Patent Publication Number: US-2022235543-A1

Title: Systems and methods for the construction of structures utilizing additive manufacturing techniques

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a divisional of and claims priority to pending U.S. patent application Ser. No. 16/230,616, filed Dec. 21, 2018, titled SYSTEMS AND METHODS FOR THE CONSTRUCTION OF STRUCTURES UTILIZING ADDITIVE MANUFACTURING TECHNIQUES, the entire contents of which are hereby incorporated by reference herein and relied upon. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not applicable. 
     BACKGROUND 
     This disclosure is generally directed to the design and construction of structures (e.g., dwellings, buildings, etc.). More particular, this disclosure is directed to the design and construction of structures utilizing additive manufacturing techniques. 
     Structures (e.g., dwellings, buildings, sheds, etc.) may be manufactured with a multitude of different materials and construction methods. Among the materials commonly used in the construction of structures is concrete. For example, concrete may be utilized in the foundation of a structure and possibly in the construction of exterior walls. 
     BRIEF SUMMARY 
     Some embodiments disclosed herein are directed to a construction system for constructing a structure atop a foundation. In an embodiment, the construction system includes a rail assembly. The rail assembly is configured to be mounted to the foundation. In addition, the construction system includes a gantry movably disposed on the rail assembly. The gantry is configured to translate along a first axis relative to the rail assembly. Further, the construction system includes a printing assembly movably disposed on the gantry. The printing assembly is configured to translate along a second axis relative to the gantry. The second axis is orthogonal to the first axis. The printing assembly is configured to deposit vertically stacked layers of an extrudable building material onto a top surface of the foundation to construct a structure. 
     In other embodiments, the construction system includes a pair of rail assemblies that are configured to be mounted to the foundation. In addition, the construction system includes a gantry including a pair of vertical support assemblies movably disposed on the rail assemblies. The vertical support assemblies are configured to translate along a first axis relative to the rail assemblies. In addition, the gantry includes a trolley bridge assembly coupled to and spanning between the vertical support assemblies. Further, the construction system includes a printing assembly movably coupled to the trolley bridge assembly. The printing assembly is configured to translate along a second axis relative to the trolley bridge assembly. The second axis is orthogonal to the first axis. The printing assembly is configured to deposit vertically stacked layers of an extrudable building material onto a top surface of the foundation to construct a structure. 
     In still other embodiments, the constructions system includes a pair of rail assemblies that are configured to be mounted to the foundation. In addition, the construction system includes a gantry including a pair of vertical support assemblies movably disposed on the rail assemblies. The vertical support assemblies are configured to translate along a first axis relative to the rail assemblies. In addition, the gantry includes a trolley bridge assembly coupled to and spanning between the vertical support assemblies. The trolley bridge assembly is configured to translate along a third axis relative to the vertical support assemblies. Further, the construction system includes a printing assembly movably coupled to the trolley bridge assembly. A portion of the printing assembly is configured to translate along a second axis relative to the trolley bridge assembly. The first axis is orthogonal to the second axis and the third axis, and the second axis is orthogonal to the third axis. The printing assembly is configured to deposit vertically stacked layers of an extrudable building material onto a top surface of the foundation to construct a structure. 
     Embodiments described herein comprise a combination of features and characteristics intended to address various shortcomings associated with certain prior devices, systems, and methods. The foregoing has outlined rather broadly the features and technical characteristics of the disclosed embodiments in order that the detailed description that follows may be better understood. The various characteristics and features described above, as well as others, will be readily apparent to those skilled in the art upon reading the following detailed description, and by referring to the accompanying drawings. It should be appreciated that the conception and the specific embodiments disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes as the disclosed embodiments. It should also be realized that such equivalent constructions do not depart from the spirit and scope of the principles disclosed herein. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a detailed description of various exemplary embodiments, reference will now be made to the accompanying drawings in which: 
         FIG. 1  is a perspective view of a construction system and a structure according to some embodiments; 
         FIG. 2  is another perspective view of the construction system of  FIG. 1  according to some embodiments; 
         FIG. 3  is a schematic front view of the rail assemblies of the construction system of  FIG. 1  according to some embodiments; 
         FIG. 4  is a schematic side view of one of the vertical support assemblies disposed on one of the rail assemblies of the construction system of  FIG. 1  according to some embodiments; 
         FIG. 5  is an enlarged schematic view of one of the wheel assemblies of the vertical support assembly of  FIG. 4  coupled to the rail assembly of  FIG. 4  according to some embodiments; 
         FIGS. 6 and 7  are schematic side and bottom views, respectively, of one of the connection block assemblies of the construction system of  FIG. 1  according to some embodiments; 
         FIG. 8  is a schematic side view of one of the vertical support assemblies disposed on an alternative rail assembly of the construction system of  FIG. 1  according to some embodiments; 
         FIG. 9  is an enlarged, schematic front view of the rail assembly of the vertical support assembly coupled to the rail assembly of  FIG. 8  according to some embodiments; 
         FIG. 10  is a front schematic view of the vertical support assembly of  FIG. 4  according to some embodiments; 
         FIG. 11  is a top view of the printing assembly of the construction system of  FIG. 1  according to some embodiments; 
         FIG. 12  is a schematic side view of the printing assembly of  FIG. 11  according to some embodiment; 
         FIG. 13  is a diagram of the construction system of  FIG. 1  according to some embodiments; 
         FIGS. 14 and 15  are side views of the printing system of  FIG. 11  supported on a trolley bridge assembly of the construction system of  FIG. 1  according to some embodiments; 
         FIG. 16  is a diagram of the construction system of  FIG. 1  according to some embodiments; 
         FIGS. 17 and 18  are block diagrams of methods according to some embodiments; 
         FIG. 19  is a schematic, perspective view of a construction system according to some embodiments; 
         FIG. 20  is a schematic, perspective view of a construction system according to some embodiments; 
         FIG. 21  is a diagram of a floor plan of a structure constructed according to some embodiments; 
         FIG. 22  is a line diagram of the structure of  FIG. 21  according to some embodiments; 
         FIG. 23  is a shell diagram of the structure of  FIG. 21  according to some embodiments; 
         FIG. 24  is an infill diagram of the structure of  FIG. 21  according to some embodiments; 
         FIG. 25  is a diagram showing a super-imposition of the infill diagram of  FIG. 24  atop the shell diagram of  FIG. 23  according to some embodiments; 
         FIG. 26  is an enlarged schematic diagram of a wall segment according to some embodiments; 
         FIG. 27  is a diagram of a master slice defined according to some embodiments; 
         FIG. 28  is a side view of the structure of  FIG. 21  according to some embodiments; 
         FIGS. 29-32  are diagrams of various slices from the structure of  FIG. 21  according to some embodiments; 
         FIGS. 33 and 34  are sequential schematic views of tool paths for forming or printing a layer of a structure according to some embodiments; 
         FIG. 35  is a schematic view of a system for designing and constructing a structure according to some embodiments; and 
         FIG. 36  is a diagram of a method for designing and constructing a structure according to some embodiments. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     The following discussion is directed to various exemplary embodiments. However, one of ordinary skill in the art will understand that the examples disclosed herein have broad application, and that the discussion of any embodiment is meant only to be exemplary of that embodiment, and not intended to suggest that the scope of the disclosure, including the claims, is limited to that embodiment. 
     The drawing figures are not necessarily to scale. Certain features and components herein may be shown exaggerated in scale or in somewhat schematic form and some details of conventional elements may not be shown in interest of clarity and conciseness. 
     In the following discussion and in the claims, the terms “including” and “comprising” are used in an open-ended fashion, and thus should be interpreted to mean “including, but not limited to . . . .” Also, the term “couple” or “couples” is intended to mean either an indirect or direct connection. Thus, if a first device couples to a second device, that connection may be through a direct connection of the two devices, or through an indirect connection that is established via other devices, components, nodes, and connections. In addition, as used herein, the terms “axial” and “axially” generally mean along or parallel to a given axis (e.g., central axis of a body or a port), while the terms “radial” and “radially” generally mean perpendicular to the given axis. For instance, an axial distance refers to a distance measured along or parallel to the axis, and a radial distance means a distance measured perpendicular to the axis. 
     As used herein, the terms “about,” “approximately,” substantially,” “generally,” and the like mean plus or minus 10% of the stated value or range. In addition, as used herein, an “extrudable building material” refers to a building material that may be delivered or conveyed through a conduit (e.g., such as a flexible conduit) and extruded (e.g., via a nozzle or pipe) in a desired location. In some embodiments, an extrudable building material includes a cement mixture (e.g., concrete, cement, etc.). Further, as used herein, the term “computing device” refers to any suitable device (or collection of devices) that is configured to execute, store, and/or generate machine readable instructions (e.g., non-transitory machine readable medium). The term may specifically include devices, such as, computers (e.g., personal computers, laptop computers, tablet computers, smartphones, personal data assistants, etc.), servers, controllers, etc. A computing device may include a processor and a memory, wherein the processor is to execute machine readable instructions that are stored on the memory. 
     As previously described above, structures (e.g., dwellings, buildings, sheds, etc.) may be manufactured with a multitude of different materials and construction methods. Traditionally, a building (e.g., a dwelling) may be constructed upon a composite slab or foundation that comprises concrete reinforced with re-bar or other metallic materials. The structure itself may then be framed (e.g., with wood and/or metal framing members), and then an outer shell and interior coverings (e.g., ply-wood, sheet rock, etc.) may be constructed around the structural framing. Utilities (e.g., water and electrical power delivery as well as vents and ducting for air conditioning and heating systems) may be enclosed within the outer shell and interior covers along with insulation. This method of designing and constructing a structure is well known and has been successfully utilized in constructing an uncountable number of structures; however, it requires multiple constructions steps that cannot be performed simultaneously and that often require different skills and trades to complete. As a result, this process for designing and constructing a structure can extend over a considerable period (e.g., 6 months to a year or more). Such a lengthy construction period is not desirable in circumstances that call for the construction of a structure in a relatively short period of time. 
     Accordingly, embodiments disclosed herein include construction systems, methods of construction, and even methods for structure design that allow a structure (such as a personal dwelling) to be constructed in a fraction of the time associated with traditional construction methods. In particular, embodiments disclosed herein utilize additive manufacturing techniques (e.g., three dimensional (3D) printing) in order to produce a structure more quickly, economically, and in a systematic manner. 
     Referring now to  FIGS. 1 and 2 , a construction system  10  according to some embodiments is shown. In this embodiment, construction system  10  generally includes a pair of rail assemblies  20 , a gantry  50  movably disposed on rail assemblies  20 , and a printing assembly  100  movably disposed on gantry  50 . As will be described below, construction system  10  is configured to form a structure, such as for example the structure  5  shown in  FIG. 1 , via additive manufacturing, specifically 3D printing. In particular, system  10  (via rail assemblies  20  and gantry  50 ) is configured to controllably move or actuate printing assembly  100  relative to the foundation  4  of structure  5  along each of a plurality of orthogonal movement axes or directions  12 ,  14 ,  16  such that printing assembly  100  may controllably deposit an extrudable building material in a plurality of vertically stacked layers to form structure  5 . As shown in  FIG. 2 , axes  12 ,  14 ,  16  are each orthogonal to one another—with axis  12  being orthogonal to both axes  14 ,  16 , axis  14  being orthogonal to axes  12  and  16 , and axis  16  being orthogonal to axes  12  and  14 . In addition, the origin (not shown) of axes  12 ,  14 ,  16  is generally disposed at the printing assembly  100 . 
     To ensure the clarity of the following discussion of construction system  10 , the details of example structure  5  will be quickly described. In particular, as shown in  FIG. 1 , structure  5  includes a plurality of walls  7 , a plurality of windows  3  extending through the walls  7 , and a door frame  9  also extending through one of the walls  7 . Structure  5  is formed upon a foundation  4 . In this embodiment, foundation  4  is a reinforced concrete slab that is formed by first building an exterior form or mold (not shown), then placing a plurality of metallic rods (e.g., rebar) within the form in a desired pattern (e.g., in a grid pattern), and finally filling the mold with liquid or semi liquid concrete mixture. Once the concrete has sufficiently dried and/or cured (e.g., such that the foundation  4  may support the weight of structure  5 ), structure  5  may be constructed (e.g., printed) atop foundation  4  utilizing construction system  10 . As shown in  FIG. 1 , foundation includes a planar (or substantially planar) top surface  4   a , and a perimeter  6 . In some embodiments, axes  12  and  14  form or define a plane that is parallel to top surface  4   a  of foundation, and axis  16  extends in a normal direction from top surface  4   a . Thus, in instances where top surface  4   a  is substantially level (or perpendicular to the direction of gravity), axes  12 ,  14  define a level, horizontal or lateral plane, and axis  16  defines the vertical direction. 
