Patent Publication Number: US-11034074-B2

Title: Multi-nozzle extruder for use in three-dimensional object printers

Description:
PRIORITY CLAIM 
     This application is a continuation application of pending U.S. patent application Ser. No. 14/962,067, which is entitled “System And Method For Operation Of Multi-Nozzle Extrusion Printheads In Three-Dimensional Object Printers,” which was filed on Dec. 8, 2015, and which issued as U.S. Pat. No. 10,335,991 on Jul. 2, 2019. 
    
    
     TECHNICAL FIELD 
     This disclosure is directed to printheads and extruders used in three-dimensional object printers and, more particularly, to extrusion printheads that extrude an extrusion material through two or more nozzles. 
     BACKGROUND 
     Three-dimensional printing, also known as additive manufacturing, is a process of making a three-dimensional solid object from a digital model of virtually any shape. Many three-dimensional printing technologies use an additive process in which an additive manufacturing device forms successive layers of the part on top of previously deposited layers. Some of these technologies use extrusion printing in which an extrusion printhead emits a melted build material, such as heated and softened ABS plastic, in a predetermined pattern. The printer typically operates the extrusion printhead to form successive layers of the build material that form a three-dimensional printed object with a variety of shapes and structures. While printing each layer of the three-dimensional printed object, the extrusion printhead emits build material that cools and hardens after extrusion from the printhead to form another layer of the three-dimensional printed object. Three-dimensional printing is sometimes called additive manufacturing and is distinguishable from traditional object-forming techniques, which mostly rely on the removal of material from a work piece by a subtractive process, such as cutting or drilling. 
     Many existing three-dimensional printers use a single printhead that extrudes material through a single nozzle. The printhead moves in a predetermined path to emit the build material onto selected locations of a support member or previously deposited layers of the three-dimensional printed object based on model data for the three-dimensional printed object. However, using a printhead with only a single nozzle to emit the build material often requires considerable time to form a three-dimensional printed object. Additionally, a printhead with a larger nozzle diameter can form three-dimensional printed object more quickly but loses the ability to emit build material in finer shapes for higher detailed objects while nozzles with narrower diameters can form finer detailed structures but require more time to build the three-dimensional object. 
     One solution known to the art to increase printer throughput and provide high-resolution printing includes a single printhead with removable nozzles that have multiple diameters for higher throughput or higher precision operations, but such solutions require a unit to switch nozzles and still only provide a single nozzle to emit the build material. Another solution that is known to the art incorporates multiple independent printheads in a single printer. However, the multiple independent printheads increase the complexity of the printer and each printhead requires a separate supply of build material during operation. Furthermore, existing extrusion printheads require activation and deactivation of heaters and drive motors to start and stop the extrusion of build material, which reduces the precision of extruding the build material during operation or reduces the speed at which the printheads form different arrangements of build material. Consequently, improvements to extrusion printheads and methods for the operation of extrusion printheads during three-dimensional object formation processes would be beneficial. 
     SUMMARY 
     In one embodiment, a method of operating a three-dimensional object printer including a multi-nozzle extrusion printhead has been developed. The method includes operating with a controller an actuator to generate relative movement between a printhead including a plurality of nozzles and an image receiving surface along a path corresponding to an outline of a predetermined region of the image receiving surface with reference to image data for one layer of a three-dimensional printed object, activating with the controller at least one nozzle in the plurality of nozzles in the printhead to extrude a pattern of an extrusion material on the image receiving surface corresponding to the outline, operating with the controller the actuator to generate relative movement between the printhead and the image receiving surface in another path corresponding to a swath within the pattern of the extrusion material corresponding to the outline with reference to the image data for the one layer of the three-dimensional printed object, and activating with the controller a plurality of the nozzles in the printhead simultaneously to extrude another pattern of the extrusion material on the image receiving surfaces corresponding to the swath. 
     In another embodiment, a three-dimensional object printer that includes a multi-nozzle extrusion printhead has been developed. The three-dimensional object printer includes a support member, a printhead including a plurality of nozzles configured to extrude an extrusion material to form at least one layer of a three-dimensional object, at least one actuator configured to generate relative movement between the printhead and the support member, a memory configured to store image data corresponding to plurality of layers for the three-dimensional printed object, and a controller operatively connected to the printhead, the at least one actuator, and the memory. The controller is configured to operate the at least one actuator to generate relative movement between the printhead including a plurality of nozzles and an image receiving surface formed on the support member along a path corresponding to an outline of a predetermined region of the image receiving surface with reference to image data for one layer of a three-dimensional printed object, activate at least one nozzle in the plurality of nozzles in the printhead to extrude a pattern of an extrusion material on the image receiving surface corresponding to the outline, operate the at least one actuator to generate relative movement between the printhead and the image receiving surface in another path corresponding to a swath within the pattern of the extrusion material corresponding to the outline with reference to the image data for the one layer of the three-dimensional printed object, and activate a plurality of the nozzles in the printhead simultaneously to extrude another pattern of the extrusion material on the image receiving surfaces corresponding to the swath. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing aspects and other features of extrusion printheads and extruders with multiple nozzles are explained in the following description, taken in connection with the accompanying drawings. 
         FIG. 1  is a diagram of a three-dimensional object printer that includes a multi-nozzle extrusion printhead. 
         FIG. 2A  is a diagram of a multi-nozzle extrusion printhead in a first orientation. 
         FIG. 2B  is a diagram of the multi-nozzle extrusion printhead of  FIG. 2A  in a second orientation. 
         FIG. 3  is a diagram of a multi-nozzle extrusion printhead forming an outline of extrusion material around the perimeter of a region on a surface. 
         FIG. 4  is a diagram of the multi-nozzle extrusion printhead of  FIG. 3  applying an extrusion material to the region surrounded by the outline of extrusion material on the surface. 
         FIG. 5  is a diagram of a multi-nozzle extrusion printhead forming two concentric outlines of extrusion material having a first distance between the two concentric outlines. 
         FIG. 6  is a diagram of the multi-nozzle extrusion printhead of  FIG. 5  forming two concentric outlines of extrusion material having a second distance between the two concentric outlines. 
         FIG. 7  is a diagram of a multi-nozzle extrusion printhead that forms curved arrangements of extrusion material with an oscillating motion to increase the linear length of an arrangement of an inner curve formed by one nozzle to correspond to an outer curve formed by another nozzle. 
         FIG. 8  is a diagram of a multi-nozzle extrusion printhead that forms curved arrangements of extrusion material with intermittent operation of a nozzle that forms an inner curve to form the inner curve with a similar density of extrusion material as an outer curve formed by another nozzle in the printhead. 
         FIG. 9A  is a diagram of a multi-nozzle extrusion printhead with a first portion of an array of nozzles that operate concurrently to fill a region on a surface. 
         FIG. 9B  is a diagram of a multi-nozzle extrusion printhead forming a corner from two linear swaths and a curved swath of extrusion material. 
         FIG. 10  is a diagram of the multi-nozzle extrusion printhead of  FIG. 9A  with a second portion of the array of nozzles operating concurrently to fill the region on a surface. 
         FIG. 11A  is a schematic diagram of an extrusion material supply and dispensers for a multi-nozzle extruder or a multi-nozzle printhead in a three-dimensional object printer. 
         FIG. 11B  is a schematic diagram of another embodiment of an extrusion material supply and dispenser for a multi-nozzle extruder or a multi-nozzle printhead in a three-dimensional object printer. 
         FIG. 11C  is a schematic diagram of another embodiment of an extrusion material supply and dispenser for a multi-nozzle extruder or a multi-nozzle printhead in a three-dimensional object printer. 
         FIG. 11D  is a schematic diagram of another embodiment of an extrusion material supply and dispenser for a multi-nozzle extruder or a multi-nozzle printhead in a three-dimensional object printer. 
         FIG. 12A  is a schematic diagram of multiple extrusion material supply and dispensers that supply multiple extrusion materials to different nozzles of a multi-nozzle extruder or multi-nozzle printheads in a three-dimensional object printer. 
         FIG. 12B  is a schematic diagram of another embodiment of multiple extrusion material supply and dispensers that supply multiple extrusion materials to different nozzles of a multi-nozzle extruder or multi-nozzle printheads in a three-dimensional object printer. 
         FIG. 13A  is a schematic diagram of a multi-nozzle extrusion printhead that includes a chamber to store melted extrusion material and provide the melted extrusion material to one or more outlets with valves that control the extrusion of the melted extrusion material during a three-dimensional object printing operation. 
         FIG. 13B  is another schematic diagram of nozzles in the extrusion printhead of  FIG. 13A  depicting opened and closed valves for different nozzles in a single extrusion printhead. 
