermost portion of thegroove 64 may also be thinned or constructed of a different material than the raisedring 52 to alter the amount of movement of the raisedring 52. For example, thebase 64A may be softer or thinner than thetab ring 52 to facilitate collapse of thering 52 toward the gripping podcentral axis 42 and/or theactuator tab 44, as described below. The transition of thegroove 64 to theinner edge 54 of the tab ring may include a chamfer, fillet, etc.
Thesole assembly 14 may also include one or more secondgripping compartments 70 similar to the firstgripping compartments 40 described above. Thesecond grip compartment 70 may comprise: asecond actuator protrusion 74 aligned with the secondcentral axis 72 and/or centered on the secondcentral axis 72; and asecond projection ring 82 surrounding thesecond actuator projection 74. The secondgripping compartment 70 also includes a second collapsingchamber 90, the second collapsingchamber 90 being defined by thesole assembly 14 above thesecond actuator tab 74 and thesecond tab ring 82. Additionally, thesoft material 62 may be contained within the second collapsingchamber 90.
As shown in the exemplary embodiment of fig. 3, the secondgripping pod 70 and the firstgripping pod 40 may be remote from each other. The firstgripping pod 40 is shown located in theheel region 26 of the footwear 10, and the secondgripping pod 70 is shown located in theforefoot region 22 of the footwear 10. According to one example, the grippingpods 40, 70 may extend through a majority of the side-to-side width W of thesole assembly 14 in their respective positions. Although the illustrated example shows two firstgripping pods 40 and three secondgripping pods 70, more or fewer of either pod and other arrangements of pods are contemplated herein. Alternatively, the grippingpods 40, 70 may contain different configurations and different numbers of raisedrings 52, 82 depending on the application. The projection rings 52, 82 may also vary in structure, height, and location relative to each other and theactuator projections 44, 74 depending on the location along thesole assembly 14 and/or the location in thesole assembly 14 along the heel-to-toe longitudinal length L.
The grippingpods 40, 70 may also include a plurality of channels or voids 66, 96 recessed upwardly into the raised ring ground contact surfaces 58, 88 and extending through the raised ringinner edges 54, 84. For example, thevoids 66, 96 extend radially away from theactuator protrusions 44, 74 and may be evenly or unevenly spaced about the protrusion rings 52, 82. Thus, the raised ring ground contact surfaces 58, 88 and the raised ringinner edges 54, 84 may be interrupted by thevoids 66, 96 such that the raised ring ground contact surfaces 58, 88 are discontinuous. Thevoids 66, 96 may provide local bending in the surrounding area. Thevoids 66, 96 may be linear, curved, angled, segmented, circular, and/or polygonal in cross-section.
When the article of footwear 10 is worn, the shape of theoutsole 30 may change as the wearer exerts pressure on the footwear due to the weight of the wearer and contact with the ground surface. More specifically, the first and secondgripping pods 40, 70 are each configured to move between an extended mode (shown in fig. 2 and 4) and a retracted mode or gripping mode (shown in fig. 5). In the extended mode, the grippingpods 40, 70 are not under compressive force due to the weight of the wearer. In the gripping mode, the grippingpods 40, 70 are under compressive force due to the weight of the wearer. It should be understood that the grippingpods 40, 70 are independent and may be in either the extended or gripping mode, regardless of which mode the other pod is in. In some cases, for example, when all of the pods are engaging the ground surface, all of the gripping pods may be in the same mode.
Referring to fig. 4-5, in the gripping mode, the grippingpods 40, 70 are at least partially collapsed into themselves and/or upwardly into the sole assembly to grip the underfoot surface and terrain. Referring to the firstgripping compartment 40, when the footwear 10 is worn and initially contacts the ground to bear the weight of the wearer, the first actuator lugs 44 engage the ground surface before thefirst lug ring 52 and move at least partially upward into the first collapsingchambers 60 in thesole assembly 14 and/or toward the first collapsingchambers 60 in thesole assembly 14. The upward movement of thefirst actuator tab 44 pulls theadjacent tab ring 52 toward the first actuator tab. The inward collapse of thefirst actuator tab 44 and the pull-in of thefirst tab ring 52 causes those elements to move toward the firstcentral axis 42 of the firstgripping pod 40 and grip the ground surface therebelow with a predetermined force. The density of thematerial 62 within thecollapse chamber 60 may be selected to provide a sufficient amount of compression to allow the firstgripping compartment 40 to collapse as desired. When transitioning from the extended mode to the gripping mode, theactuator protrusions 44 and protrusion rings 52 collapse inwardly into thesofter foam material 62.