     Referring now to  FIGS. 2-3 , in this embodiment, each rail assembly  20  is disposed on top surface  4   a  of foundation and includes a central axis  25 , a first end  20   a , and a second end  20   b  opposite first end  20   a . Axes  25  of rail assemblies  20  are parallel and radially spaced from one another across top surface  4   a  such that first ends  20   a  and second ends  20   b  of rail assemblies  20  are generally aligned with one another across top surface  4   a . In addition, each of the axes  25  of rail assemblies  20  extend parallel to axis  12  (and thus, each axis  25  also extends in a direction that is perpendicular to the direction of axis  14  and the direction of axis  16 ). As best shown in  FIGS. 2 and 3 , each rail assembly  20  includes an elongate channel member  22  extending axially between ends  20   a ,  20   b  along axis  25  that includes a pair of axially extending walls  24  defining a recess  26  extending therebetween. In particular, elongate channel member  22  includes a first wall  24   a , and a second wall  24   b  radially spaced from first wall  24   a  with respect to axis  25 , so that recess  26  is disposed radially between walls  24   a ,  24   b.    
     An axially extending elongate angle member  28  is secured (e.g., welded, bolted, riveted, etc.) within recess  26  between walls  24   a ,  24   b . As will be described in more detail below, angle members  28  of rail assemblies  20  form tracks to guide movement of gantry  50  (and printing assembly  100 ) across foundation  4  along axis  12  during construction operations. As is best shown in  FIG. 3 , in this embodiment angle member  28  is radially positioned closer to first wall  24   a  than second wall  24   b  (i.e., angle member  28  is not equidistantly spaced between walls  24   a ,  24   b  within recess  26  in this embodiment). Thus, a space or clearance  29  is formed radially between angle member  28  and second wall  24   b . As is also best shown in  FIG. 3 , channel members  22  of rail assemblies  20  are positioned along foundation such that second walls  24   b  radially face one another across top surface  4   a , and first walls  24   a  radially face away from one another. 
     Referring now to  FIGS. 3 and 4 , an elongate rack  32  is secured to first wall  24   a  of each rail assembly  20  via a corresponding frame  34 . Accordingly, each rack  32  extends axially with respect to the corresponding axis  25  as well as axis  12 . As best shown in  FIG. 4 , each rack  32  includes a plurality of teeth  36  that are axially adjacent one another along the corresponding rail assembly  20 . 
     Referring again to  FIGS. 1 and 2 , gantry  50  generally includes a pair of vertical support assemblies  60 , an upper bridge assembly  70  spanning between vertical support assemblies  60 , and a trolley bridge assembly  80  also spanning between vertical support assemblies  60 , below upper bridge assembly  70 . As will be described in more detail below, each of the vertical support assemblies  60  is movably coupled to a corresponding one of the rail assemblies  20  so that vertical support assemblies  60  may traverse along axis  12  during operations. In addition, trolley bridge assembly  80  is movably coupled to each of the vertical support assemblies  60  so that trolley bridge assembly  80  may traverse along axis  16  during operations. Each of these components will now be described in more detail below. 
     Referring to  FIG. 4 , each vertical support assembly  60  includes a longitudinal axis  65 , a first or lower support girder  62 , and a second or upper support girder  64  axially spaced from lower support girder  62  along axis  65 . In addition, vertical support assembly  60  includes a plurality of support legs  66  extending axially between girders  62 ,  64  with respect to axis  65 . In this embodiment, axis  65  extends in the vertical direction, or along the direction of the force of gravity, and thus, axis  65  of each vertical support assembly  60  is parallel to axis  16 , and support legs  66  of each vertical support assembly  60  extend vertically between the corresponding girders  62 ,  64 . 
     Referring still to  FIG. 4 , each vertical support assembly  60  further includes a pair of roller assemblies  68  coupled to lower support girder  62 . Each roller assembly  68  includes a corresponding roller  67  that engages with angle member  28  within the corresponding rail assembly  20 . More specifically, referring briefly to  FIG. 5 , each roller  67  includes a circumferential channel  67   a , which in this embodiment is a v-shaped channel or groove extending circumferentially about roller  67 . Channel  67   a  engages and mates with elongate angle member  28  of a corresponding one of the rail assemblies  20 . Thus, during operations, each vertical support assembly  60  (and thus also gantry  50 —See  FIGS. 1 and 2 ) is configured to traverse axially with respect to axes  25  of rail assemblies  20  and axis  12  (see  FIG. 2 ) along and relative to top surface  4   a  of foundation via rolling engagement between rollers  67  and elongate angle members  28 . 
     Referring now to  FIGS. 4, 6, and 7 , a lateral actuation assembly  40  is coupled between each vertical support assembly  60  and the corresponding rail assembly  20  (that is, there is a corresponding lateral actuation assembly  40  coupled between each vertical support assembly  60  and corresponding rail assembly  20  within construction system  10 ). However, it should be appreciated that in other embodiments, a single lateral actuation assembly  40  is coupled between a select one of the vertical support assemblies  60  and a corresponding one of the rail assemblies  20 . Each lateral actuation assembly  40  generally comprises a driver  42  and a connection block assembly  46  for coupling driver to lower girder  62  of vertical support assembly  60 . 
     Driver  42  includes an output shaft  41  and is configured to rotate shaft  41  about an axis  45  that extends in a direction that is generally perpendicular to the direction of axis  25  of the corresponding rail assembly  20  (however, it should be appreciated that such precise alignment may not exist in other embodiments). Driver  42  may comprise any suitable driver or prime mover for rotating output shaft  41  about axis  45 , such as, for example, an electric motor, a hydraulic motor, a pneumatic motor, etc. In this embodiment, driver  42  comprises an electric motor (e.g., a servo motor). In addition, driver  42  is configured to rotate shaft  41  in either direction (e.g., clockwise, counterclockwise, etc.) about axis  45 . As best shown in  FIG. 7 , shaft  41  includes a plurality of teeth  41   a  mounted thereto that are configured to mesh with the teeth  36  of rack  32  of the corresponding rail assembly  20  (see  FIG. 4 ). Thus, teeth  41   a  of shaft  41  may form a pinion gear that is configured to mesh with the teeth  36  of rack  32 . 
     Referring still to  FIGS. 4, 6, and 7 , connection block assembly  46  includes a first block or member  44  mounted to driver  42 , a second block or member  48  mounted to lower girder  62 , and a third block or member  47 . First block  44  includes an aperture  43  (see  FIG. 7 ) that receives shaft  41  of driver  42  therethrough along axis  45 . In addition, second block  48  is secured to girder  62  by a plurality of bolts  48   a . A plurality of connector studs  38  (or more simply “studs  38 ”) extend through each of the first block  44 , second block  48 , and third block  47 . In this embodiment, connector studs  38  extend through blocks  44 ,  48 ,  47  in a direction that is perpendicular to the directions of the axis  45  of shaft  41  and the axis  25  of the corresponding rail assembly  20 . Each stud  38  has a first end  38   a , and a second end  38   b  opposite first end  38   a . First block  44  is proximate first ends  38   a  of each stud  38 , third block  47  is proximate second ends  38   b  of each stud  38 , and second block  44  is disposed between blocks  44 ,  47 . 
     In addition, studs  38  are fixed within first block  44  and third block  47  due to the engagement of nuts  39  about studs  38  on either side of blocks  44 ,  47 . Accordingly, studs  38  may not move relative to blocks  44 ,  47  during operations. In other embodiments, some other technique may be used to fix studs  38  relative to blocks  44 ,  47  (e.g., threaded engagement of studs within blocks  44 ,  47 , welding, etc.). In addition, in this embodiment, studs  38  may freely slide within and relative to second block  48 . A biasing member  49  is disposed between second block  48  and third block  47 . Biasing member  49  is configured to bias second block  48  away from third block  47  (or third block  47  away from second block  48 ) along studs  38 . In this embodiment, biasing member  49  comprises a coiled spring; however, any suitable biasing member configured to linearly bias to members apart from one another may be used in other embodiments, such as, for example, a piston. Because studs  38  are fixed within first block  44  and third block  47 , and are free to slide within second block  48  as previously described, biasing third block  47  from second block  48  along studs  38  also biases first block  44  toward second block  48 . As best appreciated in  FIG. 6 , the biasing of first block  44  toward second block  48  further biases shaft  41  into engagement with rack  32  mounted to first wall  24   a  of the corresponding rail assembly  20 . Accordingly, connection block assembly  46  is configured to bias teeth  41  mounted to shaft  41  into cooperative engagement with the corresponding teeth  36  on rack  32  of the corresponding rail assembly  20 . 
     Referring again to  FIGS. 2 and 4 , during operations, driver  42  of each lateral actuation assembly  40  is selectively actuated rotate the corresponding shaft  41 . Due to the engagement between teeth  41   a  of shafts  41  (see  FIG. 7 ) and the teeth  36  of the corresponding racks  32  on rail assemblies  20 , the rotation of shafts  41  about the corresponding axes  45  causes traversal of each vertical support assembly  60  axially along the corresponding rail assembly  20  with respect to axis  12 . Accordingly, the actuation of drivers  42  causes movement or translation of gantry  50  along axis  12  relative to foundation  4 . 
     Referring now to  FIGS. 8 and 9 , while the embodiment of  FIGS. 1-7  has included rail assemblies  20  that are secured to the top surface  4   a  of foundation  4 , it should be appreciated that other embodiments of construction system  10  (see  FIGS. 1 and 2 ) include rail assemblies that are mounted to other surfaces of foundation  4 , such as, for example, the perimeter  6 . In particular,  FIGS. 8 and 9  depict another embodiment of rail assemblies  120  for supporting gantry  50  (see  FIGS. 1 and 2 ) on foundation  4 . Rail assemblies  120  each include a central axis  125  (that extends in the same direction as axis  25  of rail assemblies  20  and thus is parallel to axis  12  shown in  FIG. 2  as previously described) and an elongate angle member  122  in place of elongate channel member  22  (see  FIG. 3 ). Elongate angle member  122  includes a first portion  122   a  and a second portion  122   b  extending perpendicularly from first portion  122   a . First portion  122   a  includes a plurality of apertures  123  extending therethrough. In this embodiment, apertures  123  are slots that are elongated axially with respect to axis  125 . Elongate angle member  122  is secured to foundation  4  by inserting bolts  124  or other suitable connection members through the apertures  123  and into perimeter  6  of foundation  4 . Accordingly, once elongate angle member  122  is secured to perimeter  6  of foundation  4 , second portion  122   b  of angle member  122  extends parallel to and may be flush with top surface  4   a  of foundation  4 . 
     Rack  32  and elongate angle member  28 , both of which are the same as previously described above, are coupled to second portion  122   b  of elongate angle member  122 . Thus, as best shown in  FIG. 8 , rollers  67  of vertical support assembly  60  are engaged with elongate angle member  28  in the same manner as described above, and shaft  41  of driver  42  is meshed or engaged with the teeth  36  of rack  32  in the same manner as described above. Further, connection block assembly  46  is configured to bias shaft  41  into engagement with rack  32  via lower girder of vertical support assembly  60  in the same manner as previously described above. Thus, the traversal of gantry  50  (see  FIGS. 1 and 2 ) (including vertical support assemblies  60 ) along axis  12  across top surface  4   a  utilizing rail assemblies  120  is substantially the same as that described above for rail assemblies  20 , and a detailed description of these operations is omitted in the interest of brevity. However, it should be appreciated that by use of rail assemblies  120  that are mounted to perimeter  6  of foundation  4 , all (or substantially all) of top surface  4   a  is available for the construction of a structure (e.g., structure  5  shown in  FIG. 1 ). 
     Referring back now to  FIG. 2 , upper bridge assembly  70  includes a pair of girders  72  that are mounted to and span between upper girders  64  of vertical support assemblies  60 . In particular, each girder  72  includes a first end  72   a  and a second end  72   b  opposite first end  72   a . The first end  72   a  of each girder  72  is mounted or secured to the upper girder  64  of one vertical support assemblies  60 , and the second end  72   b  of each girder  72  is mounted or secured to upper girder  64  of the other vertical support assembly  60 . In this embodiment, each girder  72  extends in a direction that is parallel to axis  14 ; however, such precise alignment is not achieved in some embodiments. In addition, upper bridge assembly  70  further includes a plurality of cross-braces  74 , each extending between a corresponding one of the girders  72  to a corresponding one of the support legs  66  of vertical support assemblies  60 . Accordingly, vertical support assemblies  60  are secured to one another via upper bridge assembly  70 , so that each of the vertical support assemblies  60  are moved together about top surface  4   a  of foundation  4  along axis  12  during printing operations. 
     Referring still to  FIG. 2 , trolley bridge assembly  80  includes a pair of girders  82 ′,  82 ″ (namely a first girder  82 ′ and a second girder  82 ″) coupled to and spanning between vertical support assemblies  60 . In addition, printing assembly  100  is movably coupled to girders  82 ′,  82 ″. As will be described in more detail below, girders  82 ′,  82 ″ of trolley bridge assembly  80  are movably coupled to vertical support assemblies  60 , such that girders  82 ′,  82 ″ may traverse along axis  16  during operations. In addition, printing assembly  100  is movably coupled to girders  82 ′,  82 ″ such that printing assembly  100  is configured to traverse along axis  14  between girders  82 ′,  82 ″ during operations. 
     Referring now to  FIGS. 2, 4, and 10 , each girder  82 ′,  82 ″ includes a first end  82   a , and a second end  82   b  opposite first end  82   a . First ends  82   a  of girders  82 ′,  82 ″ are coupled to one of the vertical support assemblies  60 , and second ends  82   a  of girders  82 ′,  82 ″ are coupled to the other vertical support assembly  60 .  FIGS. 4 and 10  depict the coupling between first ends  82   a  of girders  82 ′,  82 ″ and one of the vertical support assemblies  60 ; however, it should be appreciated that second ends  82   b  of girders  82 ′,  82 ″ are coupled to the other vertical support assembly  60  in the same manner. 
