Abstract:
A system for fabricating an object includes an extruder for one or more deposition materials having at least one nozzle and a movable support for the nozzle. The nozzle has a nozzle axis and is rotatably attached to the movable support via a connector that is actuatable relative to the movable support to change an angular orientation of the nozzle axis, thus varying an angle between the nozzle axis and a deposition surface. The system also includes a controller that can apply a correction factor calculated for a path of the nozzle when an acute angle is formed between the nozzle axis and the deposition surface, the correction factor for moving toward the acute angle being different from that when moving away from it. The correction factor removes differences in thickness of the deposited material caused by variations in the angle formed between the nozzle axis and the deposition surface.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit under 35 U.S.C. §119(e) of U.S. Patent Application No. 62/014,453, titled MATERIAL DEPOSITION SYSTEMS WITH FOUR OR MORE AXES, filed Jun. 19, 2014. The disclosure of the above application is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     This specification relates to three dimensional (3D) printing or additive manufacturing, such as fused deposition modeling (FDM). 
     FDM using extruded polymer filament has evolved rapidly and is useful for creating reasonably accurate three dimensional objects quickly. Current FDM printing is typically accomplished by forcing a solid plastic feedstock through a heated nozzle with smaller diameter than the original feedstock. The filament is liquefied before or as it passes through the constriction in the nozzle, and the feed pressure causes material to be extruded with a cross section approximately equal to the nozzle exit. Other 3D printing techniques referred to in this application include selective laser sintering (SLS), stereolithography (SLA), direct metal laser sintering (DMLS) and material jetting processes such as ObJet. 
     SUMMARY 
     This specification relates to 3D printing or additive manufacturing, such as FDM. 
     According to one aspect, a system for fabricating an object includes: an extruder for one or more deposition materials, the extruder including at least one nozzle and a movable support for the nozzle, wherein the nozzle has a nozzle axis and is rotatably attached to the movable support via a connector that is actuatable relative to the movable support to change an angular orientation of the nozzle axis relative to the movable support so as to vary an angle between the nozzle axis and a deposition surface during deposition of a deposition material; and a controller coupled with the extruder, the controller configured and arranged to apply a correction factor calculated for a path of the nozzle based on the angle formed between the nozzle axis and the deposition surface being an acute angle, the correction factor for the nozzle moving toward the acute angle being different from the correction factor for the nozzle moving away from the acute angle. The correction factor removes differences in thickness of the deposited material caused by variations in the angle formed between the nozzle axis and the deposition surface. 
     Implementations according to this aspect may include one or more of the following features. For example, the connector can be configured to be actuated with at least two degrees of freedom for the nozzle relative to the movable support. The extruder can include a softening zone positioned upstream of an actuation point of the connector, the softening zone being configured to increase flexibility of a feedstock material passing through the softening zone. The softening zone can be configured to apply heat to the feedstock material passing therethrough. The extruder can include forming rollers that are configured to flatten the feedstock material passing therethrough. The nozzle can include the connector. The system can be configured to move the movable support and the nozzle relative to the object being fabricated along three orthogonal axes to thereby provide three degrees of freedom relative to the object, the nozzle being rotatably attached to the movable support via the connector to rotate about a first axis that is transverse to the nozzle axis to thereby provide a fourth degree of freedom relative to the object, and the system can include a rotatable base on which the object being fabricated is placed, the controller being configured to rotate the base during deposition to thereby provide a fifth degree of freedom between the nozzle and the object. In some cases, the system can be configured to move the movable support and the nozzle relative to the object being fabricated along three orthogonal axes to thereby provide three degrees of freedom relative to the object, the nozzle being rotatably attached to the movable support via the connector to rotate about a first axis that is transverse to the nozzle axis to thereby provide a fourth degree of freedom relative to the object, and the connector can be rotatably connected to the movable support to allow the connector and the nozzle to rotate about the nozzle axis to thereby provide a fifth degree of freedom relative to the object. In some cases, the system can be configured to move the nozzle relative to the object being fabricated along three orthogonal axes to thereby provide three degrees of freedom relative to the object, and the connector can include a multi-link coupler that is rotatably attached to the movable support to rotate about a first axis that is transverse to the nozzle axis, the nozzle being rotatably attached to the multi-link coupler to rotate about a second axis that is transverse to the first axis to thereby provide two additional degrees freedom relative to the object. The correction factor can cause the path of the nozzle to become farther from the surface of the object when the nozzle is moving away from the acute angle. The correction factor can cause the path of the nozzle to become closer to the surface of the object when the nozzle is moving toward the acute angle. Based on the nozzle moving away from the acute angle, the controller can be apply the correction factor that causes the path of the nozzle to become farther from the surface of the object, and based on the nozzle moving toward the acute angle, the controller can apply the correction factor that causes the path of the nozzle to become closer to the surface of the object. Based on determining that the nozzle makes contact with any portion of the system or the object, the controller can cause the angular orientation of the nozzle to change to avoid making contact. The extruder can include a feedstock channel through which a feedstock material passes during deposition, the feedstock channel providing a curved path between the extruder and the rotated nozzle, and wherein the controller is configured to change a volume flow rate of the feedstock material according to a curvature of the feedstock channel. 
     According to another aspect, a non-transitory computer-readable medium storing software includes instructions executable by one or more computers, which, upon such execution, cause the one or more computers to perform operations for controlling a 3D printer to create a 3D object, the 3D printer including an extruder for one or more deposition materials, the extruder including at least one nozzle and a movable support for the nozzle, wherein the nozzle has a nozzle axis and is rotatably attached to the movable support via a connector that is actuatable relative to the movable support to change an angular orientation of the nozzle axis relative to the movable support so as to vary an angle between the nozzle axis and a deposition surface during deposition of a deposition material. The operations include applying a correction factor calculated for a path of the nozzle based on the angle formed between the nozzle axis and the deposition surface being an acute angle, the correction factor for the nozzle moving toward the acute angle being different from the correction factor for the nozzle moving away from the acute angle, and causing movement of the nozzle along the path to deposit material to form the object, wherein the correction factor removes differences in thickness of the deposited material caused by variations in the angle formed between the nozzle axis and the deposition surface. 