         FIG. 14A  is a schematic diagram of another extrusion printhead that includes a chamber to store melted extrusion material, fluid outlets that provide the melted extrusion material to a plurality of nozzles, and an array of valves that control block or enable the flow of extrusion material through individual nozzles.  FIG. 14B  is a cross-sectional view of the printhead in  FIG. 14A  looking up into the printhead from below the printhead and  FIG. 14C  is a cross-sectional side view of the printhead in  FIG. 14A . 
         FIG. 15  is a block diagram of a process for the operation of a multi-nozzle extrusion printhead. 
     
    
    
     DETAILED DESCRIPTION 
     For a general understanding of the environment for the device disclosed herein as well as the details for the device, reference is made to the drawings. In the drawings, like reference numerals designate like elements. 
     As used herein, the term “extrusion material” refers to a material that one or more nozzles in an extrusion printhead emit to form layers of material that either form an object or provide structural support for the object during operation of a three-dimensional object printer. The extrusion materials include, but are not strictly limited to, both “build materials” that form permanent portions of the three-dimensional printed object and “support materials” that form temporary structures to support portions of the build material during a printing process and are then optionally removed after completion of the printing process. Examples of build materials include, but are not limited to, Acrylonitrile butadiene styrene (ABS) plastic, polylactic acid (PLA), aliphatic or semi-aromatic polyamides (Nylon), plastics that include suspended carbon fiber or other aggregate materials, electrically conductive polymers, other thermoplastics, and any other form of material that is suitable for emission through the nozzles of an extrusion printhead in a liquid or semi-liquid form and then for solidification to form a durable three-dimensional printed object. Examples of support materials include, but are not limited to, high-impact polystyrene (HIPS), polyvinyl alcohol (PVA), and other extrudable materials. In some extrusion printers, the extrusion material is supplied as continuous elongated strand of material that is referred to as a “filament”. More generally, the printer receives the extrusion material in a solid phase, such as the solid filament, solid pellets, or a solid granular powder. The extrusion material filament has sufficient flexibility to unwind from a spool or other supply and be supplied to a heater within the printhead. The heater melts the extrusion material filament and a nozzle in the printhead extrudes the extrusion material during a three-dimensional object printing operation. As used herein, the term “melt” as applied to extrusion material refers to any elevation of temperature for the extrusion material that softens the extrusion material to enable extrusion through one or more nozzles in a printhead during operation of a three-dimensional object printer. The melted extrusion material is also referred to as being liquefied to enable extrusion through the nozzles, although those of skill in the art will recognize that certain amorphous extrusion materials do not truly transition to a pure liquid state during operation of the printer. 
     As used herein, the terms “extrusion printhead” or “printhead” are used interchangeably and refer to a component of a printer that melts extrusion material in a single fluid chamber and provides the melted extrusion material to multiple nozzles in an on-demand manner to form swaths of the extrusion material during a three-dimensional printing operation. As described in more detail below, a valve assembly in the printhead enables the simultaneous operation of multiple nozzles to extrude the extrusion material at different times during the printing operation. Multi-nozzle printheads incorporate two or more nozzles that extrude the extrusion material simultaneously or at different times during a three-dimensional object printing process. As used herein, the term “nozzle” refers to an orifice in an extrusion printhead that extrudes a liquid or semi-liquid extrusion material during a three-dimensional printing operation to form extruded patterns of the extrusion material corresponding to a path of relative movement between the printhead and the image receiving surface. During operation, the nozzle extrudes a substantially continuous linear arrangement of the melted material along the process path of the printhead. The extrusion printhead controls a rate at which the nozzle extrudes the extrusion material and as described in more detail below, the printhead optionally includes valves to activate and deactivate the emission of extrusion material from the nozzle. The diameter of the orifice in the nozzle affects the width of the extruded line of extrusion material. Different printhead embodiments include nozzles having a range of orifice sizes with wider orifices producing wider arrangements of the extrusion material while narrower orifices producing narrower arrangements of the extrusion material. As described in more detail below, some multi-nozzle extrusion printhead embodiments include a plate or other planar member that includes a linear one-dimensional or a two-dimensional arrangement of nozzles. Extrusion printheads that include arrays of multiple nozzles are described in more detail below. 
     As used herein, the term “pressure chamber” refers to a cavity formed within a housing of a printhead that holds a supply of liquefied extrusion material and supplies the liquefied extrusion material to one or more nozzles in the printhead during a three-dimensional object printing operation. The pressure chamber is further configured to maintain a predetermined level of pressure on the liquid extrusion material to control a rate at which one or more nozzles extrude the extrusion material onto an image receiving surface. In some embodiments, an external feed system for the build material that is connected at an inlet of the pressure chamber supplies liquefied build material under pressure to maintain the predetermined pressure level within the pressure chamber during operation of the printhead. As described in more detail below, because some extrusion printheads include multiple nozzles that are activated and deactivated on an individual basis using valves, the pressure chamber supplies liquefied extrusion material so that any activated nozzles in the printhead extrude extrusion material at a substantially constant rate even as the number of activated nozzles changes during a printing operation. 
     As used here, the term “multi-nozzle extruder” refers to a device in a printer that emits extrusion material through two or more nozzles that each receive a supply of solid extrusion material. A heater that is coupled to one or more nozzles melts the extrusion material as the extrusion material exits each nozzle. A mechanical controller, such as rollers or an auger, pushes the solid extrusion material into the nozzle to supply the extrusion material during a printing operation. Unlike a printhead, a multi-nozzle extruder does not supply multiple nozzles with extrusion material from a single fluid chamber and does not include a valve assembly to activate and deactivate the operation of individual nozzles. 
     As used herein, the term “arrangement of extrusion material” refers to any pattern of the extrusion material that the extrusion printhead forms on an image receiving surface during a three-dimensional object printing operation. Common arrangements of extrusion material include straight-line linear arrangements of the extrusion material and curved arrangements of the extrusion material. In some configurations, the printhead extrudes the extrusion material in a continuous manner to form the arrangement with a contiguous mass of the extrusion material while in other configurations the printhead operates in an intermittent manner to form smaller groups of extrusion material that are arranged along a linear or curved path. The three-dimensional object printer forms various structures using combinations of different arrangements of the extrusion material. Additionally, a digital controller in the three-dimensional object printer identifies image data and printhead path data that correspond to different arrangements of the extrusion material prior to operating the extrusion printhead to form each arrangement of the extrusion material. As described below, the controller optionally adjusts the operation of multi-nozzle extrusion printheads to form multiple arrangements of the extrusion material using multiple nozzles during a three-dimensional printing operation. 
     As used herein, the term “swath” refers to a straight-line or curved linear arrangement of extrusion material that a printhead extrudes onto a region of an image receiving surface within the boundaries of extrusion material that forms an outline around the region. As described in more detail below, a printhead uses two or more extrusion nozzles to form swaths of extrusion material to form one or more layers of extrusion material during a three-dimensional object printing operation. 
     As used herein, the term “process direction” refers to a direction of relative movement between a printhead and an image receiving surface that receives extrusion material from one or more nozzles in the printhead. The image receiving surface is either a support member that holds a three-dimensional printed object or a surface of the partially formed three-dimensional object during an additive manufacturing process. In the illustrative embodiments described herein, one or more actuators move the printhead in the print zone, but alternative printer embodiments move the support member to produce the relative motion in the process direction while the printhead remains stationary. 
     As used herein, the term “cross process direction” refers to an axis that is perpendicular to the process direction. The process direction and cross-process direction refer to the relative path of movement of the extrusion printhead and the surface that receives the extrusion material. In some configuration, the printhead includes an array of nozzles that extend along the cross-process direction with a predetermined distance in the cross-process direction between adjacent nozzles in the printhead. As described in more detail below, in some configurations the printer rotates the extrusion printhead to adjust the effect cross-process direction distance that separates different nozzles in the printhead to adjust the corresponding cross-process direction distance that separates arrangements of the extrusion material that are extruded from the nozzles in the printhead. 
     As described below, an extrusion printhead moves in the process direction along both straight and curved paths relative to a surface that receives extrusion material during the three-dimensional object printing process. Additionally, an actuator in the printer optionally rotates the printhead about the Z axis to adjust the effective cross-process distance that separates nozzles in the printhead to enable the printhead to form two or more arrangements of extrusion material with predetermined distances between each arrangement of the extrusion material. The extrusion printhead moves both along the outer perimeter to form outer walls of a two-dimensional region in a layer of the printed object and within the perimeter to fill all or a portion of the two dimensional region with the extrusion material. 