Optionally, the secondgripping pod 70 collapses in the same manner as the firstgripping pod 40. Thesecond actuator protrusion 74 and thesecond protrusion ring 82 at least partially collapse into thesecond collapse chamber 90, with thesecond protrusion ring 82 moving toward the secondcentral axis 72 of the secondgripping capsule 70. In this manner, a portion of the second raisedring 82 moves away from the firstcentral axis 42 of the firstgripping pod 40, while a second portion of the second raisedring 82 moves toward the firstcentral axis 42 of the firstgripping pod 40.
During the wearer's gait cycle and transition between the extension mode and the grip mode, the protrusion ringinner edges 54, 84 travel toward the actuator protrusionouter walls 50, 80, optionally following a substantially curvilinear or arcuate path AP as shown in fig. 4. When this occurs, theinner edges 54, 84 of the projection rings 52, 82 may be raised above the ground contact surfaces 46, 76 of theactuator projections 44, 74, as shown in fig. 5. The projecting ringinner edges 54, 84 may also travel on the arcuate path AP toward theinner walls 56, 86 such that a portion of the ground contact surfaces 58, 88 of the projectingrings 52, 82 is no longer at the same level as the actuator ground contact surfaces 46, 86. Instead, theactuator protrusions 44, 74 travel upward toward therespective collapse chambers 60, 90 along a substantially linear path during transition from the extended mode to the gripping mode.
In the extended mode, the actuator protrusion ground contact surfaces 46, 86 may be disposed a first distance D1 (see fig. 4) below the protrusion ring ground contact surfaces 58, 88. During transition to the gripping mode, the actuator raised ground contact surfaces 46, 86 retract upwardly relative to the raised ring ground contact surfaces 46, 86. In the gripping mode, the actuator protrusion ground contact surfaces 46, 86 may be disposed a second distance D2 (see fig. 5) below the protrusion ring ground contact surfaces 58, 88. The second distance D2 may be less than the first distance D1. As an example, the first distance D1 may be at least 1 mm (inclusive), and thus the second distance D2 is less than 1 mm.
Additionally, in the extended mode, the protrusion ringinner walls 56, 86 may be disposed at a first angle a1 (see fig. 4) relative to a vertical plane. During transition to the gripping mode, the protrusion ringinner walls 56, 86 are pulled and/or tilted toward theactuator protrusions 44, 74 indicated by the arrows in fig. 4. Once in the gripping mode, the protrusion ringinner walls 56, 86 may be disposed at a second angle a2 (see fig. 5) with respect to the vertical plane. The second angle a2 may be at least 2 degrees greater than the first angle a 1. As shown in fig. 4, the first angle a1 appears substantially vertical; however, angles other than vertical are also contemplated herein. For example, the first angle a1 may alternatively be plus or minus about 20 ° with respect to the vertical plane, and further alternatively may be plus or minus about 30 °, 45 °, or 60 ° with respect to the vertical plane.
The tabinner edge 54 and the actuator tabouter wall 50 are separated by a first distance D3 (see fig. 4) in the extended mode. Upon transitioning to the gripping mode, the tabinner edge 54 and the actuator tabouter wall 50 are separated by a second distance D4 (see fig. 5). The second distance D4 is less than the first distance D3. When the grippingpod 40, 70 transitions from the extended mode to the gripping mode, the protrusion ringinner edge 54, 84 and/or theinner wall 56, 86 moves toward the actuator protrusionouter wall 50, 80. When this occurs, the distance between these elements decreases from the first distance D3 to a smaller distance D4. Thus, any floor surface material between the raised rings 52, 82 and theactuator projections 44, 47 can be caught, gripped or pinched between theactuator projections 44, 47 and the raised rings 52, 82. Specifically, ground surface material is captured or grasped between theinner edge 54, 84 and/orinner wall 56, 86 of the tab ring and theouter wall 50, 80 of the actuator tab to improve friction.
A first alternative embodiment of footwear is shown in fig. 6 and is generally designated 110. The footwear may be similar in structure, function and operation to the embodiments described above with some exceptions. For example, thefootwear 110 may include acushion 162, thecushion 162 substantially filling the collapse chamber 160 without leaving gaps as described in the above embodiments. The grippingpods 140, 170 cover thesofter foam pad 162 to provide a certain amount of compression. When transitioning from the extended mode to the gripping mode, theactuator protrusions 144, 174 and thering protrusions 152, 182 are able to collapse inwardly into thesoft pad 162.Footwear 110 may also eliminate the grooves of the previous embodiments to affect the local flexibility ofoutsole 130 as desired. Although thecushion 162 and eliminated groove may alter the footwear response, the collapse of thepods 140, 170 is generally similar to that described above, and the actuator lugs 144, 174 and lug rings 152, 182 are still compressed and pulled in as described above.