     As shown in  FIGS. 4 and 10 , first ends  82   a  of girders  82 ′,  82 ″ are each mounted to a connection bracket  84 . In this embodiment, connection bracket  84  comprises a plate and includes a pair of support sleeves  86  and a threaded collar  88  mounted thereto. A threaded rod  83  extends axially with respect to the vertically oriented axis  65  of vertical support assembly  60  between lower girder  62  and upper girder  64  of vertical support assembly  60 . Thus, threaded rod  83  also extends axially with respect to axis  16  (see  FIG. 2 ). Threaded rod  83  includes a first or lower end  83   a  mounted to lower girder  62  via a mounting plate  81 , and a second or upper end  83   b  cooperatively engaged within a driver  87  that is mounted to upper girder  64  via a mounting plate  89 . A plurality of support rods  76  also extend axially between mounting plates  81 ,  89  with respect to axis  65 . Threaded rod  83  is threadably engaged within threaded collar  88  (i.e., threaded collar  88  includes internal threads that engage and mesh with the external threads extending about threaded rod  83 ). In addition, support rods  76  are slidably received within support sleeves  86  on connection bracket  84 . 
     Driver  87  may comprise any suitable driver or prime mover, such as previously described above for driver  42 . In this embodiment, driver  87  comprises an electric motor (e.g., a servo motor) that is configured to rotate threaded rod  83  in either a clockwise or counterclockwise direction about a central or longitudinal axis (not shown) of rod  83  (note: the longitudinal axis of rod  83  may extend parallel to axis  65 ). As a result, the coupling between threaded rod  83  and mounting plate  81  may include any suitable bearing(s) or other support device(s) configured to support the rotation of threaded rod  83  relative to plate  81  during operations. During operations, driver  87  selectively rotates threaded rod  83  as previously described above so that threaded rod  83  rotates within threaded collar  88 . Because collar  88  is threadably engaged with threaded rod  83  as previously described, the rotation of threaded rod  83  within collar causes collar  88 , connection bracket  84 , and girders  82 ′,  82 ″ to translate axially between ends  83   a ,  83   b  along axis  65  (and axis  16 ). In addition, the axial movement of connection bracket  84 , and girders  82 ′,  82 ″ is further guided by the sliding engagement between support rods  76  and support sleeves  86 . Accordingly, the actuation of drivers  87  is configured to translate trolley bridge assembly  80  and printing assembly  100  along axis  16  during operations. 
     Referring now to  FIGS. 2 and 11 , printing assembly  100  is coupled to girders  82 ′,  82 ″ and is configured to move or translate between ends  82   a ,  82   b  of girders  82 ′,  82 ″ along axis  14  during operations. Generally speaking, printing assembly  100  is movably supported between girders  82  via a pair of trolley members  92 ,  94 . 
     Referring now to  FIGS. 11-13 , printing assembly  100  generally includes a supply conduit  101 , a hopper  102 , a pump assembly  105 , and an outflow conduit  110 . As best shown in  FIG. 13 , supply conduit  101  is configured to deliver an extrudable building material (e.g., a cement mixture) from a source  130 , which may comprise any suitable tank or vessel that is configured to contain a volume of extrudable building material therein. For example, in some embodiments, source  130  may comprise a tank, a cement mixer (e.g., such as that found on a stand-alone cement mixer or on a cement truck), or other suitable container. Source  130  may be disposed immediately adjacent foundation  4  and gantry  50 , or may be relatively remote from foundation  4  and gantry  50 . 
     In this embodiment, conduit  101  comprises a hose; however, other suitable conduits or channels for delivering the extrudable building material from the source  130  may be used in other embodiments (e.g., pipes, open channels, tubing, etc.). Supply conduit  101  includes an outlet  101   a  that is disposed above hopper  102  so that cement emitted from outlet  101   a  is provided into hopper  102  during operations. 
     As best shown in  FIG. 12 , hopper  102  includes a first or upper end  102   a , and a second or lower end  102   b  opposite upper end  102   a . In addition, hopper  102  includes a plurality of converging walls  103  that converge toward one another moving from upper end  102   a  to lower end  102   b . As a result, extrudable building materials that is emitted into to hopper  102  (e.g., from outlet  101   a  of supply conduit  101 ) is funneled or channeled toward lower end  102   b  by converging walls  103  under the force of gravity. 
     As is also best shown in  FIG. 12 , pump assembly  105  is coupled to lower end  102   b  of hopper  102  and includes a pump housing  104 , a screw  106  disposed within housing  104 , and a driver  108  coupled to screw  106 . While not specifically shown, screw  106  includes one or more helical blades that engage with extrudable building material disposed within housing  104 . Driver  108  may comprise any suitable driver or prime mover, such as previously described above for drivers  42 ,  87 . In this embodiment, driver  108  comprises an electric motor that is configured to rotate screw  106  within pump housing  104  to advance extrudable building material within housing  104  into outflow conduit  110 . 
     Outflow conduit  110  is fluidly coupled to pump housing  104  at a proximal end  110   a  and includes a second or distal end  110   b  extending away from pump housing  104 . Distal end  110   b  includes an outlet  112 . In some embodiments, outlet  112  may comprise a nozzle or other flow control device. 
     Referring still to  FIGS. 11-13 , during operations, an extrudable building material is flowed from source  130  via a pump  132  (see  FIG. 13 ) that is proximate source  130  and adjacent (and potentially distal) to foundation  4 . The building material is then conducted along supply conduit  101  and emitted from outlet  101   a  into hopper  102 . The converging walls  103  of hopper  102  channel the extrudable building material down toward lower end  102   b  of hopper  102  such that the building material then enters pump housing  104  and surrounds screw  106 . Driver  108  rotates screw  106  such that the helical blades (not specifically shown) of screw  106  engage with and advance the building material within pump housing  104  toward outflow conduit  110 . Thereafter, the extrudable building material flows through outflow conduit  110  and out of outlet  112  at distal end  110   b , so that is may be deposited at a desired location along foundation  4  (or on previously deposited or printed building material). 
     Referring again to  FIG. 11 , trolley members  92 ,  94  are disposed about printing assembly  100  and are configured to support printing assembly  100  between girders  82 ′,  82 ″ during operations. First trolley member  92  is disposed about outflow conduit  110 , and second trolley member  94  is disposed about driver  108 . Thus, in this embodiment, trolley members  92 ,  94  are disposed on axially opposing sides of hopper  102  along axis  14 . 
     Referring now to  FIGS. 11, 14, and 15 , in addition to ends  82   a ,  82   b  (see  FIGS. 2 and 10 ), as depicted in  FIGS. 11 and 13 , girders  82 ′,  82 ″ also each include an inner side  82   c , and outer side  82   d , a top side  82   e , and a bottom side  82   f . Each of the sides  82   c ,  82   d ,  82   e , and  82   f  extend axially between the ends  82   a ,  82   b  of the corresponding girder  82 ′,  82 ″ with respect to axis  14 . Girders  82 ′,  82 ″ extend parallel to one another along axis  14  such that inner sides  82   c  face one another, and outer sides  82   d  face away from one another. In addition, printing assembly  100  suspended between inner sides  82   c  of girders  82 ′,  82 ″ via trolley members  92 ,  94 . 
     Referring specifically now to  FIGS. 11 and 14 , first trolley member  92  is disposed between inner sides  82   c  of girders  82 ′,  82 ″ and includes an outer housing  93  that defines an inner cavity or space  96 . Outer housing  93  includes a first or upper side  93   a  that is proximate upper side  82   e  of girders  82 ′,  82 ″, and a second or lower side  93   b  that is opposite upper side  93   a  and is proximate lower side  82   f  of girders  82 ′,  82 ″. In addition, outer housing  93  includes a first lateral side  93   c  extending between upper and lower sides  93   a  and  93   b , respectively, and a second lateral side  93   d  also extending between upper and lower sides  93   a  and  93   b  and opposite first lateral side  93   c . Thus, first lateral side  93   c  is proximate the inner side  82   c  of first girder  82 ′ and second lateral side  93   d  is proximate the inner side  82   c  of second girder  82 ″. As shown in  FIG. 11 , a support bracket  107  is mounted to upper side  93   a  of trolley member  93  to support supply conduit  101  above hopper  102  (note: supply conduit  101  and bracket  107  are omitted from  FIG. 14  so as to simplify the figure). 
     Cavity  96  receives outflow conduit  110  therethrough. A conduit support member or bracket  97  is mounted to frame member  92  within cavity  96  that engages with outflow conduit  110 . Thus, outflow conduit  110  is supported by outer housing  93  of trolley member  92  via bracket  97 . In addition, a plurality of first or upper rollers  98  extend from lateral sides  93   c ,  93   d  and engage with upper sides  82   e  of girders  82 ′,  82 ″, and a plurality of second or lower rollers  99  extend from lateral sides  93   c ,  93   d  and engage with lower sides  82   d  of girders  82 ′,  82 ″. As will be described in more detail below, rollers  98 ,  99  are configured to freely rotate relative to outer housing  93 . Accordingly, during operations trolley member  92  may traverse along axis  14  between girders  82 ′,  82 ″ via rolling engagement of rollers  98  along upper sides  83   e , and rolling engagement of rollers  99  along lower sides  82   f.    
     Referring specifically to  FIGS. 11 and 15 , second trolley member  94  is also disposed between inner sides  82   c  of girders  82 ′,  82 ″ and includes an outer housing  91  that defines an inner cavity or space  120 . Outer housing  91  includes a first or upper side  91   a  that is proximate upper side  82   e  of girders  82 ′,  82 ″, and a second or lower side  91   b  that is opposite upper side  91   a  and is proximate lower side  82   f  of girders  82 ′,  82 ″. In addition, outer housing  91  includes a first lateral side  91   c  extending between upper and lower sides  91   a  and  91   b , respectively, and a second lateral side  91   d  also extending between upper and lower sides  91   a  and  91   b  and opposite first lateral side  91   c . Thus, first lateral side  91   c  is proximate the inner side  82   c  of first girder  82 ′ and second lateral side  91   d  is proximate the inner side  82   c  of second girder  82 ″. 
     Cavity  120  receives driver  108  of printing assembly  100 . A driver support member or bracket  111  is mounted to frame member  94  within cavity  95  that engages with driver  108 . Thus, driver  108  is supported by outer housing  91  of trolley member  94  via bracket  111 . An elongate rack  114  is mounted to the inner side  82   c  of second girder  82 ″ such that rack  114  extends axially with respect to axis  14 . Specifically, in this embodiment rack  114  is mounted to the inner side  82   c  of second girder  82 ″ proximate second lateral side  91   d  of trolley frame member  94 . Rack  114  has a first or upper side  114   a  and a second or lower side  114   b  opposite upper side  114   a . Upper side  114   a  of rack  114  is more proximate upper side  82   e  than lower side  82   f  of the second girder  82 ″, and lower side  114   b  of rack  114  is more proximate the lower side  82   f  than the upper side  82   e  of second girder  82 ″. Lower side  114  includes a plurality of axially adjacent teeth  113  (note: only one tooth  113  is shown with a hidden line in  FIG. 15 ). 
     Referring still to  FIGS. 11 and 15 , a first or upper roller  112  extends from first lateral side  91   c  of outer housing  91  and engages with upper side  82   e  of first girder  82 ′. In addition, a second or lower roller  109  also extends from lateral side  91   c  of outer housing  91  and engaged with lower side  82   f  of first girder  82 ′. Further, a third roller  119  extends from second lateral side  91   d  of outer housing  91  and engages with upper side  114   a  of rack  114 . As will be described in more detail below, rollers  112 ,  109 ,  119  are configured to freely rotate relative to outer housing  91 . Accordingly, during operations trolley member  94  may traverse along axis  14  between girders  82 ′,  82 ″ via rolling engagement of roller  112  along upper side  83   e  of first girder  82 ′, rolling engagement of roller  109  along lower side  82   f  of first girder  82 ′, and rolling engagement of roller  119  along upper side  114   a  of rack  114 . 
     A driver  116  is mounted to second lateral side  91   d  of trolley frame member  94 . Driver  116  includes an output shaft  118  and is configured to rotate shaft  118  about an axis  115  that extends in a direction that is generally perpendicular to the direction of axis  14  (however, it should be appreciated that such precise alignment may not exist in other embodiments). Specifically, driver  116  is disposed within cavity  120  of trolley frame member  94  and shaft  118  extends through an aperture  117  in first lateral side  91   d  along axis  115  toward rack  114 . 
     Driver  116  may comprise any suitable driver or prime mover, such as previously described above for drivers  42 ,  87 ,  108 . In this embodiment, driver  116  comprises an electric motor (e.g., a servo motor). In addition, driver  116  is configured to rotate shaft  118  in either direction (e.g., clockwise, counterclockwise, etc.) about axis  115 . While not specifically shown in  FIG. 15 , shaft  118  includes a plurality of teeth mounted thereto (e.g., similar to teeth  41   a  mounted to shaft  41  as shown in  FIG. 7 ) that are configured to mesh with the teeth  113  of rack  114  mounted to second girder  82 ″. Thus, the teeth (not shown) of shaft  118  may form a pinion gear that is configured to mesh with rack  114 . 