       FIG. 1  depicts a three-dimensional object printer  100  that is configured to operate an extrusion printhead to form a three-dimensional printed object  140 . The printer  100  includes a support member  102 , a multi-nozzle extrusion printhead  108 , printhead support arm  112 , controller  128 , memory  132 , X/Y actuators  150 , an optional Zθ actuator  154 , and a Z actuator  158 . In the printer  100 , the X/Y actuators  150  move the printhead  108  to different locations in a two-dimensional plane (the “X-Y plane”) along the X and Y axes to extruded patterns of the extrusion material that forms one layer in a three-dimensional printed object, such as the object  140  that is depicted in  FIG. 1 . For example, in  FIG. 1  the X/Y actuators  150  translate the support arm  112  and printhead  108  along guide rails  113  to move along the Y axis while the X/Y actuators  150  translate the printhead  108  along the length of the support arm  112  to move the printhead along the X axis. The extruded patterns include both outlines of one or more regions in the layer and extruded swaths of the extrusion material that fill in the regions within the outline of extrusion material patterns. The Z actuator  158  controls the distance between the printhead  108  and the support member  102  along the Z axis to ensure that the nozzles in the printhead  108  remain at a suitable height to extrude extrusion material onto the object  140  as the object is formed during the printing process. The Zθ actuator  154  controls an angle of rotation of the printhead  108  about the Z axis (referenced as Zθ in  FIG. 1 ) for some embodiments of the printhead  108  that rotate about the Z axis to control the separation between nozzles in the printhead  108 , although some printhead embodiments do not require rotation during the printing process. As described in more detail below, the angle of rotation of the printhead relative to the process direction affects the distance that separates different sets of extrusion material extruded by multiple nozzles in printhead  108  during a printing operation. In the printer  100 , the X/Y actuators  150 , Zθ actuator  154 , and the Z actuator  158  are embodied as electromechanical actuators, such as electric motors, stepper motors, or any other suitable electromechanical device. In the illustrative embodiment of  FIG. 1 , the three-dimensional object printer  100  is depicted during formation of a three-dimensional printed object  140  that is formed from a plurality of layers of an extrusion material. 
     The support member  102  is a planar member, such as a glass plate, polymer plate, or foam surface, which supports the three-dimensional printed object  140  during the printing process. In the embodiment of  FIG. 1 , the Z actuator  158  also moves the support member  102  in the direction Z away from the printhead  108  after application of each layer of extrusion material to ensure that the printhead  108  maintains a predetermined distance from the upper surface of the object  140 . The printhead  108  includes a plurality of nozzles and each nozzle extrudes extrusion material onto the surface of the support member  102  or a surface of a partially formed object, such the object  140 . In the example of  FIG. 1 , the extrusion material supply  110  includes a spool of ABS plastic or another suitable extrusion material filament that unwraps from the spool to supply extrusion material to the printhead  108 . In the illustrative embodiment of  FIG. 1 , the single extrusion material supply  110  provides extrusion material to each of the nozzles in the printhead  108 . In different embodiments that are described in more detail below, two or more extrusion material supplies optionally supply different types or colors of extrusion material to selected nozzles in a multi-nozzle printhead. 
     The support arm  112  includes a support member and one or more actuators that move the printhead  108  during printing operations. In the printer  100 , one or more actuators  150  move the support arm  112  and printhead  108  along the X and Y axes during the printing operation. For example, one of the actuators  150  move the support arm  112  and the printhead  108  along the Y axis while another actuator moves the printhead  108  along the length of the support arm  112  to move along the X axis. In the printer  100 , the X/Y actuators  150  optionally move the printhead  108  along both the X and Y axes simultaneously along either straight or curved paths. The controller  128  controls the movements of the printhead  108  in both linear and curved paths that enable the nozzles in the printhead  108  to extrude extrusion material onto the support member  102  or onto previously formed layers of the object  140 . The controller  128  optionally moves the printhead  108  in a rasterized motion along the X axis or Y axis, but as described below, the X/Y actuators  150  also move the printhead  108  along arbitrary linear or curved paths in the X-Y plane. 
     The controller  128  is a digital logic device such as a microprocessor, microcontroller, field programmable gate array (FPGA), application specific integrated circuit (ASIC) or any other digital logic that is configured to operate the printer  100 . In the printer  100 , the controller  128  is operatively connected to one or more actuators that control the movement of the support member  102 , the support arm  112 , and the movement of the roll  144  from the supply spindle  146  to the uptake spindle  148 . The controller  128  is also operatively connected to the printhead  108  to control operation of the plurality nozzles in the printhead  108 . 
     The controller  128  is also operatively connected to a memory  132 . In the embodiment of the printer  100 , the memory  132  includes volatile data storage devices, such as random access memory (RAM) devices, and non-volatile data storage devices such as solid-state data storage devices, magnetic disks, optical disks, or any other suitable data storage devices. The memory  132  stores programmed instruction data  134  and three-dimensional (3D) object image data  136 . The controller  128  executes the stored program instructions  134  to operate the components in the printer  100  to form the three-dimensional printed object  140  and print two-dimensional images on one or more surfaces of the object  140 . The 3D object image data  136  includes, for example, a plurality of two-dimensional image data patterns that correspond to each layer of extrusion material that the printer  100  forms during the three-dimensional object printing process. The printhead path control data  138  include a set of geometric data or actuator control commands that the controller  128  processes to control the path of movement of the printhead  108  using the X/Y actuators  150  and to control the orientation of the printhead  108  using the Zθ actuator  154 . The controller  128  operates the actuators to move the printhead  108  and activates and deactivates different nozzles in the printhead  108  to form arrangements of the extrusion material in each layer of the three-dimensional printed object  140 . 
       FIG. 2A  and  FIG. 2B  depict one embodiment of a multi-nozzle extrusion printhead  208 . The printhead  208  includes three (3) extrusion nozzles  212 ,  216 , and  220  that each extrudes extrusion material during operation. A single fluid chamber and valve assembly (not shown) control the flow of extrusion material through the nozzles  212 ,  216 , and  220  during operation of the printhead  208 . In the printhead  208 , the nozzles  212 ,  216 , and  220  each form an opening through a planar member  245 , which forms a printhead face with a uniform surface. As described in more detail below, in some embodiments the printhead  208  includes valves that enable the printhead  208  to control extrusion of the extrusion material from the nozzles  212 - 220  in a selective manner. In the printer  100 , the controller  128  is operatively connected to the printhead  208  to operate one or more of the nozzles  212 - 220  during a three-dimensional object printing process. 
     In the printhead  208 , the nozzles  212 - 220  are arranged linearly with a predetermined separation distance between adjacent nozzles along the cross-process direction axis CP.  FIG. 2A  depicts the printhead  208  in a configuration where the printhead  208  moves along the process direction P with the maximum cross-process direction separation between adjacent nozzles in the printhead  208 . In  FIG. 2A , the dimension line  232  depicts the cross-process direction separation between the nozzles  212  and  216 . In the configuration of  FIG. 2A , adjacent nozzles in the printhead  208  form extruded arrangements of the extrusion material with a gap between the arrangements that corresponds to the separation between the nozzles in the cross-process direction. 
       FIG. 2B  depicts the printhead  208  in another orientation that changes the cross-process direction distance between the nozzles from the orientation of  FIG. 2A . In  FIG. 2B , the printhead  208  is rotated about the Z axis as depicted by the rotation Zθ to adjust the relative positions of the nozzles  212 - 220  along the cross-process direction CP. In the printer  100 , the controller  128  operates the actuator  154  to rotate the printhead  108  about the Zθ axis to adjust the cross-process direction separation between nozzles. Since the process direction P refers to the relative direction of movement of the printhead relative and the image receiving surface, such as the support member  102  or upper surface of the three-dimensional printed object  140 , the relative separation between nozzles in the cross-process direction is affected by both the orientation and relative direction of movement of the printhead. Referring again to  FIG. 2B , the printhead  208  is rotated relative to the process direction axis CP. In  FIG. 2B , a narrower cross-process direction distance  252  separates the nozzles  212  and  216  in comparison to the orientation of  FIG. 2A . 
       FIG. 2A  and  FIG. 2B  depict two orientations of the printhead  208 . More generally, the distance between any two nozzles in the printhead  208  when moving in the process direction is expressed using the following equation: D CP =M (cos (ϕ)), where M is maximum cross-process direction separation between the two nozzles, which is a physical parameter of the sizes and arrangements of the nozzles in the printhead, and ϕ refers to a rotational angle about the Z axis relative to the process direction axis. (ϕ−0) and process direction axis (ϕ=½π) although the printhead may rotate to other angles as well. 