     According to yet another aspect, a process for additively fabricating components with improved resistance to delamination includes using a material deposition system and depositing one or more first material segments of a first material with at least one first locking portion and one or more secondary material segments of a second material with at least one second locking portion. The second locking portions have a shape that is defined by the shape of the first locking portions such that the second locking portions form an interlock with the first locking portions. The first and second material segments can each include a continuous material. Components can be fabricated from such continuous materials to have comparable resistance to delamination or breakage in all directions. 
     Implementations according to this aspect may include one or more of the following features. For example, the first and/or second materials can include continuous fibers. The materials can include composite materials such as fibers and a matrix material. The matrix material can be a thermoplastic. The fibers can have a range of lengths, and the matrix material can be, for example, concrete or another cement-like or similar hardening mineral compound. In some cases, the matrix material can be a thermoset. The first and second materials can be deposited through a nozzle having an orifice. In some cases, the first and second materials can be made from the same material. The first material segments and second material segments can be formed from a continuous material (i.e. forming the second material segment after the first material segment without cutting the material so they are connected and continuous). Avoiding cutting fibers and restarting the deposition process can have several benefits including improving speed and reliability of the process as well as part strength. The first interlocking portions can include gaps, and second interlocking portions can include tabs. Here, the tabs can be formed by forcing the second material into the gaps. In some cases, the gaps can include a narrow region and a wider region, and the second material can be forced through the narrow region into the wider region to form a physical interlock between the second interlocking portion and the first interlocking portion. The first material segments can take the form of one or more first material layers, and the secondary material segments take the form of one or more secondary material layers. The interlock can prevent delamination of the second material layers from the first material layers. The material layers can be curved or non-planar. The material deposition system can control at least two translational and one rotational degrees of freedom (i.e. axes of motion) between the component being built and the material deposition system. 
     The details of one or more implementations of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the invention will become apparent from the description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an example FDM 3D printing system. 
         FIGS. 2 a  and 2 b    show a fixed angle nozzle depositing material on a sloped surface. 
         FIGS. 3 a -3 f    show an example variable angle nozzle depositing material on a sloped surface according to an implementation of this disclosure. 
         FIG. 4  shows a cross section view of a sample part made using a 5-axis FDM system. 
         FIG. 5  shows a cross section of a sample part with interlocking layers made using a 5-axis FDM system. 
         FIGS. 6 a -6 b    show side cross section views of an example implementation of an articulating material dispensing system. 
         FIGS. 7 a -7 b    show side cross section and isometric views of another example implementation of an articulating material dispensing system. 
         FIGS. 8 a -8 d    show various views of an example material guide system. 
         FIG. 9  shows an isometric view of another example implementation of an articulating material dispensing system. 
         FIGS. 10 a -10 c    show example implementations of a roller-based feeding system. 
         FIGS. 11 a -11 b    show an example implementation of an articulating material dispensing system having drive dogs. 
         FIG. 12  shows an isometric view of an example implementation of an articulating material dispensing system having a rotating base. 
         FIGS. 13 a -13 b    show side and front cross sections views of another example implementation of an articulating material dispensing system. 
         FIGS. 14 a -14 b    show side cross section views of another example implementation of an articulating material dispensing system. 
         FIGS. 15 a -15 e    show various views of another example implementation of an articulating material dispensing system. 
         FIG. 16  shows a side view of another example implementation of an articulating material dispensing system. 
         FIGS. 17 a -17 c    show isometric, top, and front views of an example deposited element having an interlocking feature. 
         FIG. 18  shows multiple elements from  FIGS. 17 a -17 c    deposited next to each other. 
         FIGS. 19 a -19 c    show isometric, top, and front views of another example deposited element having an interlocking features. 
         FIG. 20  shows multiple elements from  FIGS. 19 a -19 c    deposited next to each other. 
         FIGS. 21 a -21 b    show front and isometric views of an example two-layer interlocking structure. 
         FIGS. 22 a -22 b    show front and isometric views of an example three-layer interlocking structure. 
         FIGS. 23 a -23 b    show front and isometric views of an example four-layer interlocking structure. 
         FIGS. 24 a -24 b    show front and isometric views of an example twelve-layer interlocking structure. 
     
    
    
     Like reference numbers and designations in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , an example FDM 3D printing system  100  includes an extruder or 3D printer  102 , a controller  104 , and a communication link  106  that links the extruder  102  to the controller  104 . The 3D printer  102  includes an extruder nozzle  108 . The FDM system  100  can produce 3D products such as item  120 . The controller  104  can include one or more processors, memory, hard drive, solid-state drive, and/or input devices such as touch screen, mouse, or voice input capability. In some cases, the controller  104  can be an internet server or some other device, computer, processor, phone, or tablet. In some cases, the controller  104  and extruder  102  are integrated into a single 3D printing device. 
     Referring now to  FIG. 2 a   , a nozzle  200 , for example from an FDM system such as system  100 , is shown depositing material  202  on a sloped part surface  204  with a motion of travel in a downward sloping direction along part surface  204 . The nozzle  200  can be a nozzle tip designed for use with an FDM system or it can be from a different material deposition system such as a welding tip or electrode, syringe, adhesive material deposition system, material solidification system, material curing system or material pump, or combinations thereof. As shown the nozzle  200  is constrained to maintain its vertically oriented position. In other words, the nozzle  200  can move along, for example, the x, y, and z coordinates during deposition but will not be able to further change the angle at which it deposits material. Accordingly, the system depicted in  FIG. 2 a    may be referred to as a 3-axis FDM system. Implementations of the 3-axis FDM system are further described in related U.S. patent application Ser. No. 14/663,393, filed Mar. 19, 2015, titled SYSTEMS AND METHODS FOR IMPROVED 3D PRINTING, hereby incorporated by reference in its entirety. 