     Referring now to  FIGS. 11, 14, and 15 , during operations, driver  116  rotates shaft  118  about axis  115  to selectively engage the teeth on shaft  118  with the teeth  113  on rack  114  to translate or propel printing assembly  100  along axis  14  between ends  82   a ,  82   b  of girders  82 ′,  82 ″. The movement or translation of printing assembly  100  along axis  14  further facilitated by rolling engagement of rollers  98 ,  99 ,  112 ,  109 ,  119  and girders  82 ′,  82 ″ as previously described above. 
     Referring again to  FIGS. 2 and 11 , supply conduit  101  is supported on upper side  83   e  of second girder  82 ″. As printing assembly  100  moves or traverses between girders  82 ′,  82 ″ along axis  14 , outlet  101   a  of conduit  101  is translated along with conduit  101  via the engagement with support bracket  107  on first trolley member  92 . Thus, during these operations, the remaining portions of conduit  101  are allowed to bend and flex to accommodate the movement of printing assembly  100  and outlet  101   a  along axis  14 . In some embodiments, additional cable shielding or other compliant conduit support track may be disposed about supply conduit  101  so as to facilitate and control the radius of curvature imparted to supply conduit  101  during these operations. In addition, while not specifically shown, it should be appreciated that additional cables or conduits may also be routed alongside supply conduit  101 . For example, in some embodiments, electrical cabling (e.g., cabling for routing electrical power and/or control signals to drivers  108 ,  116 ) may also be routed alongside supply conduit  101  (and thus also routed through any cable shielding or support track as described above). 
     Referring again to  FIGS. 1 and 2 , during a construction operation, printing assembly  100  is traversed along axes  12 ,  14 ,  16  about foundation  4  via gantry  50  and rail assemblies  20 . Simultaneously, printing assembly  100  is actuated (e.g., via pump assembly  105 ) to extrude or deposit building material (e.g., a cement mixture) in a plurality of vertically stacked layers thereby forming structure  5 . In particular, during these operations printing assembly  100  is traversed along the axis  12  via actuation of drivers  46  and the engagement between teeth  41   a  on shafts  41  and elongate racks  32  mounted on rail assemblies  20  (see  FIG. 4 ). In addition, printing assembly  100  is traversed along axis  14  via actuation of driver  116  and the engagement between the teeth on shaft  118  and the elongate rack  114  mounted to second girder  82 ″ of trolley bridge assembly  80  (see  FIG. 11 ). Further, printing assembly  100  is traversed along the axis  16  via actuation of drivers  87  and the threaded engagement between threaded rods  83  and the corresponding threaded collars  88  on trolley bridge assembly  80  (see  FIG. 4 ). Thus, the selective actuation of drivers  46 ,  116  (see  FIGS. 4 and 11 ) causes printing assembly  100  to be controllably maneuvered within a plane that is parallel to top surface  4   a  of foundation  4 , and the selective actuation of drivers  87  causes printing assembly  100  to be controllably translated vertically (or along axis  16 ). 
     Referring again to  FIG. 13 , the actuation of drivers  46 ,  116 ,  87  (see  FIGS. 4 and 11 ) may be monitored and controlled by a central controller  202 . Controller  202  may comprise any suitable device or assembly which is capable of receiving an electrical or informational signal and transmitting various electrical, mechanical, or informational signals to other devices (e.g., valve  201 , pump assembly  105 , etc.). In particular, in this example, controller  202  includes a processor  204  and a memory  205 . The processor  204  (e.g., microprocessor, central processing unit, or collection of such processor devices, etc.) executes machine readable instructions provided on memory  205  to provide the processor  204  with all of the functionality described herein. The memory  205  may comprise volatile storage (e.g., random access memory), non-volatile storage (e.g., flash storage, read only memory, etc.), or combinations of both volatile and non-volatile storage. Data consumed or produced by the machine readable instructions can also be stored on memory  205 . A suitable power source may also be included within or coupled to controller  202  to provide electrical power to the components within controller  202  (e.g., processor  204 , memory  205 , etc.). The power source may comprise any suitable source of electrical power such as, for example, a battery, capacitor, a converter or a local power grid, etc. 
     Controller  202  may be coupled to each of the drivers  87 ,  116 ,  46  via a plurality of communication paths  203 . Communication paths  203  may comprise any suitable wired (e.g., conductive wires, fiber optic cables, etc.) or wireless connection (e.g., WIFI, BLUETOOTH®, near field communication, radio frequency communication, infrared communication, etc.). In this embodiment, communications paths  203  comprise conductive wires that are configured to transmit power and/or communication signals during operations. In addition, as shown in  FIG. 13 , controller  202  is also coupled to each of the pump assembly  105  and pump  132  via additional conductive paths  203 . 
     During operations, controller  202  selectively actuates drivers  87 ,  116 ,  46  to controllably maneuver printing assembly  100  along each of the axes  12 ,  14 ,  16 , as previously described. In addition, controller  202  also actuates pump assembly  105  and pump  132  to controllably emit extrudable building material from outlet  112  of outflow conduit  110  as previously described. Specifically controller  202  selectively maneuvers printing assembly  100  along axes  12 ,  14 ,  16  and emits building material from outlet  112  per machine readable instructions (e.g., software) that is stored on memory  205  and executed by processor  204 . Embodiments of the machine readable instructions are discussed in more detail below; however, it should be appreciated that by executing the machine readable instructions, layers of cement are deposited on foundation  4  such that a structure (e.g., structure  5 ) is formed or printed vertically from foundation upward via construction system  10 . Referring briefly to  FIGS. 1 and 2 , in this embodiment, controller  202  may be disposed within an storage cabinet  209  that is mounted or secured to one of the vertical support assemblies  60  of gantry  50 . However, it should be appreciated that the location of controller  202  may be varied in other embodiments. 
     Referring now to  FIG. 16 , in the embodiments described above pump assembly  105  of printing assembly  100  is maneuvered carried by gantry  50  along axes  12 ,  14 ,  16  to deposit controlled layers of extrudable building material to form a structure (e.g., structure  5 ) (see  FIGS. 1, 2, 11, and 13 ). Without being limited to this or any other theory, by placing pump assembly  105  proximate to outflow conduit  110 , relatively fine control both of the flow rate and the timing of initiation and cessation of flow of building material from outlet  112  may be exercised. Thus, cement may be deposited on foundation  4  with a high level of precision. 
     However, in other embodiments, it may be desirable to locate the pump assembly  105  (and also hopper  102 ) distal to gantry  50 , so that gantry  50  need not carry the additional weight imparted by these components during a construction operation. For example, referring now to  FIG. 16 , another embodiment of printing assembly  200  is shown coupled to gantry  50  of construction system  10 . Printing assembly  200  is substantially the same as printing assembly  100 , and thus, shared components are shown with like reference numerals in  FIG. 16  and the discussion below will focus on the features of printing assembly  200  that are different from printing assembly  100 . In addition, many features of construction system  10  are not shown in  FIG. 16 , since they are not pertinent to the discussion of printing assembly  200 . However, it should be appreciated that such un-depicted features would also be included within construction system  10  in the same manner as described above. Therefore, the simplified depiction in  FIG. 16  is merely mean to simplify the figure and associated text. 
     As shown in  FIG. 16 , printing assembly  200  includes outflow conduit  110  and a pump assembly  207  that is disposed adjacent foundation  4  (or distal thereto) and therefore is not carried on gantry  50  along with outflow conduit  110 . Pump assembly  207  may be similar or the same as pump assembly  105  in some embodiments. However, in other embodiments, pump assembly  207  may be any other suitable pump(s) for pressurizing and delivering an extrudable building material from source  130  to outflow conduit  110  along supply conduit  101 . It should be appreciated that pump  132  is omitted in this embodiment due to the placement of pump assembly  207 . 
     In addition, printing assembly  200  includes a valve  201  disposed between outflow conduit  110  and pump assembly  207  along supply conduit  101 . In this embodiment (such as shown in  FIG. 16 ), valve  201  is disposed along supply conduit  101  proximate outflow conduit  110  and outlet  112 . In other embodiments, valve  201  may be disposed within or along outflow conduit  110  and may be proximate outlet  112 . Regardless, valve  201  and outflow conduit  110  are carried by gantry and are maneuvered along axes  12 ,  14 ,  16  by construction system  10  in substantially the same manner as described above for printing assembly  100 . 
     Valve  201  is an actuatable member that is configured to selectively close off or adjust the flow of extrudable building material to outflow conduit  110  from pump assembly  207 . In some embodiments, valve  201  comprises a pinch valve; however, other valve designs or arrangement may be used in other embodiments (e.g., ball valve, gate valve, butterfly valve, etc.). Valve  201  may be actuated between a fully open position, where valve  201  has little to no effect on the flow rate of building material flowing between pump assembly  207  and outflow conduit  110 , and a fully closed position, where valve  201  prevents all extrudable building material from progressing to outflow conduit  110  from pump assembly  207  via supply conduit  101 . In addition, valve  201  may also be actuated to a plurality of positions that are between the fully open and fully closed positions to progressively adjust the flow of building material between pump assembly  207  and outflow conduit  110 . Further, in this embodiment, valve  201  is pneumatically actuated with compressed air; however, other actuation methods are possible, such as, for example, electrical actuation, hydraulic actuation, mechanical actuation, or some combination thereof. 
     Referring still to  FIG. 16 , controller  202  (previously described) is communicatively coupled to each of the valve  201  and pump assembly  207  via conductive paths  203 , which are the same as previously described above (and thus may be any suitable wireless or wired connection(s)). During operations, controller  202  may actuate valve  201  (e.g., via a compressed air or other actuation system) to a desired position—including the fully closed position, the fully open position, or any of the plurality of positions between the fully open position and fully closed position. In some embodiments, controller  202  is configured to actuate valve  201  based on a number of factors, such as, for example, the operating status of pump assembly  207 , the portion of the structure (e.g., structure  5  shown in  FIG. 1 ) that is to be constructed (e.g., printed), the length of supply conduit  101  between pump assembly  207  and valve  201  (and/or outflow conduit  110 ), etc. 
     Without being limited to this or any other theory, the actuation of valve  201  may allow for precise control of the outflow of extrudable building material from outflow conduit  110  during operations even though pump assembly  207  is not disposed on gantry  50 . For example, referring now to  FIGS. 16 and 17 , a method  210  for actuating valve  201  within printing assembly  200  is shown. Method  210  may be practiced wholly or partially by controller  202  (e.g., by processor  204  executing machine readable instructions stored on memory  205 ) within printing assembly  200 . As a result, continuing reference is made to printing assembly  200  shown in  FIG. 16  in describing the features of method  210  of  FIG. 17 . However, it should be appreciated that other assemblies, systems, and/or personnel may be used to carry out method  210  in other embodiments. Thus, in describing method  210 , any reference to the actions or functions of controller  202  or the features of printing assembly  200  are merely meant to explain or describe particular embodiments of method  210  and should not be interpreted as limiting all possible embodiments of method  210 . 
     Initially method  210  begins at  212  by activating a pump assembly (e.g., pump assembly  205 ) to initiate the flow of an extrudable building material (e.g., a cement mixture) from a source (e.g., source  130 ) toward an outflow conduit (e.g., outflow conduit  110 ) of a printing assembly (e.g., printing assembly  200 ) for printing a structure (e.g., structure  5  of  FIG. 1 ). In some embodiments, a central controller (e.g., controller  202 ) may be utilized to activate the pump assembly; however, other activation methods may be used in other embodiments. For example, personnel or a separate controller may be used to activate the pump assembly and thus initiate the flow of building material toward the outflow conduit. 
     Next, method  210  includes waiting for a predetermined period of time after activating the pump assembly at  214 . For example, with reference to printing assembly  200 , block  214  may include waiting for a sufficient amount to allow building material to flow through supply conduit  101  and reach valve  201 , so that subsequent flow of cement from outlet  112  may be more precisely controlled by the actuation of valve  201 . In some embodiments, the predetermined period of time may be previously determined and stored on memory  205 , or may be calculated or determined each time the pumping of cement is initiated at  212 . In addition, the predetermined period of time from  214  may be calculated or determined based on a number of different factors and variables. For example, the predetermined period of time may be a function of the viscosity of the extrudable building material being conveyed by the pump assembly (e.g., pump assembly  207 ), the length of a supply conduit (e.g., supply conduit  101 ) between the pump assembly and the outflow conduit (or a valve deposed therealong such as valve  201 ), the diameter of the supply conduit, the flow rate of building material from the pump assembly, the local temperature and humidity, etc. 
     Referring still to  FIG. 17 , after waiting the predetermined period of time at  214  (i.e., after the predetermined period of time has elapsed), method  210  next proceeds to actuate a valve disposed proximate an outlet of the outflow conduit (e.g., valve  201 ) from a fully closed position to an open position at  216 . In some embodiments, the open position in  216  may be a fully open position for the valve or a position between the fully open position and the fully closed position. The determination of specifically which opening position (or opening degree) to place valve in at  216  may be influenced by a number of factors, such as, the desired flow rate of extrudable building material from the outlet (e.g., outlet  112 ), the viscosity of the building material, the movement rate of printing assembly (e.g., movement via gantry  50 ), etc. 