     As described above, the multi-nozzle printhead  108  in the printer  100  receives extrusion material from a single extrusion material supply  110 . An extrusion material dispenser that is located within the printhead  108  or external to the printhead  108  in the three-dimensional object printer  100  provides the extrusion material from the extrusion material supply  110  to the nozzles in the printhead  108  during operation of the printer  100 . 
       FIG. 11A  depicts one embodiment of an extrusion material dispenser  1120  that receives a filament of extrusion material  1108  from a spool  1102  in an extrusion material supply. The dispenser  1120  supplies extrusion material to either multiple channels that supply different nozzles in a multi-nozzle extruder, which is depicted in  FIG. 11A , or supplies the extrusion material to a single fluid chamber in a printhead, which is depicted in more detail in the embodiment of  FIG. 11D  depicted below. In  FIG. 11A , the dispenser  1120  includes guide rollers  1140  that receive the extrusion material filament and a disc  1121  or other rotating member with an inlet opening  1122  that receives the filament of extrusion material and an outlet opening  1124  that dispenses the extrusion material. The dispenser  1120  also includes guide rollers  1142  between the inlet  1122  and outlet  1124  and a fixed position cutter  1132 . The guide rollers  1140  and  1142  are operatively connected to actuators that control the movement of the filament  1108  from the extrusion material supply  1102  through the dispenser  1120  and to different channels in the multi-nozzle extruder at different times. 
     The dispenser  1120  provides extrusion material to the channels that are located in the multi-nozzle extruder and supply portions of the filament to the individual nozzles in the multi-nozzle extruder, such as the nozzle  1136 . The outlet opening  1124  is aligned with one channel at a time to provide a portion of the filament to the one channel. An actuator in the dispenser moves the outlet  1124  into alignment with different channels at different times to provide different segments of the filament from a single extrusion material supply to two or more nozzles in the multi-nozzle extruder using two or more of the channels. For example, the channel  1128  receives a portion of the extrusion material filament and provides the filament to the nozzle  1136 , and the dispenser moves the outlet  1124  into alignment with other channels to supply the extrusion material to different nozzles. Note that to simplify the diagrams in  FIGS. 11A through 12B , the guide channels  1128  are shown stopping when they reach the rollers  1146 , however the guide channels  1128  extend past rollers  1146  and  1147  and engage the melters  1136  in some dispenser embodiments. 
     In  FIG. 11A , rollers  1144  and  1146  control the movement of the filament through the channel  1128  to the nozzle  1136 . In  FIG. 11A , each of the nozzles includes a heater that melts the extrusion material in the filament near the outlet of each nozzle for extrusion of the melted extrusion material onto an image receiving surface, although in other embodiments a single heater melts the extrusion material for each of the nozzles in the multi-nozzle extruder. 
     During operation, the extrusion material supply provides a predetermined length of the extrusion material filament  1108  to the dispenser  1120 . For example, in one configuration the disc  1121  receives a length of the filament that extends from the inlet  1122  to the outlet  1124 . An actuator in the dispenser rotates the disc  1121  to move the filament into contact with the cutter  1132 , which occupies a fixed position in the embodiment of  FIG. 11A . The cutter  1132  separates the portion of the filament that is within the disc  1121  from the remaining portion of the filament  1108  in the extrusion material supply. In some configurations, the rotation of the disk  1121  drives the filament against the stationary blade in the cutter  1132  to cut the filament. The actuator then rotates the disc  1121  to align the filament at the outlet  1124  with one of the channels corresponding to one nozzle in the multi-nozzle extruder. For example, in  FIG. 11A  the disc  1121  rotates the outlet  1124  to align the portion of the cut filament with the opening of the channel  1128 . The rollers  1142  in the disc  1121  rotate to move the cut portion of the filament into the channel  1128  where the rollers  1144  and  1146  engage the filament to control the movement of the filament to the nozzle  1136 . In the dispenser  1120 , the actuator returns the inlet  1122  in the disc  1121  to alignment with the free end of the filament at the rollers  1140  to receive additional filament for another channel and nozzle in the multi-nozzle extruder. In another embodiment, the dispenser optionally receives different types of build material from two or more extrusion material supplies. The actuator moves the inlet  122  on the disc  1121  into alignment with the outlets of different extrusion material supplies to receive segments of the extrusion materials from more than one supply at different times during operation of the dispenser  1120 . During operation, the controller  128  operates the dispenser  1120  to maintain a supply of the extrusion material from one or more of the extrusion material supplies for each of the nozzles in the multi-nozzle extruder. 
       FIG. 11B  depicts another configuration of the dispenser  1120 . In  FIG. 11B , the dispenser  1120  includes a cutter  1133  that is mounted to the disc  1121  proximate to the outlet  1124 . An actuator  1134  moves the cutter  1133  to cut the filament after the dispenser  1120  moves a predetermined length of the filament through the outlet  1124  and into one of the channels, such as channels  1128  and  1129  in  FIG. 11B . Rollers in each of the channels, such as rollers  1146  and  1147 , receive the filament from the dispenser  1120  and control the movement of the filament to the corresponding nozzle in the multi-nozzle extruder. In the configuration of  FIG. 11B , the filament remains in a conduit within the disc  1121  after the cutter  1133  separates a portion of the filament that is provided to each nozzle from the remaining portion of the filament  1108 . 
       FIG. 11C  depicts another embodiment of a dispenser  1164 . The dispenser  1164  includes a pivoting member  1122  that pivots a conduit  1162  with an inlet  1122  and outlet  1124  to align the outlet  1124  with the channels in the multi-nozzle extruder that provide the filament to the nozzles in the multi-nozzle extruder. During operation, the pivoting member  1122  moves the outlet of the conduit  1162  into alignment with an opening of one of the channels and the dispenser  1164  moves the filament  1108  from the supply  1102  to the channel to provide extrusion material to one of the nozzles in the multi-nozzle extruder. The actuator  1134  operates the cutter  1133  to separate the filament that has been supplied to the channel of the multi-nozzle extruder from the remaining filament in the supply and the dispenser continues operation to provide the extrusion material to the channels for each of the nozzles in the multi-nozzle extruder. In  FIG. 11C , the rollers  1140  and  1142  control the movement of the extrusion material filament  1108  through the dispenser  1164 . The rollers in the multi-nozzle extruder, such as roller  1146  and  1147 , control the movement of the filament through the channel to the corresponding nozzle, such as channel  1128  and nozzle  1136 , respectively. 
       FIG. 11D  depicts another embodiment of a dispenser  1172 . In  FIG. 11D , the dispenser  1172  includes a moving member  1166  with an inlet  1122 , outlet  1124 , and guide rollers  1142 . An actuator in the dispenser  1172  moves the member  1166  along a linear path to align the inlet  1122  with the filament  1108  from the extrusion material supply  1102  that passes through the guide rollers  1140 . The actuator also moves the member  1166  along the linear path to align the outlet  1124  with the openings in each of the plurality of channels, such as the channel  1128  that provides the filament to the nozzle  1136 . The dispenser  1172  includes a cutter  1132  that is located at a fixed position. The member  1166  receives a portion of the filament  1108  and the actuator moves the member  1166  and filament into contact with the cutter  1132  to separate the portion of the filament in the member  1166  from the remaining portion of the filament in the extrusion material supply  1102 . 
       FIG. 12A  depicts two dispensers that provide two different types of extrusion material to different nozzles in a single multi-nozzle extruder.  FIG. 12A  includes dispensers  1120  and  1124 . The dispenser  1120  receives a first extrusion material  1208  from a first extrusion material supply  1202  and the dispenser  1224  receives a second extrusion material  1212  from a second extrusion material supply  1204 . Each of the dispensers  1220  and  1120  is similar in configuration to the dispenser  1120  of  FIG. 11B , although alternative configurations include two or more dispensers from any of the embodiments in  FIG. 11A - FIG. 11D . During operation, the first dispenser  1220  supplies the first extrusion material to a first portion of the channels and corresponding nozzles in the multi-nozzle extruder, such as the channel  1228  and nozzle  1236  in the example of  FIG. 12B . Heaters in the multi-nozzle extruder melt the extrusion material as the extrusion material approaches the nozzles and one or more of the activated nozzles extrudes the melted extrusion material onto an image receiving surface. The second dispenser  1224  supplies the second extrusion material  1212  from the second extrusion material supply  1212  to a second portion of the channels and nozzles in the multi-nozzle extruder, such as channel  1232  and nozzle  1238 . 