       FIG. 2 b    shows the nozzle  200 , likewise constrained to the vertical orientation, depositing material  202  on the sloped part surface  204  with a motion of travel in an upward direction along the part surface  204 . Here, the nozzle  200  is shown moving uphill relative to the part surface  204  instead of downhill as in  FIG. 2 a   . The nozzle  200  can be a nozzle designed for use with an FDM system or it can be from a material deposition system such as a welding tip or electrode, syringe, adhesive material deposition system, material solidification system, material curing system or material pump or combinations thereof. 
     As shown in  FIGS. 2 a  and 2 b   , the distance between the nozzle  200  and the part surface  204  can be varied depending on whether the nozzle  200  is moving downward or upward to thereby ensure that the resulting deposited material thickness can be similar or the same when the nozzle travels downhill or uphill or horizontally. 
     For example, in one method of correcting the position or path of the nozzle  200 , corrections can be made in the following way: a first nominal path or set of positions for the nozzle  200  is computed independent of the direction of travel of the nozzle  200  or the slope of the path of the nozzle  200 . Then a second path can be created by adjusting vertical position values by an amount dependent on the slope of the path of the nozzle  200 . The slope of the path may be defined as vertical distance moved over an interval divided by horizontal distance moved over the same interval, or as rate of instantaneous vertical motion divided by rate of instantaneous horizontal motion. 
       FIGS. 3 a , 3 b , and 3 c    show material deposition on a sloped surface by an FDM system with a nozzle that is not constrained to be vertical. This can be for example an FDM system with additional axes to allow rotation of the nozzle, which is discussed in further detail below. 
     Referring to  FIG. 3 a   , a nozzle  300  is shown depositing material  302  along a surface with the nozzle axis perpendicular to a local surface  304 . In this case, the nozzle  300  can deposit the material  302  to have the same thickness while traveling in either direction along a given path. That is, the path can be the same for a nozzle moving in either direction to deposit material of a desired thickness. 
     Referring to  FIG. 3 b   , the nozzle  300  is shown depositing the material  302  along a sloped surface in an orientation such that the nozzle axis is not perpendicular to the local surface  304 . The nozzle  300  shown in  FIG. 3 b    can have one or more movable angle motion degrees of freedom or actuation so that the angle of a nozzle axis  306  with respect to vertical can be changed or can change along a path. The nozzle  300  in  FIG. 3 b    can have an acute angle  308  between its axis and the surface on one side (the “acute angle side”). The nozzle  300  in  FIG. 3 b    is shown traveling toward the side that forms the acute angle side as it deposits material that is left behind on the local surface  304 . 
     Referring to  FIG. 3 c   , the nozzle  300  is shown in a similar configuration as in  FIG. 3 b   , that is, in the same orientation as in  FIG. 3 b    while depositing material along the same sloped surface, but is instead shown moving away from the side that forms the acute angle. In order to deposit material of a given desired thickness, the nozzle  300  must follow a different path while moving toward the acute angle side as in  FIG. 3 b    as compared to moving away from the acute angle side as in  FIG. 3 c   . The path that the nozzle  300  follows can be closer to the surface  304  when the nozzle moves toward the acute angle as in  FIG. 3 b    and the path can be farther away from the surface  304  when the nozzle  300  moves away from the acute angle as in  FIG. 3 c    in order to deposit material of the same thickness in both cases. 
     Generally, a nominal path may be a path that a nozzle with axis perpendicular to the local surface should follow to deposit material of a given thickness in either direction. A nominal path may be adjusted to accommodate a non-perpendicular angle between the nozzle and the local surface while still depositing material of the same thickness by adjusting the path away from the local surface in areas where the nozzle moves away from the acute angle between the nozzle axis and the surface and adjusting the path to be closer to the surface in areas where the nozzle moves toward the acute angle. 
     Referring now to  FIG. 3 d   , a nozzle  310  with an orientation angle Φ 1  between a nozzle axis  312  and a part surface  314 . The angle between the surface  314  and a plane perpendicular to the nozzle axis can be defined as angle Φ 2 . Φ 2  can therefore represent the angle of the nozzle tip to the part surface at a specific location. As shown, the nozzle has a tip outer diameter D o  and a tip inner diameter D i . Nozzle tip inner diameter D i  can represent a nozzle exit orifice. A nominal path for the nozzle to follow can be represented by a series of position points, such that at each point along the nominal path there can be a distance, h o , between the local surface and the center of the nozzle exit orifice, where h o  can be measured perpendicular to the local surface. 
       FIG. 3 e    shows the nozzle  310  of  FIG. 3 d    traveling toward the side that forms the acute angle Φ 1 . The angle Φ 2  is similarly shown as in  FIG. 3 d   . In order for the nozzle  310  with angle Φ 1  to deposit material having the same thickness as a nozzle that is perpendicular to the local surface (for example, see  FIG. 3 a   ), an adjustment can be made to the path of travel such that a new distance between the surface and the center of the nozzle exit orifice, h 1 , is less than h o . One example way to accomplish this adjustment can be by making the following calculation: adjustment′=(D i /2)*sin(Φ 2 ). The new path point can be found as: h 1 =h o −adjustment 1 . Corresponding x,y,z coordinates or other suitable coordinates can be calculated with knowledge of Φ 2 , h o , and h 1 . The path in this case can be closer to the surface than the nominal path because the inside edge of the nozzle orifice largely determines the resulting material thickness. 