     Referring still to  FIGS. 16 and 17 , when performing method  210  with printing assembly, waiting the predetermined amount of time at block  214  allows the flow of building material from outlet  112  of outflow conduit  110  to be more precisely timed at block  216 . Specifically, the delay at block  214  may be sufficient to allow extrudable building material to flow along supply conduit  101  from pump assembly  207  to valve  201  so that there is little to no delay between the opening of valve at block  216  and the ultimate outflow or deposition of the building material. In addition, in some embodiments, controller  202  may wait the predetermined period of time at block  214  to allow to allow gantry  50  to maneuver outflow conduit  110  of printing assembly  200  (e.g., along axis  12 ,  14 ,  16 ) to the desired location on foundation  4  prior to initiating the flow of building material from outlet  112 . 
     Referring now to  FIG. 18 , another method  220  for actuating valve  201  within printing assembly  200  is shown. As with method  210  previously described, method  220  may be practiced by controller  202  (e.g., by processor  204  executing machine readable instructions stored on memory  205 ) within printing assembly  200 . As a result, continuing reference is made to  FIG. 16  in describing the features of method  220  in  FIG. 18 . However, it should be appreciated that other assemblies, systems, and/or personnel may be used to carry out method  220  in other embodiments. Thus, in describing method  210 , any reference to the actions or functions of controller  202  or the features of printing assembly  200  are merely meant to explain or describe particular embodiments of method  210  and should not be interpreted as limiting all possible embodiments of method  210 . 
     Initially, method  220  begins by stopping the pumping of extrudable building material toward an outflow conduit mounted to a printing assembly for printing a structure at  222 . For example, in the printing assembly  200  of  FIG. 16 , block  222  may include stopping the pumping of building material from pump assembly  207  (e.g., either by controller  202  or some other actuation method as previously described above). In some embodiments, the stopping of pumping with pump assembly  207  may be desirable at the cessation of printing operations (either temporarily or permanently) or at the ending of a movement of the printing assembly  200  along foundation  4  (e.g., along one or more of the axes  12 ,  14 ,  16 ). 
     Next, method  220  includes actuating a valve disposed proximate an outlet of the outflow conduit (e.g., valve  201 ) from an open position to a fully closed position at  224 . With reference to printing assembly  200 , in some embodiments the actuation of valve  201  at  224  is carried out as quickly as possible after stopping the pumping of extrudable building material from pump assembly  207 . For example, in some embodiments, the actuation of valve  201  at  224  may be carried out simultaneously, or nearly simultaneously with the stopping of pumping of building material with the pump assembly  207  at  222 . In other embodiments, the actuation of valve  201  may be carried out after a second predetermined period of time, following the stopping of pumping of building material from pump assembly  207 . Without being limited to this or any other theory, it may be desirable to quickly actuate valve  201  to the fully closed position at  224  after stopping the pumping of building material from the pump assembly  105  so that the additional cement that is still within supply conduit  101  between pump assembly  207  and valve  201  does not flow onto foundation  4 . Thus, by quickly closing valve  201  (e.g., via controller  202 ), the cessation of extrudable building material flow from outlet  112  may be more precisely controlled during operations. In other embodiments, controller  202  may close valve  201  while pump assembly  207  continues to operate. 
     While embodiments disclosed herein have utilized gantry  50  to support and maneuver a printing assembly (e.g., printing assembly  100 ,  200 ) about a foundation  4  for the additive manufacturing (e.g., 3D printing) of a structure (e.g., structure  5 ) (see  FIGS. 1 and 2 ), it should be appreciated that other embodiments of gantry  50  may be utilized in other embodiments. In particular, in some embodiments, gantry (e.g., gantry  50 ) may be collapsible in at least one dimension. Without being limited to this or any other theory, collapsing gantry (or other support and actuation structure for the printing assembly) may facilitate transportation of the construction system  10  (e.g., between job sites or between a job site a storage facility) and the storage of construction system  10  when not in use. 
     For example, referring now to  FIG. 19 , another construction system  300  for constructing a structure (e.g., structure  5 ) via 3D printing is shown. Construction system  300  is similar to construction system  10  in a number of ways, and thus, the focus of the following description and figures will be on the features and elements of construction system  300  that are different from construction system  10 . Generally speaking, construction system  300  includes a gantry  350  that movably supports a printing assembly  390  above top surface  4   a  of foundation  4 . Printing assembly  390  may be the same or similar to printing assembly  100  and/or  200 , previously described above. For example, in some embodiments, printing assembly  390  (or the portion of printing assembly  390  that is directly supported by gantry  350 ) may comprise an outflow pipe and valve similar to outflow conduit  110  and valve  201  previously described above (see  FIG. 16 ). However, printing assembly  390  may comprise a variety of different components and assemblies that are configured to controllably emit or deposit an extrudable building material onto foundation  4  during construction operations. In addition, as previously described above for gantry  50 , during operations gantry  350  may be actuated to maneuver printing assembly  390  along one or more of the axes  12 ,  14 ,  16  relative to foundation  4 . 
     Gantry  350  includes a pair of rail assemblies  320 , a pair of vertical support assemblies  360 , and a trolley bridge assembly  380 . Rail assemblies  320  may be similar to rail assemblies  20 ,  120  previously described, and thus many of the details of rail assemblies  320  are not discussed or depicted in great detail herein. Generally speaking, rail assemblies comprise a rail  322  to provide a track or path for gantry  350  to move along axis  12 . In some embodiments, rail  322  may be formed from an elongate angle member (such as angle member  28  previously described see  FIG. 3 ). 
     Referring still to  FIG. 19 , each vertical support assembly  360  includes a lower girder  368  that is movably supported on a corresponding one of the rail assemblies  320  via one or more roller assemblies (e.g., such as like roller assemblies  68  previously described above). During operations, each vertical support assembly  360  may be actuated or driven axially along rail assemblies  320  with respect to axis  12 . For example, vertical support assemblies  360  may be driven along rail assemblies  320  by an actuatable rack and pinion system (e.g., such as driver  46 , shaft  41 , and rack  32  previously described above). 
     In addition, each vertical support assembly  360  comprises a plurality of telescoping vertical pistons—namely a first or lower piston  362 , a second or middle piston  364 , and a third or upper piston  366 . Each of the pistons  362 ,  364 ,  366  is an elongate member that includes a first or upper end  362   a ,  364   a ,  366   a , respectively, and a second or lower end  362   b ,  364   b ,  366   b , respectively, opposite upper end  362   a ,  364   a ,  366   a , respectively. Further, pistons  362 ,  364 ,  366  are axially coupled to one another in a direction that is parallel to axis  16 . Specifically, lower end  366   b  of upper piston  366  is axially received within upper end  364   a  of middle piston  364 , and lower end  364   b  of middle piston  364  is axially received within upper end  362   a  of lower piston  362 . During operations, middle piston  364  may be axially actuated (again in a direction that is parallel to axis  16 ) into and out of lower piston  362 , and upper piston  366  may be similarly axially actuated into and out of middle piston  364 . Thus, the axial actuation of pistons  362 ,  364 ,  366  may controllably adjust a vertical height of vertical support assemblies  360 . Any suitable mechanism or system may be used to axially actuate pistons  362 ,  364 ,  366 , such as, for example, a hydraulic actuation system, an electric actuation system, a pneumatic actuation system, or some combination thereof. 
     Referring still to  FIG. 19 , the lower end  362   b  of lower piston  362  is coupled to lower girder  368 , and the upper end  366   a  of upper piston  366  is coupled to a mounting block  369 . Thus, the axial actuation of pistons  362 ,  364 ,  366  may adjust or change an axial spacing or distance between lower girder  368  and mounting block  369  during operations. 
     Trolley bridge assembly  380  may comprise one or more support girders  382  that extend between mounting blocks  369  of vertical support assemblies  360  along a direction that is parallel to axis  14 . Girder(s)  382  may be the same or similar to girders  82  in some embodiments. In addition, printing assembly  390  may be movably supported by girder(s)  382 . For example, printing assembly  390  may be supported by girder(s)  382  in a similar manner to that described above for printing assembly  100  and girders  82 . In addition, printing assembly  390  may be actuated to traverse along girder(s)  382  and axis  14 . In some embodiments, printing assembly  390  may be driven along girder(s)  382  by an actuatable rack and pinion system (e.g., such as driver  116 , shaft  118 , and rack  114  previously described above). 
     Construction or printing operations with construction system  300  are substantially the same as that described above for construction system  10 . However, in addition to these general operations, upon the completion of construction operations, gantry  350  may be collapsed vertically (or along axis  16 ) by telescoping each vertically support assembly  360  axially downward. Specifically, each vertical support assembly  360  may be vertically collapsed by actuating upper piston  362  into middle piston  364 , and by actuating middle piston  364  into lower piston  362 . Without being limited to this or any other theory, the axial collapse of vertical support assemblies  360  may facilitate the transportation of gantry  350  within a standard shipping container (or other suitable container) without the need to fully disassemble gantry  350 . 
     Referring now to  FIG. 20 , another construction system  400  for constructing a structure (e.g., structure  5 ) via 3D printing is shown. Construction system  400  is similar to construction systems  10  and  300  in a number of ways, and thus, the focus of the following description and figures will be on the features and elements of construction system  400  that are different from construction systems  10 ,  300 . Generally speaking, construction system  400  includes a gantry  450  that movably supports a printing assembly  490  above top surface  4   a  of foundation  4 . Printing assembly  490  may be the same or similar to printing assembly  100 ,  200 ,  390 , previously described above. For example, in some embodiments, printing assembly  490  (or the portion of printing assembly  490  that is directly supported by gantry  450 ) may comprise an outflow pipe and valve similar to outflow conduit  110  and valve  201  previously described above (see  FIG. 16 ). However, printing assembly  490  may comprise a variety of different components and assemblies that are configured to controllably emit or deposit an extrudable building material onto foundation  4  during construction operations. In addition, as previously described above for gantry  50 , during operations gantry  450  may be actuated to maneuver printing assembly  490  along one or more of the axes  12 ,  14 ,  16  relative to foundation  4 . 
     Gantry  450  includes a pair of rail assemblies  420 , a pair of vertical support assemblies  460 , and a trolley bridge assembly  480 . Rail assemblies  420  may be similar to rail assemblies  20 ,  120 ,  320  previously described, and thus many of the details of rail assemblies  420  are not discussed in great detail herein. Generally speaking, rail assemblies  420  comprise a rail (not shown in  FIG. 20 ) to provide a track or path for gantry  450  to move along axis  12 . In some embodiments, the rail (not shown) may be formed from an elongate angle member (such as angle member  28  previously described—see  FIG. 3 ). 
     Referring still to  FIG. 20 , each vertical support assembly  460  includes a lower girder  468  that is movably supported on a corresponding one of the rail assemblies  420  via one or more roller assemblies (e.g., such as like roller assemblies  68  previously described above). During operations, each vertical support assembly  460  may be actuated or driven axially along rail assemblies  420  with respect to axis  12 . For example, vertical support assemblies  460  may be driven along rail assemblies  420  by an actuatable rack and pinion system (e.g., such as driver  46 , shaft  41 , and rack  32  previously described above). 
     In addition, each vertical support assembly  460  comprises a mounting block  469 , and a scissor lift assembly  462  coupled between lower girder  468  and mounting block  469 . Scissor lift assembly  462  comprises a plurality of linking members  464  that are pivotably coupled to one another at the respective ends. During operations, hydraulic pistons or other suitable actuators (not shown) may selectively rotate linking members  464  relative to one another about their respective ends to axially raise or lower mounting block  469  relative to lower girder  468 . A central guide post  466  may be disposed within scissor lift assembly  462  and extend axially with respect to axis  16  between lower girder  468  and mounting block  469 . During operations, mounting block  469  may sliding engage with guide post  466 , via a central aperture  469   a , as mounting block  469  is raised or lowered via actuation of scissor lift assembly  464  to ensure a substantially axial movement of mounting block  469  with respect to axis  16 . 
     Trolley bridge assembly  480  may comprise one or more support girders  482  that extend between mounting blocks  469  of vertical support assemblies  360  along a direction that is parallel to axis  14 . Girders  482  may be the same or similar to girders  82  in some embodiments. In addition, printing assembly  490  may be movably supported by girders  482 . For example, printing assembly  490  may be supported by girders  482  in a similar manner to that described above for printing assembly  100  and girders  82 . In addition, printing assembly  490  may be actuated to traverse along girders  482  and axis  14 . In some embodiments, printing assembly  490  may be driven along girders  482  by an actuatable rack and pinion system (e.g., such as driver  116 , shaft  118 , and rack  114  previously described above). 
     Construction or printing operations with construction system  400  are substantially the same as that described above for construction system  10 . However, as is similarly described above for gantry  350 , in addition to general operations, upon the completion of construction operations, gantry  450  may be collapsed vertically (or along axis  16 ) by controllably lowering or collapsing vertical support assemblies  460 . In particular, vertical support assemblies  460  may be collapsed by pivoting linking members  464  within scissor lift assemblies  462  relative to one another to axially collapse mounting block  469  toward lower girder  468 . Without being limited to this or any other theory, the axial collapse of vertical support assemblies  460  may facilitate the transportation of gantry  450  within a standard shipping container (or other suitable container) without the need to fully disassemble gantry  450 . 