       FIG. 12B  depicts another embodiment of multiple dispensers that supply two types of extrusion material to nozzles in a multi-nozzle extruder. In  FIG. 12B , two dispensers  1266  and  1268  are formed from a single member that moves linearly along a predetermined path to receive two types of extrusion material from the extrusion material supplies  1202  and  1206 , respectively. During operation, the dispenser  1266  receives a portion of the extrusion material  1208  from the extrusion material supply  1202  and the dispenser  1268  receives a portion of the extrusion material  1212  from the extrusion material supply  1206 . An actuator moves the dispensers  1266  and  1268  in two linear directions to cut the filament of extrusion material  1208  with the cutter  1231  and cut the filament of extrusion material  1212  with the cutter  1233 . The dispensers  1266  and  1268  then move to align the filaments of extrusion material with the channels that are associated with different portions of the nozzles in the extrusion multi-nozzle extruder. For example, in  FIG. 12B  the dispenser  1266  moves the filament into alignment with the channel  1228  and the nozzle  1236  to dispense the filament of the extrusion material  1208 . The actuator moves the dispensers  1266  and  1268  along the linear path to align the dispenser  1268  into alignment with the channel  1232  and nozzle  1238  to dispense the filament of the extrusion material  1212 . The embodiment of  FIG. 12B  includes the two dispensers  1266  and  1268  that are otherwise similar to the dispenser  1172  of  FIG. 11D . In alternative embodiments, a single dispenser receives extrusion material from two or more spools and dispenses the different extrusion materials to selected channels for different nozzles in the multi-nozzle extruder. Additionally, a single rotational dispenser optionally receives material from a plurality of material spools by simply stopping at the appropriate location and then distributes the material to a plurality of channels and melters. 
     The embodiments of  FIG. 12A  and  FIG. 12B  enable a three-dimensional object printer to supply multiple types of extrusion material to different nozzles in a single multi-nozzle extruder. For example, some three-dimensional printed objects are formed using multiple colors of extrusion material, and the dispenser configurations of  FIG. 12A  and  FIG. 12B  enable a first portion of the nozzles to extrude the extrusion material with the first color and a second portion of the nozzles to extrude the extrusion material with the second color to form a multi-color object. In other embodiments, the three-dimensional object printer uses two different types of extrusion materials to form different structures in the three-dimensional printed object, and the dispensers provide different types of extrusion material to selected nozzles to enable a single extrusion multi-nozzle extruder to form the object using multiple types of extrusion material. 
     In one configuration, each dispenser provides one type of extrusion material to one-half of the available nozzles in the multi-nozzle extruder for printing operations that use approximately equal amounts of the extrusion material. However, in other configurations the dispensers provide one type of extrusion material to a larger portion of the nozzles while one nozzle or a smaller number of nozzles receive the second type of extrusion material. For example, in one configuration the dispensers provide an extrusion material that forms most of the interior volume of an object to most of the nozzles in the multi-nozzle extruder while a smaller number of nozzles receive another type of extrusion material that forms portions of the exterior of the object. Additionally, after a nozzle has exhausted a supply of one type of extrusion material in the corresponding channel, the dispensers optionally provide a different type of extrusion material to the channel to enable one nozzle to extrude different types of extrusion material at different times during a three-dimensional object printing operation. 
     While  FIGS. 11A-11D  and  FIGS. 12A-12B  depict extrusion material dispensers that use various sets of rollers to control the movement of the filament, these illustrations are merely examples of some configurations of rollers. Alternative embodiments include one or more sets of guide rollers that control the movement of filaments through channels to the nozzles. In particular, the dispensers cut the filaments of extrusion material with minimum lengths and arrange the rollers to ensure that the filaments do not become lodged within the channels in the dispenser or a multi-nozzle extruder. 
     While  FIGS. 12A and 12B  depict dispensers that supply two different extrusion materials to nozzles in one or more multi-nozzle extruders, other embodiments include additional dispensers and extrusion material supplies to provide three or more types of extrusion material to a multi-nozzle extruder. Three-dimensional objects printers incorporate multi-nozzle extruders in a similar manner to the printhead  108  depicted in  FIG. 1  to form patterns of the extrusion material on an image receiving surface. Additionally, the dispensers described herein are also capable of providing extrusion material to a heater and pressure chamber assembly that supply liquefied extrusion material to a plurality of nozzles in an extrusion printhead. As depicted in  FIG. 11D , the dispenser  1172  alternatively provides the extrusion material to rollers  1184  and melter assembly  1186  to supply extrusion material to a pressure chamber  1190  for one or more nozzles  1192  in an extrusion printhead. The dispenser  1172  provides the extrusion material to two or more printheads within a three-dimensional object printer. Each of the printheads includes an inlet with the rollers  1184  and heaters  1186  that receive the extrusion material from the outlet  1124  of the dispenser  1172  or the corresponding outlets of any of the other dispensers described herein. During operation, the dispenser provides portions of the extrusion material filament  1108  to the inlets of different printheads, such as to a first printhead and a second printhead in a configuration of a printer that includes two printheads. The configuration depicted in  FIG. 11D  is also suitable for use with any of the other dispenser embodiments that are disclosed herein in  FIG. 11A - FIG. 11D  and  FIGS. 12A-12B . 
       FIG. 13A  and  FIG. 13B  depict an embodiment of an extrusion printhead  1300  that includes a pressure chamber and at least one valve to control the extrusion of liquefied extrusion material through one or more nozzles. The printhead  1300  is one embodiment of the printhead  108  that is suitable for use in the printer  100  and other three-dimensional object printers that employ extrusion printheads. The printhead  1300  includes a melter assembly  1312  that melts an extrusion material filament  1308  fed to the melter assembly  1312  via drive rollers  1342 , a housing  1304  that includes a pressure chamber  1320 , at least one nozzle  1326 , at least one valve member  1330 , a valve seal  1344 , and at least one actuator  1336 . 
     In the embodiment of  FIG. 13A , the melter assembly  1312  is formed from stainless steel and includes one or more heating elements  1316 , such as electrically resistive heating elements, that melt the filament of extrusion material  1308  in a fluid channel  1318 . The melter assembly  1312  receives extrusion material in a solid phase, such as the solid filament  1308  or, in alternative embodiments, solid phase powdered or pelletized extrusion material. The melter assembly  1312  controls the movement of the solid phase extrusion material through the channel to supply the extrusion material to the heaters  1316  that melt the extrusion material and supply melted extrusion material to the pressure chamber  1320 . A portion of the extrusion material that remains solid in the fluid channel  1318  proximate to the inlet by the drive rollers  1342  forms a seal in the fluid channel  1318  that prevents liquefied extrusion material from exiting the melter assembly from any other opening than the connection to the pressure chamber  1320 . In the example of  FIG. 13A , the drive rollers  1342  move portions of the extrusion material  1308  into the melter assembly  1312  to maintain a supply of the extrusion material in the pressure chamber  1320 . The fluid channel  1318  is fluidly coupled to the pressure chamber  1320  that is formed in the housing  1304 . The pressure chamber  1320  receives the melted extrusion material and additional heating elements  1316  in the housing  1304  maintain an elevated temperature within the pressure chamber  1320  to keep the extrusion material in a liquefied state within the housing  1304 . In some embodiments a thermal insulator covers portions of the exterior of the housing  1304  to maintain a temperature within the pressure chamber  1320 . 
     While  FIG. 13A  depicts a feed system that uses an electromechanical actuator and the driver rollers  1342  to control the movement of the filament  1308  into the melter assembly  1312 , alternative embodiments use one or more actuators to operate a rotating auger or screw to control the movement of the solid phase extrusion material into the melter assembly where the extrusion material melts and flows into the pressure chamber. For example, a rotating auger or screw moves solid phase extrusion materials such as powders or pellets of the extrusion material into the melter channel  1318 . More generally, the melter assembly  1312  includes a mechanical drive member that controls the movement of the extrusion material and one or more actuators, such as electric motors, that operate the drive member to move the extrusion material and maintain a supply of the extrusion material in the printhead. 
     To maintain a predetermined level of fluid pressure within the pressure chamber  1320 , the controller  128  adjusts the feed rate to maintain a supply of the melted extrusion material in the pressure chamber  1320 . In some configurations, the controller adjusts the feed rate based on either the number of valves in the valve assembly  1326  that are opened to enable extrusion of the extrusion material or on a fluid pressure level sensed within the pressure chamber  1320 . In another embodiment, a DC electric motor controls the rotation of the drive rollers  1342 , and the controller  128  adjusts the level of electrical current supplied to the DC motor to maintain a level of torque for the motor and rollers at a pre-defined level during material extrusion. The operation of the DC motor at a substantially constant level of torque provides a controlled level of pressure within the pressure chamber and provides automatic compensation for variations in the number of open nozzles in the system. 