       FIG. 3 f    shows the nozzle  310  of  FIG. 3 d    traveling in a direction away from acute angle Φ 1 . Again, Φ 2  is defined the same as in  FIG. 3 d   . In order for the nozzle  310  with angle Φ 1  to deposit material in the same thickness as a nozzle that is perpendicular to the local surface (not shown here, but see  FIG. 3 a   ), an adjustment can be made to the path of travel such that a new distance between the surface and the center of the nozzle exit orifice, h 2 , is greater than h o . One example way to accomplish this adjustment can be by making the following calculation: adjustment 2 =(D o /2)*sin(Φ 2 ). The new path point can be found as: h 1 =h o +adjustment 2 . Corresponding x,y,z coordinates or other suitable coordinates can be calculated with knowledge of Φ 2 , h o , and h 2 . The path in this case can be farther from the surface than the nominal path because the outside edge of the nozzle tip largely determines the resulting material thickness. 
     Other calculations can be used to make corresponding adjustments based on Φ 2 , h o , and h 1 . In some cases, one or more of nozzle geometry, type of material being deposited, surface properties, etc. can be used to determine the necessary adjustments. 
     Referring now to  FIG. 4 , a cross-section of an example part  400  is shown. The part  400  may be made by using a 5-axis FDM system or other material deposition system with a nozzle that can change angular orientation relative to the part. Part  400  is made of multiple layers  402  of deposited material that may be non-planar. In some cases, such layers  402  of deposited material may have a tendency to split or delaminate at layer interfaces. 
       FIG. 5  shows a cross section of a part  500  that is similar to the part  400  of  FIG. 4 , except that layers  502  shown in  FIG. 5  are locked together so that they are prevented or mitigated from splitting or delaminating at layer interfaces. Layers  502  can be made up of structural members  506  which are deposited as material from a nozzle  504  that then solidifies. Structural members  506  can be formed in several types with different features which combine to create an interlocking effect. 
     For example, layers can be deposited starting with the innermost layers and proceeding to the outermost layers. An n th  layer can be deposited with one or more gaps of a first width. Then, a next layer (n+1 layer) can be deposited with gaps of a second width which can be narrower than the first width and which can be aligned with the gap(s) of the n th  layer. A subsequent layer (n+2 layer) can be deposited over or outside of the n+1 layer with sufficient material and deposition speed or pressure that the material of the n+2 layer flows through the gap in then n+1 layer and into the gap in the n th  layer. The n+2 layer material can partially or completely fill the gap(s) in the n th  and n+1 layers. If the gap(s) in the n th  layer are larger than the gap(s) in the n+1 layer, the N+2 layer material can form a physical interlock with the material of the other layers. The n+2 layer material that flows into the gaps in the other layers can be a locking feature  508 . Each layer can alternately have gaps of different widths at different locations as well as locking features so that all or nearly all of the layers can be sequentially interlocked. This construction can be effective at eliminating layer separation or delamination. The part  500 , formed in this or other similar manner, can include one or more of flat, concave, and convex portions. 
     In some cases, it can be possible to create useful layer interlocking with different layers having gaps of the same width or with combinations of just single gap-layers plus layers with locking features (i.e., without the stacking of multiple layers with aligned gaps). The layers  502  and associated gaps as well as locking features can be formed with the nozzle  504  being in various orientations. In some cases, the nozzle (and its corresponding nozzle axis) can remain vertical during material deposition, as in the case of a conventional 3-axis (x,y,z) FDM system. In some cases, the nozzle can be kept perpendicular to the local part surface during the deposition process. In some cases, the nozzle can have a variable angle with respect to the local part surface in order to facilitate certain features such as forming the base of a vertical wall next to a baseplate. For example,  FIG. 5  shows the nozzle  504  completing a section of vertical wall next to a baseplate and shows the nozzle  504  at a non-perpendicular angle to the part surface to avoid crashing into the baseplate or other portions of the FDM system. Additionally, or alternatively, the angular orientation of the nozzle may be changed from a perpendicular angle to a non-perpendicular angle, or in some cases from a first non-perpendicular angle to a second non-perpendicular angle different from the first, to avoid making contact with an already deposited portion of the object being fabricated. In some cases, by changing the angular orientation of the nozzle to avoid making contact with parts of the FDM system or the object being fabricated, the possible coverage area of the nozzle may be increased. In other words, the nozzle, by changing its angular orientation to avoid making contact, could deposit materials into tighter spaces than would be otherwise possible without making such angle re-adjustments. Referring to  FIG. 5 , as an example, the nozzle  504  can, by rotating in a clockwise direction to avoid hitting the base, deposit material closer to the intersection between the object and the base. 
     Locking features can be formed with the nozzle perpendicular to the local part surface or with the nozzle angled off of perpendicular to the local part surface. Layers and structural members can also be formed with overhangs  510  adjacent to locking features of other layers in order to create an interlocking structure. In some cases, interference members  512  can be deposited to help further improve interlocking between layers. 
     For a 5-axis FDM system or other material deposition system with a nozzle that can change angular orientation relative to the part, a compact, angularly variable distal end can help the nozzle reach into tight spaces. To achieve this, it is generally desired to have one of the angular articulation axes as close to the “tip”—or point where material is dispensed—as possible. However, based on conventional feedstock dispensing systems, it can be challenging to get a solid feedstock filament to go around such a sharp bend at the end before being pushed out of the tip. 
     Referring to  FIGS. 6 a  and 6 b   , an articulating material dispensing system  600  is shown, with  FIG. 6 a    showing the articulating material dispensing system  600  in a nominal (vertical) configuration and  FIG. 6 b    showing the articulating material dispensing system  600  in an articulated (flexed) configuration. 