     In the manner described, a construction system (e.g., construction systems  10 ,  300 ,  400 , etc.) may be utilized to construct a structure (e.g., structure  5 ) via an additive manufacturing method, such as, for example 3D printing. Accordingly, by use of the construction systems disclosed herein, the time and materials required to construct a structure may be reduced. 
     Next, systems and methods will be described for the design and construction of a structure (e.g., structure  5 ) with the construction systems described herein (e.g., construction systems  10 ,  300 ,  400 ). As a result, the systems and methods described herein are directed to the design and construction of a structure via an additive manufacturing process (e.g., 3D printing). In addition, as will be described in more detail below, any or all of the methods described herein may be practiced either partially or wholly by a computing device (e.g., controller  202 ) or a plurality of computing devices. Thus, in some embodiments, the some or all of the methods described herein may be partially or wholly deployed as machine readable instructions, such as, for example, non-transitory computer readable medium that is executable by a computing device. 
     Referring now to  FIG. 21 , a floor plan of a structure  500  that may be designed and constructed according to some embodiments is shown. In this embodiment, structure  500  is a single story structure; however multi-story structures (e.g., such as a two-story or three-story structure) may also be constructed via the system and methods described herein. Structure  500  includes a plurality of walls—including a plurality of exterior walls  502  and a plurality of interior walls  504 . In addition, structure  500  includes a plurality of windows  506  extending through exterior walls  502 , and a plurality of doors frames  508  extending through both exterior walls  502  and interior walls  504 . 
     Methods of designing structure  500  will now be described with reference to  FIGS. 22-32 . In general, the following method may be utilized to design and characterize structure  500  so that a 3D printing operation to form structure  500  may be accomplished utilizing an appropriate construction system, such as, for example, construction systems  10 ,  300 ,  400 , previously described above. 
     Referring now to  FIGS. 21 and 22 , once the floor plan of structure  500  is finalized (e.g., such as the floor plan shown in  FIG. 21 ), the floor plan, including the walls  502 ,  504 , windows  506 , and door frames  508  is reduced down to a line diagram  510  including a series of line segments representing the general layout of the structure  500 . Specifically, within the line diagram  510 , each of the walls  502 ,  504  are represented by a series of line segments  512  extending between discrete points  514 , and each of the windows  506 ,  508  are represented by gaps  516  between pairs of points  514  from different line segments  512 . Within line diagram  510 , points  514  are positioned both at the ends of the line segments  512  and at points of intersection between two or more line segments  512 . 
     In addition, in this embodiment structure  500  includes a plurality of curved walls (e.g., such as two of the exterior walls  502  on structure  500 ). To represent these curved walls within line diagram  510 , the straight portions of the walls  502  are drawn as straight line segments that end in points  514  situated at the start of the curved section or portion. Next, a focal point  518  is fixed to thereby define the radius of curvature for the curved section of the wall  502 , and a curved line segment  519  is drawn along that defined curvature between the two points  514  of the adjoining straight wall portions (which are represented by line segments  512  as previously described). As a result, the line diagram  510  represents a curved wall segment as a discrete curved line segment  519  (with a designated focal point or center of curvature  518 ) that joins or intersects with two adjoining straight line segments  512  at a pair of points  514 , which thereby simplifies the geometric representation of the relatively complex curved portions of exterior walls  502  of structure  500 . 
     Without being limited to this or any other theory, by first defining a line diagram  510  to define the wall segments, window, doors, etc. of structure  500 , the nominal placement (e.g., the centerline placement) and length of each of the walls, windows, doors, etc. of structure  500  may be defined. In some embodiments, the line diagram  510  is derived (e.g., wholly or partially) by a computing device that is executing machine readable instructions. As a result, the variables, including the length of walls, the starting and ending points of walls, the curvature (for curved wall portions) of the walls, wall centerline location, the points of intersection between walls, etc. that are determined from the line diagram  510  may be captured and stored by the computing device. Thereafter, this data may be utilized in generating subsequent diagrams and plans in the manner described herein. In addition, in some embodiments, a multiple story structure may be represented by a plurality of line diagrams (e.g., like line diagram  510 ), wherein each story or level of the structure may have its own corresponding line diagram. In addition, in some embodiments, multiple line diagrams  510  may be generated for a given story of a structure (e.g., so as to represent different vertical sections or levels of the given story). 
     Referring now to  FIGS. 21-23 , after line diagram  510  (and the variable and data associated therewith) is derived for structure  500  as previously described above, a  520  shell diagram is generated for each of the walls  502 ,  504  based on the positioning and length information provided by line diagram  510 . Generally speaking, to generate shell diagram  520 , each line segment from the line diagram  510  (e.g., line segments  512 ,  514  in  FIG. 22 ) is given a wall thickness or width. In some embodiments, the wall thickness T may be represented as a distance extending perpendicular and equidistantly on each side of the line segments from the line diagram  510 . The resulting shell diagram  520  in  FIG. 23  shows the outer shell or borders  522  of the walls  502 ,  504  of structure  500 . In this embodiment, the shell diagram  520  is derived by showing all of the windows  506  and door frames  508  open. The portions of borders  522  that form the inner edges of door frames  508  and windows  506  are referred to herein as end-cap ribs  533 . As will be described in more detail below, the end-cap ribs  533  may not be present within all of the vertical sections or levels of structure  500  (e.g., such as at the top of a window or door frame where a structural header may be placed). In addition, as will also be described in more detail below, some portions of structure  500  may include wall segments that are closed proximate the windows  506  and/or door frames  508  (e.g., such as vertical sections of structure that are above or below a window  506  or above a door frame  508 ). 
     Referring still to  FIGS. 21-23 , within the shell diagram  520 , a single enclosed border  522  is designated for connected or intersecting walls. In addition, in this embodiment, the thickness T of each wall (e.g., walls  502 ,  504 ) of structure  500  is the same; however, in other embodiments, the thickness T of the walls within a given structure may be varied. In these embodiments, the differences in thickness T for the various walls of the structure may be defined within the shell diagram  520 . Further, within shell diagram  520 , a bead thickness TB may be defined for the lines forming borders  522 . The bead thickness TB may be determined by the thickness or width of the bead of extrudable building material that is extruded by the corresponding construction system (e.g., construction systems  10 ,  300 ,  400 , etc.) during a construction operation. Because the bead thickness TB influences the relative placement of the lines forming borders  522  to provide the desired wall thickness T, it is represented and included within shell diagram  520 . In some embodiments, the bead thickness TB is a function of the construction system (e.g., the size and shape of outlet  112  of outflow conduit  110  previously described), and may either be a fixed or a ranged variable. 
     As a result of the shell diagram  520 , the foot print and perimeter of structure  500  is defined. In addition, the width of the windows  506  and door frames  508  is also defined along with the internal area (e.g., square footage) of the structure  500  and any rooms defined therein. In some embodiments, shell diagram  520  may be derived (e.g., wholly or partially) by a computing device that is executing machine readable instructions. As a result, all of the above mentioned parameters and data (along with others) that are determined or derived from the shell diagram  520  are stored within the computing device, such that this data may be utilized in generating subsequent diagrams and plans in the manner described herein. In addition, a multi-story structure may be represented by a plurality of shell diagrams (e.g., like shell diagram  520 ) wherein each story or level of the structure may have its own corresponding shell diagram. In addition, in some embodiments, multiple shell diagrams  520  may be generated for a given story of a structure (e.g., so as to represent different vertical sections or levels of the given story). 
     Referring now to  FIGS. 21, 24, and 25 , once the outer borders  522  of the walls forming structure  500  are defined by shell diagram  520 , infill  531  for partially or wholly filling the space defined within borders  522  is defined within an infill diagram  530 .  FIG. 24  shows the infill diagram  530  of structure  500 , and  FIG. 24  shows the infill diagram  530  superimposed atop the shell diagram  520  of  FIG. 23  to better illustrate the features and function of the infill defined by diagram  530 . 
     The infill  531  generated within infill diagram  530  may comprise a plurality of ribs  532  that extend perpendicularly between opposing sides (or walls) of border  522 , and a plurality of lattice lines  534  (or more simply lattice  534 ) extending within the borders  522  along the walls (e.g., along the directions of the line segments from line diagram  510 ) between ribs  532  and/or end cap ribs  533 . While end-cap ribs  533  are formed as portions of border  522  as previously described, end cap ribs  533  are represented in the infill diagram of  FIG. 24  so as to show their position with respect to infill  531 . Ribs  532  are disposed proximate each of the points  514  within line diagram  510  (see  FIG. 22 ) and define a plurality of cores  540 . Thus, cores  540  may be generally disposed at the lateral edges of door frames  508  and windows  506  and at the intersection of walls  502 ,  504  within structure  500 . Accordingly, cores  540  that are formed at the edges or windows  506  or door frames  508  will include at least one end-cap rib  533 , and at least one rib  532 . 
     Cores  540  (which are defined by ribs  532  and portions of border  522 , including end-cap ribs  533  as previously described) may be substantially hollow regions within walls  502 ,  504  that are formed by a plurality of vertically aligned ribs  532 , and borders  522  (including end cap ribs  533 ) during the construction of structure  500 . In some embodiments, following the construction (e.g., printing) of structure  500 , the completed cores  540  are filled with a plurality of elongate steel members (e.g., rebar) and a cement mixture. Without being limited to this or any other theory, filled cores  540  may serve as vertical support columns within structure  500 , thereby enhancing the structural integrity of structure  500 . 
     In this embodiment, if two or more cores  540  are immediately adjacent one another within a wall or combined wall border  522  as depicted within the shell diagram  520 , the two or more cores  540  may be merged into a single core  540 . In some embodiments, if two or more cores  540  would be disposed within a certain distance X, which may be 1-10 inches along a given wall (e.g., wall  502 ,  504 ) in some embodiments, the two or more cores  540  are merged into a single core  540 . For example, cores  540  that would be disposed at the intersection of multiple walls  502 ,  504  are merged into a single core  540 . As another example, cores  540  are to be disposed at the ends of a relative short wall segment may be merged (e.g., if the distance between the two cores  540  is within distance X, previously described). 
     In this embodiment, cores  540  are all generally polygonal in shape. However, other non-polygonal shapes may be utilized in other embodiments. More specifically, many of the cores  540  within structure  500  may be rectangular and thus are defined by two ribs (e.g., either ribs  532  or a combination of ribs  532  and end cap ribs  533 ) and some portion of the corresponding border  522  (e.g., other than end-cap ribs  533 ). In addition, some of the cores  540 , such as merged cores  540  at intersection of multiple walls  502 ,  504  may be formed by more than two ribs  532 ,  533  in addition to the portions of the corresponding border  522  (again other than end-cap ribs  533 ). 
     Referring still to  FIGS. 21, 24, and 25 , lattice  534  may extend between cores  540  along the corresponding wall  502 ,  504  (e.g., along the line segments  512  defined within line diagram  510  as shown in  FIG. 22 ). Referring briefly to  FIG. 26 , lattice  534  may extend in a zig-zag pattern between the opposing borders  522  of the corresponding wall  502 ,  504  at an angle θ relative to the corresponding line segment  512  associated with the corresponding wall  502 ,  504 . The angle θ may depend on a number of different factors, such as, for example, the length along the corresponding wall (e.g., wall  502 ,  504 ) between to ribs  532 ,  533 , the thickness T of the wall, the bead thickness TB (wherein each of the thickness T and the bead thickness TB are previously described above), etc. In some embodiments, the angle θ may range from approximately 20° to approximately 45°. 
     Referring again to  FIGS. 21, 24, and 25 , in some embodiments, the length of a wall segment between two ribs  532 ,  533  may not be suitable (e.g., may not be long enough) for the placement of lattice  534 . As result, lattice  534  may be omitted within the particular wall segment, therefore forming a void  535  (see void  535  shown in  FIG. 25 ). In this embodiment, lattice  534  may be omitted within a given wall segment (thereby forming a void  535 ) when the distance between the two adjacent cores  540  within the corresponding wall segment is within a predetermined threshold limit (e.g., such as approximately 0 to 6 inches). 
     As shown in  FIGS. 24 and 25 , infill diagram  530  may further define a first subset of the infill  531  that is referred to as a variable infill  536  and a second subset of the infill  531  that is referred to as a fixed or invariable infill  538 . As will be described in more detail below, the fixed infill  538  may be present at all vertical levels or slices of structure  500 , while the variable infill  536  may be present within less than all of the vertical levels or slices of structure  500 . Typically, the variable infill  536  is associated with windows (e.g., windows  506 ) and doors frames (e.g., door frames  508 ) extending through the walls (e.g., walls  502 ,  504 ) of the structure (e.g., structure  500 , which create discontinuities within the walls when moving vertically therealong). In  FIGS. 24 and 25 , the variable infill  536  is shown with a dotted line, while the fixed infill  538  is shown with a solid line. 
     Without being limited to this or any other theory, by defining the infill  531  within infill diagram  530 , including the variable infill  536  and fixed infill  538 , the positioning of the infill  531  throughout structure  500  may be determined. As a result, as layers of extrudable building material are deposited via a printing construction operation to form structure  500 , the infill  531  from the various layers may be properly aligned throughout the vertical height of structure  500 . In some embodiments, infill diagram  530  may be derived (e.g., wholly or partially) by a computing device that is executing machine readable instructions. As a result, all of the above mentioned parameters and data (along with others) that are determined or derived from the shell diagram  530  may be stored within the computing device, such that this data may be utilized in generating subsequent diagrams and plans in the manner described herein. In addition, a multi-story structure may be represented by a plurality of infill diagrams (e.g., like shell diagram  530 ) wherein each story or level of the structure may have its own corresponding shell diagram. 