     In the printhead  1300 , the pressure chamber  1320  is fluidly coupled to one or more outlet nozzles  1326 . In the illustrative embodiment of  FIG. 13A  and  FIG. 13B , the nozzles  1326  are directly coupled to the pressure chamber  1320 , although alternative embodiments optionally include a longer fluid path between the pressure chamber and nozzle outlets. To control the extrusion of the extrusion material, the controller  128  operates the valve actuators  1336  and valve members  1330  to open and close the nozzles  1326 . In printhead  1300 , the valve seal  1344  enables the valve members  1330  to pass through an exterior wall of the pressure chamber  1320  and to move within the pressure chamber  1320  while preventing any liquefied extrusion material from exiting the pressure chamber  1320  through any opening other than the nozzles  1326 . 
     During operation of the printhead  1300 , liquefied extrusion material from the pressure chamber  1320  extrudes through any of the nozzle outlets  1326  when the outlets are fluidly coupled to the pressure chamber  1320  and are not blocked by one of the valve members  1330 . Each of the valve members  1330  is, for example, an elongated aluminum or steel pin with a rounded or chamfered end that conforms to a shape and size of a fluid opening between the pressure chamber  1320  and a corresponding nozzle  1326  in the printhead  1300 . Each valve member  1330  is aligned with a single nozzle  1326  in the printhead  1300 . The actuators  1336  move the valve members  1330  to open and close the fluid paths through the nozzles  1326  to control the extrusion of extrusion material from the printhead  1300 . In the printhead  1300 , the electromechanical actuators  1336  are electromagnetic actuators that move the valve members  1330  via an electromagnetic force in response to an electric current, while in another embodiment the electromechanical actuator is a piezo-electric actuator that generates a mechanical force to move the member in response to an electric current. In the printhead  1300 , the electromechanical actuators  1330  are located outside of the pressure chamber  1320  and are thermally isolated from the pressure chamber  1320  and melter assembly  1312 . The actuators  1336  operate at a lower temperature than the pressure chamber  1320  and melter assemble  1312  that improves the reliability and operating life of the actuators, while the elongated valve members  1330  extend into the higher-temperature regions of the printhead  1300  through the valve seal  1344 . The actuators  1336  move the valve members  1330  between at least two positions within the pressure chamber  1320 . In a first position, the valve member  1330  blocks a flow of the extrusion material through the corresponding nozzle  1326  to block the flow of extrusion material and effectively “deactivate” the nozzle. 
       FIG. 13B  depicts a selection of nozzles and valve members in the printhead  1300 . In  FIG. 13B , the valve member  1330 A is located in a first position where the valve member  1330 A engages the fluid opening between the pressure chamber  1320  and the nozzles  1326 A. The valve members  1330 B and  1330 C are each located in a second position within the pressure chamber  1320  and these valve members are removed from the fluid openings of the nozzles  1326 B and  1326 C, respectively. The pressurized melted extrusion material in the pressure chamber  1320  flows through the outlets and corresponding nozzles  1326 B and  1326 C during a printing operation while the valve members  1330 A and  1330 B remain in the second position of  FIG. 13B . During a printing operation, the actuators  1336  move the valve members  1330 , including the valve members  1330 A- 1330 C, between the respective first and second positions to either disable or enable the extrusion of extrusion material through selected nozzles in the printhead  1330 . In the printer  100 , the controller  128  operates the actuators  1336  to control the extrusion of extrusion material during a printing operation. The controller  128  controls the actuators  1336  to form arrangements of the extrusion material using all or a selected portion of the nozzles in the printhead  1330  as the printhead  1330  moves in the process direction to form each layer of a three-dimensional printed object. 
     The nozzle array  1326  includes the nozzle openings that are formed through a planar member  1340 . In the embodiment of  FIG. 13A  and  FIG. 13B , the planar member  1340  is a metallic plate with an external surface that is optionally coated with a low-surface energy material such as polytetrafluoroethylene. In other embodiments the planar member  1340  is formed from a portion of the housing  1304  and alternative embodiments form the member from ceramic or another material with suitable mechanical and thermal properties. The planar member  1340  provides a smooth surface through which the activated nozzles  1326  extrude the extrusion material during the printing operation. In other embodiments, the planar member includes grooves or other features formed between the nozzles or each of the nozzles is formed through a separate raised planar member. The planar member  1340  also receives some of the heat from the heaters  1316  in the printhead housing  1304 . 
     In some operating modes, the printhead  1300  is positioned in close proximity to the image receiving surface and the liquefied extrusion material forms a thin layer between the planar member  1340  and the image receiving surface during the printing operation. For example,  FIG. 13B  depicts an arrangement of the extrusion material  1348  that extrudes from the activated nozzles  1326 B and  1326 C onto an image receiving surface, which is depicted as the upper surface of the three-dimensional printed object  140  of  FIG. 1  for illustrative purposes. In  FIG. 13B , the extruded extrusion material  1348  fills a gap between the surface of the object  140  and the surface of the planar member  1340 . The heated planar member  1340  smooths the extruded extrusion material  1348  and enables the extrusion material  1348  to remain liquefied for a short period while the printhead  1300  and planar member  1340  move along the process direction to form swaths of the extrusion material while operating two or more nozzles simultaneously. The planar member  1340  also prevents an undesirable accumulation of excess extruded material between the nozzles in the face of the printhead  1300 . Arrangements of the extrusion material that are located proximate to one another may merge to form a substantially continuous arrangement, such as the arrangement of extrusion material  1348  that includes merged arrangements of the extrusion material extruded from nozzles  1326 B and  1326 C. 
     In some printhead configurations two or more nozzles in a an extrusion printhead may partially or completely overlap each other in the process direction, such as when a printhead moves along a curved path or forms corners between linear segments of a process direction path. The nozzles extrude overlapping arrangements of the extrusion material that would otherwise form a thicker layer than other regions where only a single nozzle extrudes the extrusion material, which would otherwise produce a layer of the three-dimensional printed object with a non-uniform thickness. However, in the printhead  1300  the planar member  1340  spreads and smooths the overlapping arrangements of extrusion material to produce an arrangement of the extrusion material with a uniform thickness even in regions where multiple nozzles extrude overlapping arrangements of the extrusion material. 
       FIG. 14A  depicts another embodiment of an extrusion printhead  1400  that includes a pressure chamber storing liquefied extrusion material that is extruded through at least one nozzle. The printhead  1400  is another embodiment of the printhead  108  that is suitable for use in the printer  100  and other three-dimensional object printers that employ extrusion printheads. The multi-nozzle extrusion printhead  1400  includes a plurality of nozzles in the array  1426  that are each fluidly coupled to a single pressure chamber  1420  and a valve assembly  1430  that controls a flow of extrusion material from the pressure chamber  1420  to the individual nozzles  1426 . In  FIG. 14B , the valve assembly  1430  is shown in more detail in a cross-section bottom view taken along line  1450  and looking up into the valve assembly. In  FIG. 14C , the pressure chamber  1420  and nozzles in the array  1426  are shown in more detail in another cross-sectional side view taken along line  1454  and looking into the printhead. 
     The printhead  1400  includes a pressure chamber  1420  that is configured to receive extrusion material from a single supply of extrusion material, and a valve assembly  1430 . The printhead  1400  includes a housing  1404  that forms the pressure chamber  1420  including a plurality of valves that enable or disable the flow of extrusion material through individual fluid conduits that couple the pressure chamber with a plurality of nozzles in the array  1426  in the extrusion printhead  1400 . 
     In the extrusion printhead  1400 , the housing  1404  includes an opening  1410  that enables an extrusion material  1408  to enter the pressure chamber  1420 . The housing  1404  optionally includes an integrated or externally mounted heat sink (not shown) that prevents overheating of the pressure chamber  1420  and controls cool down of the printhead  1400  when the printhead  1400  is deactivated. In the illustrative embodiment of  FIG. 14A , the extrusion material  1408  is a filament  1408  of a solid ABS plastic or other suitable extrusion material from an extrusion material supply  1402 . 