     As shown, the material dispensing system  600  can include flexible strips  602  which form the sides of a material channel  604 . There can be multiple flexible strips  602  in a leaf-spring structure that enables the width of the material channel  604  to be maintained throughout the range of articulation. A nozzle  606  can be employed at the distal end of the material dispensing system  600  to create a specific exit orifice size and control the flow of material. Cables  608 , as well as pushrods or other types of actuators, can be used to pull and/or push on the material dispensing system to cause controllable articulation. In some cases, a flexible sleeve can be used to hold the flexible strips  602  in place. Heating elements  610  can be used to heat the material flowing through the flexible portion of the system or can be used to heat the nozzle itself. Heating material flowing through the flexible portion of the system can help liquefy or soften the material which may allow the material to more easily flow around a corner when the system  600  is articulated. The flexible strips  602  can be used to shift in the nozzle axial direction (or along the length of the curve) to enable articulation (see  FIG. 6 b   ). Because creating the curvature, as indicated by the changing lengths of the flexible strips  602 , may require more feedstock material to ensure a continuous flow of material, the volume flow of material per distance, or extrusion ratio, may need to be increased in cases where there are curvatures in the feedstock channel. 
     In some cases, a material drive system such as a drive wheel can be located proximal to the articulating section. Alternatively, or additionally, a material drive system such as the drive wheel can be located distal to the articulating section. In cases where the feedstock material is softened or liquefied for improved passage through the articulating section, the feedstock material can be cooled, for example via a cooling zone, prior to being driven by the driven wheel. 
     The position of the exit orifice with respect to the degree of articulation or direction of articulation may be characterized so that for a given articulation amount (i.e. amount of bending) the position of the nozzle exit orifice can be known with little error. 
     Referring to  FIGS. 7 a  and 7 b   , an articulating material dispensing system  700 , an alternative implementation, is shown. The system  700  shown in  FIGS. 7 a  and 7 b    is similar to that of  FIGS. 6 a  and 6 b    except that the material dispensing channel can be lined with or defined by a coil spring or set of material rings  702  in the articulating portion of the system. A coil spring can be used to define the material dispensing channel and can enable the channel size to stay relatively constant during articulation. A flexible sleeve  704  can surround the coil spring and further guide it or constrain its shape. Cables  706 , as well as pushrods, linkages, hydraulic actuators, inflatable bladders, muscle wires, or the like, can be used to control the degree of articulation of the system  700 . 
     In the example shown in  FIG. 7 b   , the system  700  is shown with 4 cables for articulation (one is hidden behind other components). This way, the system  700  can be articulated in multiple directions (i.e. can have multiple degrees of freedom). When combined with a 3-axis gantry system, a net system with 5 (five) axes of motion can be created (in addition to motion of the dispensed material). Additional translation and rotation axes are also possible to create 6, 7, 8, or more axes of motion and to allow the fabrication of a wide range of part shapes. 
     A nozzle  708  is shown at the distal end of the system  700  to control material flow and create an exit orifice. Heating elements  710  are shown in the nozzle  708 , but they can also or alternately be in the articulating section or proximal to (i.e. above) the articulating section.  FIG. 7 a    also shows drive wheels  712  (or a drive wheel and an idler wheel) that are shown proximal to the articulating section, though they can also be located at the articulating section or distal to it, for example in the nozzle  708 . 
     Referring to  FIGS. 8 a -8 d   , a material guide system  800  can be used in an articulating material dispensing system such as that of  FIGS. 7 a  and 7 b    to help guide the feedstock material.  FIG. 8 a    shows a cross section of a plain coil spring  802 .  FIG. 8 b    shows a cross section of the same coil spring  802  with the addition of contoured rollers  804  which can be threaded onto the spring and which can individually rotate about the spring such that material passing axially through the center of the spring might contact the rollers and might experience low resistance to axial motion due to the ability of the rollers to rotate. 
       FIG. 8 c    shows a top view of the material guide system  800  of  FIG. 8 b   , and  FIG. 8 d    shows an isometric view of the same. The material guide system  800  as shown in  FIGS. 8 a -8 d    can allow a material dispensing system to articulate (bend) while adding minimum resistance to feed motion of the material. 
     Referring to  FIG. 9 , a material dispensing system  900  having two rotational degrees of freedom is shown. As shown, the first rotational degree of freedom allows the system to rotate about an axis that can be aligned with the entering feedstock—i.e. a vertical axis in the orientation of the system shown in  FIG. 9 . The second rotational degree of freedom allows a nozzle to rotate about an axis that can be perpendicular to the axis of the first rotational degree of freedom. Continuous rotation of the first rotational degree of freedom can be possible if “winding up” of the feedstock can be eliminated. One or both of the heating zone and a cooling zone can be included. The heating zone  902  can help soften the feedstock to the point that it alleviates wind-up of the material (i.e. it allows arbitrary angular dislocation of the distal portion of the feedstock relative to the proximal portion). As material is continually fed through, any adverse effects of the local twisting of the material can be alleviated as that material is passed out of the nozzle and fresh feedstock material arrives to be heated so it can take up any further twisting of the system. A cooling zone  904  can help enable the material to solidify again before it is fed into the nozzle. A final drive wheel  906  can be used to provide the necessary driving force to controllably feed the feedstock into the nozzle. The material can be re-heated and softened or liquefied in the nozzle. An initial drive wheel  908  can be included to help drive the feedstock into the heating zone  902 . 
     In some cases, the feedstock material can be pinched and/or formed into flattened and/or ridged sections to help facilitate going around corners. For example, referring now to  FIGS. 10 a -10 c   , a material deposition system  1000  changes the cross section shape of the feedstock so that the feedstock can more easily turn a tight corner. 