An alternative embodiment of footwear is shown in fig. 7 and is generally designated 210. The footwear may be similar in structure, function and operation to the embodiments described above with some exceptions. Thegripping pod 240 may optionally contain two or more raised rings 252 concentrically disposed with respect to one another. Between the first raised ring 252a and the more outwardly positioned second raised ring 252b, a second recess 264b may be defined. The geometry and material of the grooves may be selected as described above with respect to the previous embodiments. Additionally, the collapse chamber 260 may be larger so as to be disposed above thefirst actuator protrusion 244, the first protrusion ring 252a, and the second protrusion ring 252 b.
During transition from the extension mode to the grip mode, the second protrusion ring inner wall 256b is pulled and/or tilted toward the first protrusion ring 252a in a similar manner as the protrusion ring inner wall of the first embodiment. However, the axis of rotation of the second protrusion ring inner wall 256b is different (separate and spaced) from the axis of rotation of the first protrusion inner wall 256 a. That is, the second protrusion ring inner wall 256a will not necessarily collapse at the same angle (a 2) as the first protrusion ring inner wall 256 a. The pull from the upward movement of theactuator protrusion 244 may be less than the pull experienced by the first protrusion ring 252a, given its distance from the central axis 242. However, it should be understood that both raised rings 252a and 252b can be tilted during the transition from the extended mode to the gripping mode. Of course, it should also be understood that while the above description is with respect to thefirst grip compartment 240 containing two raised rings 252, thesecond grip compartment 270 may contain multiple raised rings and need not be described in greater detail.
Another alternative embodiment of footwear is shown in fig. 8 and is generally designated 310. The footwear may be similar in structure, function and operation to the embodiments described above with some exceptions. For example, thefootwear 310 may eliminate voids in the raised ringinner edges 354, 384 and the raised ring ground-contactingsurfaces 358, 388. In this manner, the ground-contactingsurfaces 358, 388 are continuous.
Without the voids of the first embodiment, theprojection ring 352 is continuous and may completely surround the outer periphery of theactuator projection 344. When thegripping capsule 340 engages a generally flat or planar surface, the collapse of thecapsule 340 can create a negative pressure such that thegripping capsule 340 is substantially or at least partially attracted to the surface below it. As such, when the raisedring 352 is continuous, thegripping capsule 340 generates suction as it collapses, providing improved friction on wet or slippery surfaces, particularly those surfaces that are flat or planar. Of course, the same is true for the secondgripping pod 370. It is contemplated that some (but not necessarily all) of the gripping pods are continuous, while other gripping pods contain voids and are therefore discontinuous.
The footwear of any of the above embodiments provides a sole assembly having superior traction. Where the gripping pod contains actuator protrusions and protrusion rings, those protrusions may cooperate to grip the underlying floor surface. This may provide reaction and dynamic friction to the sole assembly and footwear, thereby enabling the wearer to have confidence in his or her walking. In addition, where the raised loops are continuous and the gripping pods create suction as they collapse, the sole assembly may provide improved traction on wet or slippery surfaces, particularly where those surfaces are flat or planar.
The various components and features of the embodiments herein (e.g., upper, sole, or other footwear portions) may take on various aesthetic forms, shapes, and sizes. While a particular component or feature may have functionality, the feature may be manifested in different aesthetic ways to create artistic designs and/or purely decorative designs.
Directional terms such as "vertical," "horizontal," "top," "bottom," "upper," "lower," "inner," "inward," "outer," and "outward" are used to help describe the invention based on the orientation of the embodiments shown in the drawings. The use of directional terms should not be construed to limit the invention to any particular orientation(s).
The above description is that of the current embodiment of the invention. Various modifications and changes can be made without departing from the spirit and broader aspects of the invention as defined in the appended claims, which are to be interpreted in accordance with the principles of patent law, including the doctrine of equivalents. The present disclosure is presented for illustrative purposes and should not be construed as an exhaustive description of all embodiments of the invention or to limit the scope of the claims to the particular elements shown or described in connection with these embodiments. For example, and not by way of limitation, any individual element(s) of the described invention may be replaced by alternative elements that provide substantially similar functionality or otherwise provide suitable operation. This includes, for example, alternative elements that are currently known (such as those that may currently be known to those skilled in the art) and alternative elements that may be developed in the future (such as those that may be considered substitutes by those skilled in the art at the time of development). Further, the disclosed embodiments incorporate multiple features that are described cooperatively and that may cooperatively provide a range of benefits. The present invention is not limited to only those embodiments that incorporate all of these features or provide all of the stated benefits, except as otherwise expressly set forth in the issued claims. Any reference to claim elements in the singular, for example, using the articles "a," "an," "the," or "said," is not to be construed as limiting the element to the singular. Any reference to a claim element, e.g., "at least one of X, Y and Z," is intended to include either of X, Y or Z and any combination of X, Y and Z, e.g., X, Y, Z; x, Y, respectively; x, Z, respectively; and Y, Z.