     Referring now to  FIGS. 21 and 27 , once diagrams  510 ,  520 ,  530  are derived and defined for structure  500 , a master slice  550  may be defined that represents or depicts the shared or common features of the various vertical sections or slices of the structure  500  for construction operations. In this embodiment, the master slice  550  is defined by combining many of the defined or determined parameters from each of the diagrams  510 ,  520 ,  530  shown in  FIGS. 22-25 . For example, master slice  550  may be derived by combining and superimposing the borders  522 , infill  531  (including fixed infill  538 , and variable infill  536 ) from the diagrams  520 ,  530  that are shared among multiple vertical slices of structure  500  into a single cross-sectional diagram. 
     Referring briefly to  FIG. 28 , as previously described above, according to embodiments disclosed herein, structure  500  may be constructed via a 3D printing operation, with an appropriate construction system (e.g., construction systems  10 ,  300 ,  400 , etc.). Specifically, during this process, layers  552  of extrudable building material (e.g., a cement mixture) are extruded and deposited one-by-one on a top surface  4   a  of a foundation  4  (which may comprise a concrete and rebar slab as previously described above), such that the plurality of stacked layers  552  form the structure  500 . As used herein, the term “slice” refers to a subset of vertically adjacent layers  552  within the structure  500  (e.g., such as slices  551 ,  553 ,  555 ,  557  shown in  FIG. 28  and discussed in more detail below). Accordingly, the master slice  550  of  FIG. 27  is a derived slice of structure  500  that may be imaginary (e.g., master slice  550  may not represent an actual slice of the physical structure  550 ). Once derived, the master slice  550  may be used to define the shared or common parameters and features of some or all of the slices making up the structure  500 . As a result, the design of each of the individual slices of structure  500  may be derived as a variant of the master slice  550 , so that common features (e.g., borders  522 , infill, etc.) are properly carried into each of the slices during operations. Without being limited to this or any other theory, by designing each of the actual slices of structure  500  from an imaginary master slice  550  that includes many of the shared or common components of the actual slices, vertical alignment of the shared features may be more readily and reliably achieved within structure  500 . 
     Referring now to  FIGS. 24 and 27 , master slice  550  shows all of the windows  506  and door frames  508  of structure  500  open. In addition, master slice  550  may include all infill  531  (e.g., fixed infill  538  and variable infill  536  in  FIG. 24 ) and borders  522  that are shared by multiple slices of structure  500 . Specifically, in this embodiment, master slice  550  may include all fixed infill  538  and all of the borders  522  from shell diagram  520 , including end-cap ribs  533 . As will be described in more detail below, end cap ribs  533  are not included within the vertical slice of structure  500  that includes the structural headers above the window  506  or door frames  508  (see headers  554  in  FIG. 28  which are discussed in more detail below). However, because end cap ribs  533  are included within most of the other vertical slices within structure  500  (e.g., see slices  551 ,  553 ,  557  of structure  500  shown in  FIG. 28 ), they are also included within master slice  500 . In this embodiment, the master slice  550  is identical to the slice  553  shown in  FIG. 28 ; however, this results from the specific design of structure  500 . In other embodiments, the master slice  550  may not identically match any of the sections or slices of the final structure (e.g., structure  500 ) as previously described above. 
     Referring now to  FIGS. 27 and 28 , master slice  550 , once derived, is utilized as a starting point to define specific vertical slices of structure  500  as previously described above. For example, as shown in  FIG. 28 , structure  500  includes a total of four difference slices—namely a first slice  551  extending vertically from top surface  4   a  of foundation  4  (wherein foundation  4  is the same as previously described above for structure  5 ) to the lower end of the windows  506 , a second slice  553  extending from the lower end of the windows  506  to the headers  554  of each of the windows  506  and door  508 , a third slice  555  that extends vertically through the vertical height of the headers  554 , and a fourth slice  557  extending vertically from the top of the headers  554  to the top of the walls  502 ,  504  of structure  500 . The layers  552  of extrudable building material (e.g., a cement mixture) making up each slice  551 ,  553 ,  555 ,  557  are identical within each slice (e.g., slices  551 ,  553 ,  555 ,  557 ). 
     Thus, the construction of each slice  551 ,  553 ,  555 ,  557  via a 3D printing operation may be described or represented as a repeatable set of lateral printing assembly movements (e.g., printing assemblies  100 ,  200 , etc.) relative to foundation  4  that are separated by an incrementally increasing vertical height (e.g., the height of each extruded layer of building material). Accordingly, the construction of structure  500  may then be described or represented as a finite set of lateral printing assembly movements that are each repeated a predetermined number of times, with an incrementally increasing vertical height at each repetition, wherein each specific lateral printing assembly movement is associated with one of the slices  551 ,  553 ,  555 ,  557 . The specific lateral printing movement associated with a given slice  551 ,  553 ,  555 ,  557  may also be represented as a set of instructions (e.g., machine readable instructions) that are executed by a processor (e.g., processor  204 ) of a controller (e.g., controller  202  or other computing device) associated with the construction system utilized to construct structure  500  (e.g., construction system  10 ,  300 ,  400 , etc.). Each of the specific slices  551 ,  553 ,  555 ,  557  of structure  500  will now be described with more specificity below with reference to  FIGS. 28-32 . 
     Specifically, referring first to  FIGS. 28 and 29 , first slice  551  represents the lowermost vertical slice of structure  500 . Thus, the layers  552  forming first slice  551  are stacked directly on top surface  4   a  of foundation  4 . In addition, within first slice  551 , only door frames  508  of structure  500  are open (see also  FIG. 21 ), since first slice  551  is disposed below the lower ends of the windows  506 . Accordingly, first slice  551  includes borders  522  from master slice  550  but also includes additional borders  552  disposed along the locations of windows  506 . In addition, first slice  551  includes all of the infill  531  (e.g., fixed infill  538 ) disposed within the master slice  550  (see  FIG. 27 ), and also the variable infill  536  that is disposed along windows  506  (see infill diagram  530  in  FIGS. 24 and 25 ). As a result, first slice  551  may be defined as the master slice  550  from  FIG. 27  with additional borders  522  and infill (e.g., variable infill  536 ) that is disposed along the locations of windows  506 . 
     Referring now to  FIGS. 28 and 30 , second slide  553  represents the slice of structure  500  that is vertically adjacent first slice  551  and extends vertically through the windows  506  and to the top of door frames  508 . Thus, second slice  553  includes all of the borders  522  (including end cap ribs  533 ) and fixed infill  538  from master slice  550  (see  FIG. 27 ). As a result, the second slice  552  may be defined as being a copy of the master slice  550 . 
     Referring now to  FIGS. 28 and 31 , third slice  555  represents the slice or portion of structure  50  that is encompassed by the headers  554  of door frames  508  and windows  506 . Accordingly, third slice  555  may be defined as master slice  550  but with portions of the borders  522  (including end cap ribs  533 ) removed to account for the placement of the headers  554  above the windows  506  and door frames  508 . 
     In this embodiment, headers  554  comprise elongate members that are inserted immediately above a window  506  or door frame  508  to distribute weight around the edges or sides of the windows  506  and door frames  508 . During construction of structure  500 , headers  554  are manually inserted (e.g., by a worker) before, during, or after the printing or forming of second slice  553  by the corresponding construction system (e.g., construction system  10 ,  300 ,  400 , etc.). Headers  554  may comprise any suitable material, such as, for example steel, wood, concrete (e.g., such as a concrete plank or board). As shown in  FIG. 28 , in this embodiment, headers  554  have the same vertical thickness as two layers  552  of building material, and thus third slice  555  comprises two layers  552 . In other embodiments, the vertical thickness of headers  554  may be more or less than two layers  552 . 
     Finally referring to  FIGS. 28 and 32 , fourth slice  557  extends vertically from third slice  555  (and thus from headers  554 ) to the top of the walls  502 ,  504  (see  FIG. 21 ). As can be appreciated from  FIG. 28 , the fourth slice  557  is located vertically above all of the windows  506  and door frames  508  of structure  500 . As a result, fourth slice  557  includes all of the borders  522  (including end cap ribs  533 ) included within master slice  550  and additionally includes borders  522  that extend along the locations of windows  506  and door frames  508 . In addition, fourth slice  557  includes all of the infill  531  from the master slice  550 , and additionally includes the variable infill  536  that is defined by infill diagram  530  for extending along the locations of windows  506  and door frames  508 . Therefore, fourth slice  557  may be defined as the master slice  550  with additional borders  522  and infill that extends along the locations of the windows  506  and door frames  508  within structure  500 . 
     Referring again to  FIGS. 28-32 , together, each of the slices  551 ,  553 ,  555 ,  557  may be used to form or print structure  500 . Specifically, during a printing construction operation (e.g., a construction operation utilizing a construction system  10 ,  300 ,  400 , etc.), the construction system (e.g., via a central controller, such as controller  202  previously described) may first be directed to print a predetermined number of vertically stacked layers  552  of the first slice  551 . Thereafter, the construction system may be directed to print a predetermined number of vertically layers  552  of the second slice  553  atop the previously printed layers of the first slice  551 . 
     Next, the construction system may be directed to print a predetermined number of vertically stacked layers  552  of the third slice  555  atop the previously printed layers of second slice  553 . Third slice  555  includes headers  554  as previously described above. In some embodiments, headers  554  may be placed in their positions atop the second slice  553  prior to initiating construction (e.g., printing) operations of third slice  555 . In other embodiments, headers  554  may be placed simultaneously or concurrently with printing the third slice  555 . In still other embodiments, headers  554  may be placed in their respective positions after the layers  552  of third slice  555  have been printed. 
     Regardless of the precise order or method used to place headers  554  within third slice  555 , once third slice  555  (including headers  554 ) is printed, the construction system is directed to print a predetermined number of vertically stacked layers  552  of fourth slice  557  atop third slice  553  and headers  554 . Following the printing of fourth slice  557 , a roof or other top covering (not shown) may be constructed atop fourth slice  557  to complete structure  500 . In some embodiments, the roof may be constructed atop fourth slice  557  after all of the slices  551 ,  553 ,  555 ,  557  have fully dried and cured (which may take one or several days or possibly weeks). In other embodiments, the roof may be constructed or installed atop fourth slice  557  once slices  551 ,  553 ,  555 ,  557  are partially (but not completely) dried and/or cured. 
     According, a structure  500  is constructed via a 3D printing operation, by reducing the structure down to finite sets of repeatable printing instructions or plans. These sets of instructions may be executed by the construction system (e.g., construction systems  10 ,  300 ,  400 , etc.) to print or build structure  500  layer by layer  552 , and slice by slice (e.g., slices  551 ,  553 ,  555 ,  557 ). It should be appreciated that during the printing operations described above, no forms or molds are included to contain or channel the deposited or printed extrudable building material. As will be described in more detail below, the extruable building material may be configured to stiffen relatively quickly after being deposited by the printing assembly (e.g., printing assembly  100 ,  200 ,  390 , etc.) either on top surface  4   a  of foundation  4  or on a previously printed layer  552 . However, in some embodiments, the building material does not stiffen so quickly so as not to adequately bind to the next adjacent vertical layers  552  that are subsequently deposited thereon. 
     Referring still to  FIGS. 28-32 , to facilitate the printing or forming of each layer  552  of slices  551 ,  553 ,  555 ,  557  of structure  500  as described above, a printing assembly path or a plurality of such paths (which may be more generically referred to as “tool paths”) may be defined for the depositing the layers  552  of each slice  551 ,  553 ,  555 ,  557 . The tool paths may be expressed as sets of instructions (e.g., machine readable instructions) for actuating the printing assembly relative to the foundation  4  (e.g., laterally relative to the foundation  4 ) as the printing assembly deposits beads of printing material (e.g., cement) thereon. Thus, in some embodiments the instructions for the tool paths may comprise instructions for actuating one or more drivers (e.g., drivers  42 ,  87 ,  116 ) that cause or drive a movement of a printing assembly (e.g., printing assemblies  100 ,  200 ) along a defined set of directions or axes (e.g., axes  12 ,  14 ,  16 ). 
     Referring now to  FIGS. 33 and 34 , which show sequential schematic views of a printing operation for a single layer  552  of a slice of another structure  560 . Structure  560  is a single room structure that includes a plurality of exterior walls  502  and a single door frame  508 . As with structure  500 , previously described, the walls  502  of structure  560  are defined by a plurality of borders  522  (including end cap ribs  533  at door frame  508 ). In addition, infill  531 , which further includes ribs  532  and lattice  534 , is disposed within borders  522  of walls  502 . 
     Referring first to  FIG. 33 , during a printing operation for a layer (e.g., layer  552 ) of structure  560 , a printing assembly  570  (which may be the same or similar to printing assemblies  100 ,  200 ,  390  previously described) is first traversed about foundation in a first tool path  572  while simultaneously extruding lines or beads of building material (e.g., cement) to form the outer borders  522  of walls  502 . 