       FIG. 10 a    shows a cylindrical feedstock  1002  being fed through rollers  1004  which can squeeze it and transform the fed-through portion to a ribbon section  1006  to have a thin rectangle or other cross-sectional shape with one thin dimension so that the feedstock can bend around a corner more easily or with lower force. A nozzle  1008  can provide an exit orifice  1010 . The nozzle  1008  can have an opening  1012  shaped correspondingly to accept the reshaped feedstock, for example it can have a rectangular opening. The shape of the exit orifice  1010  can be any required shape, for example it can have a circular shape. The feedstock can be heated before entering the feed rollers so that it is softened and its cross section shape can be more easily changed. The feedstock can be cooled as it passes between the rollers or it can be cooled after it passes through the rollers so that it solidifies and its shape is stable before it enters the nozzle. Additional elements of the material dispensing system  1000 , for example guides, can further be provided to improve operation. 
       FIG. 10 b    shows rollers  1014 , which is another version of the forming rollers  1004  of  FIG. 10 a   , that has roller shapes that create a resulting material shape that has positive drive features. For example, the resulting reshaped feedstock can have a constant cross section area along its length so that a constant motion of the feedstock should result in a constant material flow rate out of a nozzle. A heating zone  1016  can be positioned at an upstream position relative to the rollers  1014  to soften the feedstock material for improved formability.  FIG. 10 c    shows another possible reshaped feedstock shape with positive drive features. 
     In some cases, additional features, such as reciprocating linear feed dogs, can be used to help drive the feedstock.  FIGS. 11 a  and 11 b    show aspects of an articulating material dispensing system  1100  that is based on the reciprocating linear feed dog mechanism. 
     Referring to  FIG. 11 a   , the articulating material dispensing system  1100  has a bendable portion that creates articulation. The system includes reciprocating drive dogs  1102  which can be flexible members with asymmetric teeth that drive material feedstock when the feed dogs are moved in one direction (toward the distal nozzle end) and which can slide back along the feedstock without inducing motion in the feedstock to effect the reverse portion of the reciprocation motion. The feed dog teeth  1104  can bite into the feedstock to create a positive interlock during the forward portion of the reciprocation. Alternatively, the teeth  1104  can interlock with pre-existing serrations, indentations or other features on the feedstock. 
     The reciprocation motion can have a continuous speed or it can have different speeds for the forward and reverse portions of the motion, for example the reverse portion can happen much faster than the forward portion so that more than one feed dog can be pushing forward on the feedstock at any given time. There can be more than two feed dogs  1102 , for example there can be pairs or groups of feed dogs on each side of the feedstock so that there is always at least one feed dog on each side of the feedstock pushing forward at any given time. The motion of the various feed dogs can be coordinated so that while the motion of each individual feed dog can be reciprocal, the net motion imparted to the feed stock can be continuous forward motion or any desired motion profile. Different reverse feed dogs can be employed to effect reverse motion of the feed stock when needed. Or all feed dogs can be pulled backward at the same time which may create reverse feedstock motion. 
     Even though  FIG. 11 a    shows an articulating material dispensing system, the linear or reciprocating feed dog system described here may also be used in a non-articulating (i.e. straight) material dispensing system and may have advantages such as increased drive force and more consistent feed drive ratio with less variation of feedrate or feed ratio between different types of material feedstocks. 
       FIG. 11 b    shows one possible construction of a flexible feed dog  1102  that can be used in a system such as that shown in  FIG. 11 a   . Here, an isometric view of a part of a feed dog made of sheet metal is shown. The feed dog includes flexible teeth formed in the sheet metal. Flexible teeth can be helpful in that they can positively grab the feedstock when moving forward and can slide relative to the feedstock when moving in reverse. A feed dog made of thin, flexible sheet metal can be used to drive the feedstock around a bend as in the system of  FIG. 11   a.    
       FIG. 12  shows a different way to create a 5 (or more) axis material deposition system. The alternative system  1200  shown in  FIG. 12  can include three linear motion axes, for example X, Y and Z. The system  1200  can include movement about a first rotational axis, such as α, allows angular articulation of a nozzle very close to the exit orifice. Having a non-vertical rotation axis (in this case a horizontal axis) located close to the exit orifice, can allow the nozzle to fit into tight spaces while still articulating, for example to deposit material on the inside of cavities in parts. Moreover, a part  1202  that is being formed can be rotated about a second rotational axis, such as θ. This can be achieved, for example, by placing the part  1202  on a rotatable base  1204  that can be rotated during deposition. The combination of the X,Y,Z, α and θ movements, then, as shown in  FIG. 12 , enables full 5-axis motion without some of the complications that may be associated with articulating a nozzle with two rotational axes. 
     Referring now to  FIGS. 13 a  and 13 b   , a material dispensing system  1300  with a nozzle mounted on a rotational axis is shown. Here, feedstock within a feedstock channel  1302  can be softened or liquefied in a liquefaction zone  1304  before it reaches the nozzle rotation axis. A drive wheel  1306  can be used to drive the feedstock through. Feedstock material can then flow sideways through a jog that is coincident with the nozzle rotation axis and then flows out through the nozzle. The jog coincident with the nozzle rotation axis can allow the nozzle to articulate through a range of motion while still providing a continuous, leak-free flow path for the feedstock material. 
     Referring to  FIGS. 14 a  and 14 b   , a material dispensing system  1400  with a nozzle  1402  configured to rotate about two rotational axes is shown. The system  1400  also includes a material drive system (e.g.  1404   a - c ) that accommodates the range of motion of the nozzle rotation. An optional first rotation axis  1406  is shown with a vertical orientation. The nozzle can rotate about this vertical axis if this degree of freedom is present. A second rotational axis  1408  can be perpendicular to the first rotational axis  1406  (shown as horizontal, in/out of the page). Feedstock material  1410  is fed by a drive wheel  1404   c  to the nozzle  1402  having an exit orifice.  FIG. 14 a    shows a side view of the system  1400  in a fully articulated position, and  FIG. 14 b    shows a side view of the system  1400  in a non-articulated (vertical) position. 