     In  FIG. 14C , the housing  1404  includes one or more heaters  1412 , such as electrical resistance heaters, which heat the pressure chamber  1420  and melt the solid extrusion material  1408  to form a fluid reservoir of the melted extrusion material in the chamber  1420 . One or more rollers, such as rollers  1442 , include actuators that control a feed rate for the filament of the extrusion material  1408  into the pressure chamber  1420  in the extrusion printhead  1404 . The controller  128  adjusts the feed rate to maintain a supply of the melted extrusion material in the pressure chamber  1420  based on the number of valves in the valve assembly  1430  that are opened to enable extrusion of the extrusion material, a fluid pressure level sensed within the pressure chamber  1420 , or on an expected volume of the extrusion material that the printhead  1404  extrudes onto the image receiving surface. The three-dimensional volume between the printhead  1404  and the image receiving surface depends upon the lateral area covered by the predetermined pattern of the extrusion material, which the controller  128  optionally identifies based on the number of activated nozzles during operation, and the z-axis distance between the face of the printhead  1404  and the image receiving surface. In another embodiment, the controller  128  adjusts the feed rate of the filament based on a velocity of relative movement between the printhead and the image receiving surface in the process direction. In another embodiment, a DC electric motor drives the filament drive rollers, and the current to the DC motor is controlled to maintain a level of torque for the motor and rollers at a pre-defined level during material extrusion. The operation of the DC motor at a substantially constant level of torque provides a controlled level of pressure within the pressure chamber and provides automatic compensation for variations in the number of open nozzles in the system. 
     The extrusion printhead  1400  couples a single supply of extrusion material to a plurality of nozzles in the nozzle array  1426 . A plurality of fluid outlets in the housing  1404  place the pressure chamber  1420  in fluid communication with the nozzles in the array  1426 . For example, the fluid outlet  1424  places the pressure chamber  1420  in fluid communication with the nozzle  1428  ( FIG. 14B  and  FIG. 14C ). The melted extrusion material extrudes through the nozzles that remain in fluid communication with the chamber  1420  either through gravity or through a positive pressure force that is applied to the pressure chamber  1420  to expel the melted extrusion material through the nozzles in the array  1426 . During operation, however, the printhead  1400  only extrudes extrusion material through one or more of the nozzles at selected times to form specific arrangements of extrusion material. In the printhead  1400 , the valve assembly  1430  includes a plurality of valves that each controls the flow of extrusion material from the pressure chamber  1420  to one of the nozzles  1426 . The valve assembly  1430  includes a plurality of valves that are arranged transverse to the fluid outlets between the pressure chamber  1420  and the nozzles  1426 . Each valve includes an electromechanical actuator (not shown) and a moveable member, such as metal pins that are depicted in  FIG. 14B  including pins  1432  and  1434 . The metal pins are formed from stainless steel, aluminum, or any other metal or alloy that is suitable for use in contact with the liquefied extrusion material and in the operating temperature range of the printhead. The electromechanical actuator moves the moveable member a linear path between a first position where the member blocks the flow of the extrusion material through the fluid outlet and a second position where the member enables the extrusion material to flow through the fluid outlet. In one embodiment, the electromechanical actuator is an electromagnetic actuator that moves a metal pin via an electromagnetic force in response to an electric current, while in another embodiment the electromechanical actuator is a piezo-electric actuator that generates a mechanical force to move the member in response to an electric current. 
     In the embodiment of  FIG. 14C , the nozzles in the array  1426  are formed through a planar member  1429 . The planar member  1429  is similar in structure and function to the planar member  1340  that is described above in conjunction with the printhead  1300 . During operation of the printhead  1400 , the activated nozzles in the array  1426  extrude the extrusion material onto an image receiving surface, and the planar member  1429  engages the extruded extrusion material to fill gaps between arrangements of extrusion material that are extruded from nearby nozzles in the printhead  1400  and to maintain a uniform thickness for each layer of the extrusion material. 
     In the configuration that is illustrated in  FIG. 14C , one electromechanical actuator in the valve assembly  1430  moves the moveable member  1134  to a first position that blocks a flow of fluid through the fluid outlet  1425 . In the first position, a portion of the valve member  1434  moves into the fluid outlet  1425  to block the flow of extrusion material through the fluid outlet  1425 . In another valve, the electromechanical actuator moves the member  1432  to a second position that opens the fluid outlet  1424  to enable the extrusion material to flow from the pressure chamber  1420  through the nozzle  1428 . In the second position, the member  1432  is withdrawn from the fluid outlet  1424  to enable the fluid extrusion material to flow through the outlet  1424 . 
     In embodiments of the printer  100  that use the printheads  1300  or  1400 , the controller  128  is operatively connected to the electromechanical actuators in each valve of the valve assembly  1430 . During operation, the controller  128  operates the valves either to enable or disable the extrusion of extrusion material from different nozzles in the printhead  1400  to form arrangements of the extrusion material corresponding to the three-dimensional object image data  136  in each layers of the three-dimensional printed object  140 . More particularly, the controller  128  operates the electromechanical actuators to move one or more valve members into the first position to close a first set of selected valves while the electromechanical actuators move other valve members into the second position to open one or more of the remaining valves. The controller  128  opens and closes the valves to activate or deactivate some or all of the nozzles in the printhead at various times during a printing operation. 
     While the printheads  1300  and  1400  are depicted with a single row of nozzles and corresponding valves in a one-dimensional linear arrangement, alternative printhead configurations include multiple rows of nozzles and valves for a two-dimensional array of nozzles that cover substantially the width of the printhead in the cross-process direction. Examples of two-dimensional arrays of nozzles are depicted in  FIG. 9A ,  FIG. 9B , and  FIG. 10 . In some configurations, any one of the nozzles in a multi-nozzle extrusion printhead could be used to print the outline of a given layer, and the controller  128  distributes the operation of forming portions of the outline across some or all of the nozzles to balance the wear on the nozzles and ensure an even distribution of material flow throughout the printhead. Polymer extrusion material that remains at an elevated temperature for longer than a predetermined time can experience a degradation in material properties. The printhead embodiments described above ensure a balanced material flow throughout the extrusion printhead to reduce or eliminate degradation of the extrusion material. 
       FIG. 15  depicts a process  1500  for the operation of a three-dimensional printer, such as the printer  100  of  FIG. 1 , to form a portion of a three-dimensional printed object using a multi-nozzle extrusion printhead. The process  1500  is suitable for use with printers that employ any of the multi-nozzle extrusion printhead embodiments described herein, although the process  1500  is not exclusively limited to use with the multi-nozzle printhead configurations described herein. A three-dimensional object printer performs the process  1500  to form at least a portion of one layer of a three-dimensional printed object, and in many configurations the printer performs the process  1500  multiple times to form multi-layer three-dimensional printed objects. In the description below, a reference to the process  1500  performing a function or action refers to the operation of a controller to execute stored program instructions to perform the function or action using one or more components in a three-dimensional object printer. The process  1500  is described in conjunction with the printer  100  of  FIG. 1  for illustrative purposes. 
     The process  1500  begins as the printer produces relative motion between an extrusion printhead and an image receiving surface in a process direction along an outer perimeter of a region for one layer of a three-dimensional printed object (block  1504 ). In the printer  100 , the controller  128  operates the X/Y actuators  150  to move the printhead  108  along both linear and curved paths around the perimeter of a region on the surface of the support member  102  and the upper layer of the three-dimensional printed object  140 . In other printer configurations, a different set of actuators move the support member to produce the relative motion or move both the printhead and the support member to produce the relative motion. As described above, in the printer  100  the controller  128  retrieves image data corresponding to one layer of the 3D printed object from the 3D object data  138  in the memory  132 . In one embodiment, the controller  128  processes the image data to generate printhead path control data  138  that include a series of paths for relative motion between the extrusion printhead and the image receiving surface to form arrangements of the extrusion material. More particularly, the controller  128  operates the X/Y actuators  150  to move the printhead in a path that defines a perimeter of a region for one of layer of the three-dimensional printed object  140 . For example, as depicted in  FIG. 3 , a printhead  108  with three extrusion nozzles  312 ,  316 , and  320  moves along a perimeter path  332  while operating only a single nozzle  312  to form an arrangement of extrusion material along the outer perimeter of a region. In some printhead configurations, the diameter of the single nozzle  312  is less than than the diameters of the remaining nozzles in the printhead. Thus, the patterns of extrusion materials emitted from the orifice of the smaller diameter nozzle  312  occupy less space and can reproduce finer details than the remaining nozzles with larger nozzle orifice diameters. After forming the outline, the printer operates some or all of the nozzles in the printhead, including nozzles with the larger diameter, to fill in the region within the outline. Different portions of the path of movement for the printhead can include both linear (straight-line) segments and curved segments. In alternative embodiments, an external computing device, such as a personal computer or other suitable computing system, generates the printhead path control data  138  and provides the printhead path control data  138  to the controller  128  through a peripheral input-output (I/O) interface such as USB or through a data network interface. 