     The first tool path  572  of printing assembly  570  may include a plurality of movements. For example, in this embodiment, tool path  572  first moves printing assembly  570  along the borders  522  of the walls  502 . In particular, printing assembly  570  is traversed across foundation  4  from a starting position  573  along a continuous path while printing assembly  570  deposits a line of extrudable building material (e.g., a cement mixture) that forms the connected borders  522  of walls  502 . In this case, because structure  560  only includes exterior walls  502 , all of the walls  502  are interconnected, such that one single continuous movement of printing assembly  570  that starts and ends at starting point  573  may be performed to print an enclosed border  522 . In other embodiments (e.g., such as when printing the slices  551 ,  553 ,  555 ,  557  of structure  500 ), printing assembly  570  may be traversed along a plurality of loops or routes to form a continuous enclosed border  522  about each connected set of walls  502 ,  504  (see e.g., the separate enclosed borders  522  of shell diagram  520  in  FIG. 23 ). 
     Referring specifically to  FIG. 34 , after borders  522  of walls  502  are formed or printed by printing assembly  570 , the printing assembly  570  may then be traversed along a second tool path  574  while simultaneously extruding lines or bands of extrudable building material (e.g., a cement mixture) to form the infill  531 , including ribs  532  and lattice  534  within borders  522 . The second tool path  574  may include a plurality of movements. For example, in this embodiment, tool path  574  moves printing assembly  570  along the walls  502  from a starting point  575  along continuous path that tracks generally along walls  502 . As printing assembly  570  advances along walls  502  and tool path  574 , it is maneuvered as necessary to form the ribs  532  and lattice  534  in desired locations (e.g., printing assembly  570  may be moved in a zig-zag pattern as part of the tool path  574  to form lattice  534 ). In this embodiment, because structure  560  only includes exterior walls  502  and all the walls  502  are interconnected as previously described, one single continuous movement of the printing assembly  570  may be defined for the second tool path  574  that starts and ends at starting point  575 . In other embodiments, (e.g., such as when printing the slices  551 ,  553 ,  555 ,  557  of structure  500 ), printing assembly  570  may be traversed along a plurality of loops or routes to form the infill (e.g., including ribs  532  and lattice  534 ) within the enclosed border  522  of each connected set of walls  502 ,  504 . 
     In some embodiments, the final tool paths for printing assembly  570  (e.g., tool paths  572 ,  574 ) when printing a layer of a slice of a structure (e.g., structures  560 ,  500 , etc.) may be determined by first calculating or otherwise determining some or all of the possible tool paths that may be taken to form the borders  522 , ribs  532 , and lattice  534  of the given slice. Thereafter, the most efficient of the plurality of calculated paths may be chosen as the final path(s) for printing assembly  570 . 
     Referring now to  FIG. 35 , a system  580  for carrying out some or all of the structure design and construction methods described herein is shown. System  580  includes a first computing device  581 , a second computing device  588 , and a construction system  590 . Construction system  590  may be the same or similar as constructions systems  10 ,  300 ,  400 , previously described, and thus, the descriptions of these constructions systems  10 ,  300 ,  400  may be applied to describe construction system  590 . 
     First computing device  581  and second computing device  588  may comprise any suitable computing device (or collection of such devices). Thus, computing devices  581 ,  588  may include one or more processors, memory devices, power sources, etc. to enable the computing devices  581 ,  588  to perform all of the functions disclosed herein (e.g., such as processor  204  and memory  205  described above for controller  202 ). For example, computing devices  581 ,  588  may comprise one or more computers, servers, controllers, or the like. In some embodiments, second computing device  588  may comprise controller  202  previously described. In addition some embodiments, the first computing device  581  and the second computing device  588  may be integrated within a single computing device. 
     Referring still to  FIG. 35 , first computing device  581  includes machine readable instructions that are stored on a suitable memory device (e.g., any one or more of the memory devices discussed above for controller  202 ). In particular, first computing device  581  includes a set of slice generation instructions  582 , a set of tool path generation instructions  584 , and a set of construction instructions  586 . In some embodiments, some or all of the instructions  582 ,  584 ,  586  may be integrated into a single set of instructions. Still further, in some embodiments, any one of the instructions  582 ,  584 ,  586  may be separated out into a plurality of separate sets of instructions. 
     Slice generation instructions  582  may include machine readable instructions that, when executed by computing device  581  (or a processor of the computing device  581 ), generate a plurality of vertical slices of a structure to be constructed, such as slices  551 ,  553 ,  555 ,  557  of structure  500  previously described. When executed by computing device  581 , the slice generation instructions  582  may generate the slices for the structure based on a number of inputs (e.g., wall thickness T, bead thickness TB, structure dimensions, etc.). In addition, when executed by computing device  581 , the slice generation instructions  582  may first generate a plurality of diagrams, such as the diagrams  510 ,  520   530  previously described above, and then utilize these generated diagrams in the manner previously described to generate master slice such as, for example, master slice  550 . Further, when executed by the computing device  581 , the slice generation instructions may then generate the slices (e.g., slices  551 ,  553 ,  555 ,  557 ) of the structure based on the master slice (e.g., master slice  550 ) as previously described. 
     Tool path generation instruction  584  includes machine readable instructions, that when executed by computing device  581  (or a processor of computing device  581 ), generate one or more tool paths for a printing assembly (e.g., printing assembly  100 ,  200  etc.) during printing of the slices generated by the slice generation instructions  582 . The tool path generation instructions  584 , when executed by first computing device  581 , may generate the tool path(s) in substantially the same manner as discussed above for example structure  560 . Specifically, in some embodiments, the tool path generation instructions  584 , when executed by first computing device  581 , may generate the tool paths such that the outer borders (e.g., border  522 ) of walls (e.g., walls  502 ,  504 ) within a given slice are printed first, and then infill (e.g., ribs  532 , lattice  534 ) is printed within the previously printed borders  522 . 
     Construction instructions  586  include machine readable instructions, that when executed by computing device  581  (or a processor of computing device  581 ), generate a sequence of construction steps for a construction system (e.g., construction system  590 ) during a printing or construction process. In particular, the construction instructions  586  may, when executed by the computing device  581 , generate a series of instructions for printing a predetermined number of layers of each slice generated by the slice generation instructions  582  by moving the printing assembly of the construction system  590  along one or more of the tool paths generated by the tool path generation instructions  584 . Specifically, in some embodiments, the construction instruction  586  may, when executed by the computing device  581 , generate a set of instructions for printing a predetermined plurality of layers (e.g., layers  552 ) of a first slice (e.g., first slice  551 ) of a structure (e.g., structure  500 ) generated by the slice generation instruction  582 , by moving the printing assembly of the construction system along one or more tool paths (e.g., tool paths  572 ,  574 ) generated the tool path generation instruction  584  to form each layer. In addition, the construction instructions  586  may also provide instructions for similarly printing other layers of the other slices of the structure along designated tool paths generated by the tool path generation instructions. 
     Second computing device may receive the specific instructions and data generated by slice generation instructions  582 , tool path generation instruction  584 , and construction instruction  586  within first computing device  581  via a connection  583 . Connection  583  may be any suitable wireless or wired connection (e.g., such as any of the above described wireless or wired connections). In addition, connection  583  may comprise a removable storage device (e.g., USB thumb drive, disc, etc.) that receives and stores the specific instructions from first computing device  581 , and then transfers the received specific instructions to second computing device  588  by being connected to second computing device  588 . 
     Referring still to  FIG. 35 , second computing device (which again may comprise controller  202  previously described above), may then execute the instructions generated within first computing device  581  and therefore actuate construction system (e.g., via another connection  583 ) to print the vertically stacked layers (e.g., layers  552 ) and slices (e.g., slices  551 ,  5553 ,  555 ,  557 ) of the structure (e.g., structure  500 ) as previously described above. 
     Referring now to  FIG. 36 , an embodiment of a method  600  of designing and constructing a structure (e.g., structures  5 ,  500 ,  560 ) is shown. In describing the specific steps of method  600 , reference may be made to structure  500 , diagrams  510 ,  520   530 , slices  550 ,  551 ,  553 ,  555 ,  557  shown in  FIGS. 21-25 and 27-32 ; however, it should be appreciated that method  600  may be practiced separately from these specific embodiments. Thus, specific reference to the embodiments and descriptions associated with  FIGS. 21-25 and 27-32  is meant to provide additional clarity to method  600  and should be interpreted as limiting the potential scope thereof. In addition, some or all of the portions of method  600  may be practiced, in some embodiments, by computing devices (e.g., computing devices  581 ,  588  within system  580  previously described). 
     Initially, method  600  begins by defining a plurality of parameters for a structure to be constructed  605 . For example, with reference to structure  500 , parameters such as the bead thickness TB, the wall thickness T, the location and number of door frames  508  and windows  506 , the general layout of interior and exterior walls  504  and  502 , respectively, of the structure  500  may be predetermined and defined at  605 . In some embodiments, at least some of the above described parameters, such as, for example, the locations of door frames  508  and windows  506  may be determined and derived at  605  by generating a line diagram for structure  500 , such as the line diagram  510  shown in  FIG. 22  and previously described above. 
     Next, method  600  includes deriving the shells (or outer borders) of the internal and external walls of the structure at  610  based on the plurality of parameters defined at  605 . For example, with reference to structure  500 , a shell diagram  520  may be derived at  610  that defines the general outline or border  522  of the exterior walls  502  and the interior walls  504  of structure  500 . Method  600  also includes deriving infill to be disposed within the borders of the internal and external walls of the structure at  615 . For example, with reference to structure  500 , an infill diagram  530  may be derived at  615  that defines the infill  531  to be disposed within the borders  522  of the exterior walls  502  and the interior walls  504  at  615 . Accordingly, at  615 , a plurality of ribs (e.g., ribs  532 ) and lattice  534  may be derived and placed within borders  522 . In addition, the derivation of infill at  615  may further include the defining of fixed infill  538  and variable infill  536  in the manner previously described above. 
     Next, method  600  includes deriving a master slice at  620  that includes borders and infill derived at  610  and  615 , respectively, that are shared or are common for multiple vertical slices of the structure at  620 . For example, with reference to structure  500 , a master slice  550 , previously described, may be derived at  620 . Thereafter, method  600  progresses to derive a plurality of slices that each represents a vertical slice or section of the structure at  625 . For example, referring to structure  500 , a plurality of slices  551 ,  553 ,  555 ,  557  (see  FIGS. 28-32 ) are defined that each represent a vertical section or slice of structure  500 . In some embodiments (such as those described above), the slices derived at  625  may be defined as variants of the master slice derived at  620 , such as is previously described above for slices  551 ,  553 ,  555 ,  557  and master slice  550 . 
     Method  600  next includes generating a set of instructions at  630  for printing each slice derived at  625 . In some embodiments, the instructions generated at  630  may be instructions for a series of tool movements (e.g., tool paths  572 ,  574 ), such as, movements of a printing assembly (e.g., printing assembly  100 ,  200 ,  390 , etc.) across a foundation (e.g., foundation  4 ) as previously described above. In some embodiments, the instructions may be similar to those discussed above for printing slices  551 ,  553 ,  555 ,  557  of structure  500 . 
     Finally, method  600  includes printing a layer of a first of the slices at  635  per the instructions generated at  630 , repeating the printing at  635  to form a plurality of vertically stacked layers of the first slice at  640 , and repeating the printing at  635  and  640  to form a plurality of vertically stacked layers of each of the slices. For example, with reference to structure  500 , multiple vertically stacked layers  552  of each slice  551 ,  553 ,  555 ,  557  may be sequentially printed in a predetermined order as previously described above in order to print structure  500 . Specifically, a layer  552  of a first slice  551  may be printed, and then additional layers  552  of first slice  551  may be printed to form a plurality of vertically stacked layers  552  of first slice  551 . Then this process is repeated at number of times to sequentially form the plurality of stacked layers  552  of each of the slices  552 ,  555 ,  557  as previously described. 
     During the performance of blocks  635 ,  640 ,  645 , additional components may be inserted or installed within and amongst the plurality of vertically stacked layers. For example, other structural members (e.g., headers  554 ) as well as utility conduits (e.g., plumbing, electrical conductors, etc.) may be installed. In addition, the installation of some or all of these additional components may occur after the performance of  635 ,  640 ,  645 . 
     In the manner described, systems and methods for designing and constructing a structure via 3D printing have been described. In some embodiments, the above described methods and systems may be utilized with any one of the constructions systems previously described herein to construct a structure. Accordingly, by use of the systems and methods disclosed herein, the time and materials required to construct a structure may be reduced. 
     While exemplary embodiments have been shown and described, modifications thereof can be made by one skilled in the art without departing from the scope or teachings herein. The embodiments described herein are exemplary only and are not limiting. Many variations and modifications of the systems, apparatus, and processes described herein are possible and are within the scope of the disclosure. Accordingly, the scope of protection is not limited to the embodiments described herein, but is only limited by the claims that follow, the scope of which shall include all equivalents of the subject matter of the claims. Unless expressly stated otherwise, the steps in a method claim may be performed in any order. The recitation of identifiers such as (a), (b), (c) or (1), (2), (3) before steps in a method claim are not intended to and do not specify a particular order to the steps, but rather are used to simplify subsequent reference to such steps.