     Here, the feedstock  1410  follows a path that is off to the side so that it can wrap around the drive wheel  1404   c , and so that the drive wheel  1404   c  can be centered on the second rotational axis  1408 . Having the drive wheel centered on the second rotational axis enables the drive wheel to stay in the same location as the nozzle rotates about the second axis. Having the drive wheel stay in the same position means that it can be driven by a belt  1404   a  from above. Additionally, having the feedstock wrap around the drive wheel can facilitate bending the feedstock around the corner when the nozzle is in an articulated position. The radius of curvature can be larger in this configuration than it would be if the feedstock had to travel axially along the nozzle and the upper portion of the dispensing system. The feedstock material can exit the nozzle in-line with the nozzle axis because the feedstock path through the nozzle can guide it from being non-axial to becoming aligned with the nozzle axis just before it exits. An idler bearing can maintain pressure between the feedstock and the drive wheel. The idler bearing  1412  can be spring loaded so that it applies a relatively constant force to pinch the feedstock between itself and the drive wheel. The idler bearing can be affixed to the nozzle portion of the dispensing system so that when the nozzle rotates about the second axis, the idler bearing rotates with it so that it is always pinching the feedstock to the drive wheel just at the point before the feedstock enters the body of the nozzle, which can help in getting the feedstock to travel around the bend. The drive wheel can be actuated by a drive belt that can be driven by a motor or other actuator that is proximal of the drive wheel. In some cases, an additional set of drive belt and pulley can be used to control the articulation of the nozzle  1402  about the second rotation axis. The drive wheel motion can be coordinated with the rotation of the nozzle about the second axis so that the feedstock is not inadvertently fed or retracted when the nozzle rotates about the second axis. 
       FIGS. 15 a -15 e    show another implementation of the multi axis material deposition system. Referring to  FIG. 15 a   , an isometric view of a multi-axis material deposition system  14002  is shown. A material deposition nozzle  14004  is rotatable with respect to a base  14006  about a rotation axis  14022 . A material  14008  which can be a filament can be fed through nozzle  14004 . The base  14006  can move along, for example, the x, y, z axes and may be referred to as a movable support relative to which the nozzle  14004  can rotate. A feed drive belt  14010  can be used to transfer feed forces in order to feed material  14008 . A nozzle positioning drive belt  14012  can be used to transfer positioning forces in order to rotate nozzle  14004 . 
     Referring to  FIG. 15 b   , a path of material  14008  through nozzle  14004  is visible. Hatching has been omitted for clarity. A material drive wheel  14014  can drive material  14008  with the aid of a pinch roller  14016 . Positioning drive belt  14012  can drive a positioning pulley  14018 . 
       FIG. 15 c    shows an isometric section view of system  14002  with the section plane passing through nozzle rotation axis  14022 . As shown, a positioning pulley  14018  is driven by positioning drive belt  14012  and is connected to nozzle  14004  so that when positioning drive belt  14012  moves, it results in rotation of nozzle  14004  about axis  14022 . Drive wheel  14014  is connected to a material drive pulley  14020  which is driven by belt  14010  so that when belt  14010  moves, material  14018  (see  FIG. 15 b   ) is fed through nozzle  14004 . 
       FIG. 15 d    shows a front view of system  14002  in which nozzle  14004  is in a rotated position with respect to base  14006 .  FIG. 15 e    shows an isometric view of system  14002  with base  14006  removed for clarity to show the other components. 
     Referring now to  FIG. 16 , another version of a material dispensing system  1600  having multiple rotational degrees of freedom is shown. Here, a center coupler  1602  couples a main body  1604  and a nozzle  1606 . Additional linkage parts between the coupler and the main body and the coupler and the nozzle can be used but are not shown here for sake of clarity. 
     As shown, there are four rotation axes: two parallel rotation axes that are horizontal in the plane of the page; and another two parallel horizontal rotation axes that are projecting in and out of the plane of the page. Using multiple parallel axes means that rotation at each axis can be limited, for example limited to 45 degrees, which can be helpful in avoiding instability or lock-up conditions. Cables, pushrods or other actuators can be used to control the rotation of the nozzle relative to the base part. Elastomeric, springy, or compliant members can be connected to the nozzle, coupler and base part to create predictable, deterministic motion given simple push/pull inputs from cables or actuators. In some cases, additional linkages can be employed to further constrain motion, for example linkages or gears can be used to constrain the angular rotation about pairs of parallel axes to be equal or to be in some other deterministic ratio. 
     Referring now to  FIGS. 17-24 , additional implementations of the interlocking feature, similar to those described above in  FIG. 5 , are described.  FIG. 17 a    shows an isometric view of an element  16002  which can be made of a continuous material  16004 . Element  16002  can have an interlocking feature  16006  in one or more locations. Interlocking features  16006  can have a neck  16008  and one or more locking areas  16010 .  FIG. 17 b    shows a top view of the element  16002 , and  FIG. 17 c    shows a front view of element  16002 . Interlocking features  16006  with neck  16008  and locking areas  16010  can be seen. 
     Element  16002  can be formed by deposition of material  16004  such that element  16002  is continuous—i.e. it does not have any breaks in it. Material  16004  can be or can contain continuous fibers. Interlocking features  16006  can be formed by forcing continuous material into a cavity in another part or in previously deposited material (for example see  FIGS. 21 a  and 21 b   ). The exact structure of interlocking features  16006  can take a variety of forms and the exact packing or path of continuous material  16004  can vary considerably, but it can form neck  16008  and locking areas  16010  regardless of specific packing arrangement. This is similar to the way a length of rope pushed into a box will take the net shape of the box regardless of the specific coil or path of the rope. Material  16004  can be a thermoplastic, fibers, a thermoset, a metal, a composite, a medium with living cells, a biologic material, a mineral material or any combination thereof. 
     Referring to  FIG. 18 , a layer  17002  made up of elements  16002  deposited next to one another is shown. Elements  16002  can be joined (all formed continuously) or they can be separate. Layer  17002  can be a planar array of elements  16002  or it can be non-planar or it can be curved or it can be irregular. Gaps  17004  and  17006  are left between elements  16002  in areas where elements  16002  don&#39;t touch. Gaps  17004  can be larger than gaps  17006 . 
       FIGS. 19 a -19 c    show isometric, top, and front views, respectively, of an element  18002 , which is generally similar to element  16002  of  FIGS. 17 a - c   , but can have a different shape or be formed in a different orientation. Element  18002  can have interlocking features  18006  similar to interlocking features  16006 .  FIG. 20  shows a layer  19002  made up of elements  18002  deposited next to one another. Layer  19002  can be similar to layer  17002  but it can be formed in a different orientation and it can be formed on top of layer  17002  (see  FIG. 21 a   ). 
       FIGS. 21 a  and 21 b    show an incomplete part with two layers together. This represents layers in a partially built part. In detail,  FIG. 21 a    shows a front view of a part  20002  which includes layer  17002  and layer  19002 . Interlocking features  16006  and  18006  are visible as part of layers  17002  and  19002  respectively. Interlocking features  18006  can have their shape defined as they are formed by being pushed into spaces in the shape of layer  17002 , such as gaps  17004  and  17006 .  FIG. 21 b    shows an isometric view of part  20002 . 
     Referring now to  FIGS. 22 a  and 22 b   , a part that is being built with three interlocking layers together is shown. In more detail,  FIG. 22 a    shows a front view of a part  21002 . Part  21002  includes layers  17002 ,  19002  and a third layer  21004 . Layer  21004  can be the same as layer  17002 , but the pattern is shifted. Locking features (not visible) from layer  21004  pass though narrow gaps in layer  19002  and fill larger gaps in layer  17002 . The narrow gaps can be similar to gaps  17006  in  FIG. 18 . However, such gaps are not visible in this figure. The larger gaps can be gaps  17004 . By taking the shape of the narrow gaps in layer  19002  and then filling the larger gap in layer  17002 , an interlocking feature of layer  21004  can create a physical interference or lock between the layers which can prevent separation of the layers. A physical interference can be stronger and be more effective at preventing delamination of layers than a chemical bond alone. Material including strong fibers can thus be oriented transverse to the layers in the interlocking features and the strength of part  21002  can be closer to isotropic than in a typical part without interlocking features or transverse fibers between layers. 
       FIG. 23 a    shows a front view of a part  22002  made of four interlocking layers including layers  17002 ,  19002 ,  21004  and a fourth layer  22004 . Layer  22004  may be the same as layer  19002  but it can be shifted to fit properly and achieve the desired arrangement of gaps and locking features. A set of 4 layers such as part  22002  may form a repeating unit, that is no more unique layer shapes or states are needed to continue to build the part. A fifth layer added on top of layer  22004  can be identical in shape and lateral position (shift) to layer  17002 . Sets of these four layers can be repeated indefinitely to achieve a desired part thickness.  FIG. 23 b    shows an isometric view of part  22002 . 
     Referring now to  FIGS. 24 a  and 24 b   , a part that is being built with twelve interlocking layers together is shown.  FIG. 24 a    shows a front view of a part  23002  made of three parts  22002 , which are each four interlocking layers, arranged so that part  23002  has a total of twelve interlocking layers.  FIG. 24 b    shows an isometric view of part  23002 . 
     In all implementations shown above, all layers can be made of a single continuous material or fiber or fiber bundle. In some cases, each layer or element can be made of separate materials or fibers or fiber bundles. 
     Implementations of the subject matter described in this specification can be implemented in combination with digital electronic circuitry, or computer software, firmware, or hardware. Implementations of the subject matter described in this specification can be implemented in an additive manufacturing system that uses one or more modules of computer program instructions encoded on a computer-readable medium for execution by, or to control the operation of, data processing apparatus. The computer-readable medium can be a manufactured product, such as hard drive in a computer system or an optical disc sold through retail channels, or an embedded system. The computer-readable medium can be acquired separately and later encoded with the one or more modules of computer program instructions, such as by delivery of the one or more modules of computer program instructions over a wired or wireless network. The computer-readable medium can be a machine-readable storage device, a machine-readable storage substrate, a memory device, or a combination of one or more of them. 
     The term “data processing apparatus” encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, a runtime environment, or a combination of one or more of them. In addition, the apparatus can employ various different computing model infrastructures, such as web services, distributed computing and grid computing infrastructures. 
     A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub-programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network. 
     Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device (e.g., a universal serial bus (USB) flash drive), to name just a few. Devices suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. 
     To provide for interaction with a user, implementations of the subject matter described in this specification can be implemented using a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. 
     Implementations of the subject matter described in this specification can be implemented using a computing system that includes a back-end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front-end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described is this specification, or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), an inter-network (e.g., the Internet), and peer-to-peer networks (e.g., ad hoc peer-to-peer networks). 
     The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. 
     While this specification contains many implementation details, these should not be construed as limitations on the scope of the invention or of what may be claimed, but rather as descriptions of features specific to particular implementations of the invention. Certain features that are described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. 
     Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products. 
     Thus, particular implementations of the invention have been described. Other implementations are within the scope of the following claims.