     During the process  1500 , the controller  128  operates at least one nozzle in the plurality of nozzles in the printhead to form an arrangement of the extrusion material in an outline of the perimeter around the region as the printer generates the relative movement between the printhead and the image receiving surface along the path of the outline (block  1508 ). In other embodiments, the controller  128  operates one nozzle or a group of nozzles that have narrower outlet diameters to form the outline with narrower arrangements of the extrusion material to form the outline with a high spatial resolution. For example, in  FIG. 3  if the nozzle  312  has a narrower diameter than the nozzles  316  and  320 , then the controller  128  operates the nozzle  312  to form the outline  332 . In other embodiments, the controller  128  operates multiple nozzles in the printhead to form multiple arrangements of the extrusion material around the perimeter of the region and within the region to increase the effective throughput rate of the three-dimensional object printer. Additionally, the controller  128  deactivates nozzles in the printhead that are positioned at locations that lie outside of the outline while one or more of the remaining nozzles form the outline of extrusion material. In the embodiment of  FIG. 1 , the controller  128  identifies the nozzles that are inside or outside of the region based on the printhead path control data  138  and the predetermined geometry of the nozzles in the multi-nozzle printhead  108 . The controller  128  closes valves in the printhead or halts the supply of extrusion material to individual nozzles to prevent the deactivated nozzles from emitting the extrusion material. 
     As described above in  FIG. 2A  and  FIG. 2B , in some printhead embodiments the physical layout of the nozzles in the printhead  108  forms a maximum separation between any two nozzles in the cross-process direction, and the controller  128  optionally operates the Zθ actuator  154  to adjust the distance between nozzles corresponding to the predetermined distance in the 3D image data. In embodiments of the printer  100  that include a multi-nozzle printhead with varying cross-process direction separation between adjacent nozzles, the controller  128  identifies cross-process direction distance between a first arrangement of an extrusion material formed by a first nozzle in the printhead and a second arrangement of the extrusion material formed by a second nozzle in the printhead with reference to the 3D object image data  136  for one layer of the three-dimensional object. 
     In some printer configurations the controller  128  positions the printhead  108  over the surface of the three-dimensional printed object  140  or other suitable image receiving surface with a narrow gap between the nozzles and the image receiving surface along the Z axis. For example, in one embodiment the gap is approximately 0.1 mm, although alternative printer configurations may operate with narrower or larger gaps. In a printhead that incorporates one or more nozzles in a planar member, such as the printheads  1300  and  1400  discussed above, the extruded extrusion material fills the gap between the image receiving surface and the printhead. The planar member on the printhead engages and spreads the extrusion material while the extrusion material remains in a liquid or semi-liquid state to enable different arrangements of extrusion material from nozzles in the printhead to merge into a single arrangement of the extrusion material. Additionally, the planar member maintains spreads the extrusion material to maintain a uniform thickness of the extrusion material layer even if two or more nozzles form overlapping arrangements of the extrusion material on the image receiving surface. 
       FIG. 5  depicts two arrangements of the extrusion material  332  and  532  that the printhead  108  forms with a first cross-process direction separation  504 . The controller  128  adjusts the angle of the printhead  108  relative to the cross-process direction axis CP to produce the separation.  FIG. 6  depicts another arrangement of extrusion material with two sets of extrusion material  332  and  632  that are formed by the nozzles  312  and  316 , respectively, in the printhead  108 . In the configuration of  FIG. 6 , the controller  128  operates the Zθ actuator  154  to rotate the printhead  108  about the Z axis by an angle ϕ relative to the cross-process direction axis CP. The rotation of the printhead  108  reduces the separation between the nozzles  312  and  316  in the cross-process direction, and the printhead  108  forms the parallel arrangements of the extrusion material  332  and  632  with the two patterns of extrusion material being formed adjacent to one another with substantially no gap between the two arrangements of extrusion material. 
       FIG. 9A  depicts another configuration of a printhead  904  that includes a two-dimensional array of nozzles. In the printhead  904 , the nozzles are staggered to enable the printhead  904  to extrude extrusion material in parallel arrangements with little or no space between adjacent nozzles in the cross-process direction. In the configuration of  FIG. 9A , the controller  128  operates a selected set of nozzles in the printhead  904  simultaneously to form different portions of the outline or to form swaths within an outline of the extruded material. For example, in  FIG. 9A  the controller  128  selectively activates the nozzles in groups  908 ,  912 , and  916 , to form different arrangements of extrusion material on the image receiving surface in an outline around a predetermined region of the image receiving surface, such as the square region that is depicted in  FIG. 9A . Additionally, the controller  128  deactivates nozzles in the printhead  904  if those nozzles are positioned at locations that lie outside of the outline. For example, while the controller  128  activates the group of nozzles  908  to form a portion of the outline in  FIG. 9A , the controller  128  also deactivates the group of nozzles  922  that lie outside of the perimeter of the region  902 . As depicted in  FIG. 9A , the controller  128  selectively activates and deactivates different nozzles in the printhead as the printhead moves to different locations along the process direction to form the outline with the predetermined shape based on the 3D object image data  136  and printhead path control data  138 . 
     As depicted in  FIG. 9A , the controller  128  operates the actuators in the printer  100  to generate the relative motion between the printhead  904  and the image receiving surface to move the printhead  904  in a process-direction path P around an outline of the region  902 . The controller  128  operates different subsets of the extrusion nozzles in the printhead  904  to form different arrangements of extrusion material in the outline that surrounds the region  902 . In the illustrative embodiment of  FIG. 9A , the controller  128  operates a first group of nozzles  908 , a second group of nozzles  912 , and a third group of nozzles  916  to form three different sides of the outline around the region  902 . In the example of  FIG. 9A , the staggered nozzles in the printhead  904  form arrangements of the extrusion material that are substantially adjacent to one another without gaps between the arrangements of extrusion material. The two-dimensional array of nozzles in the printhead  904  are arranged in a staggered configuration to enable the printhead  904  to form a continuous swath when the printhead is moved in a first linear direction and when moved in a second direction which is orthogonal to the first direction, such as when forming different sides of the outline depicted in  FIG. 9A . In another operating mode, the controller  128  adjusts the cross-process direction separation between parallel arrangements of the extrusion material by selecting different sets of nozzles that correspond to the predetermined cross-process direction separation between the printed arrangements of the extrusion material. 
     The printhead  904  of  FIG. 9A  is not configured to be rotated about the Zθ axis in the same manner as the printheads depicted in  FIG. 3 - FIG. 8 . Instead, the arrangement of the nozzles in the printhead enables the printhead to form corners between linear swaths of extrusion material and curved swaths of extrusion material without requiring rotation of the printhead.  FIG. 9B  depicts a simplified printhead embodiment  932  that includes two nozzles  936 A and  936 B. In one configuration, the controller  128  operates the X/Y actuators  150  to generate relative movement between the printhead  932  and an image receiving surface to form two linear swaths  944  and  945 . Both of the nozzles  936 A and  936 B extrude the extrusion material to form the swaths. At the corner location  942  between the swaths, the two nozzles  936 A and  936 B briefly overlap one another as the process direction of the relative printhead movement turns the corner. In another configuration, the X/Y actuators  150  generate relative printhead motion along a curved swath  950 . As the printhead  932  enters the curve, the nozzles  936 A and  936 B form the exterior and interior portions of the curve, respectively, but the nozzles briefly overlap at location  948  and at the end of the curve the nozzle  936 A forms the interior and the nozzle  936 B forms the exterior of the curve. 
     Even though a portion of both of the swaths depicted above includes a region of overlap between the extruded arrangements of extrusion material from two different nozzles, the printer  100  forms both of the swaths with uniform extrusion material widths and thicknesses during a printing operation. The liquid extrusion material spreads after being extruded from the nozzles to form arrangements with uniform widths and thicknesses even if portions of the swath include overlapping arrangements of the extrusion material. Additionally, as described above in conjunction with the printheads  1300  and  1400 , the planar member on the printhead that holds the nozzles also engages the extrusion material to form a uniform layer of the extrusion material in each swath. In some configurations, a printhead that includes nozzles with a diameter d and having the nozzles arranged with a minimum separation between neighboring nozzles of a distance of 2d is suitable for use in the process  1500 . For example, in  FIG. 9B  the printhead  954  includes five nozzles  956 A- 956 E in a polar configuration with a distance of at least 2d between neighboring nozzles. While the printhead  954  is an illustrative embodiment of a suitable multi-nozzle extrusion printhead, alternative configurations include, but are not limited to, a multi-row grid or rectangular array of nozzles with a separation of at least 2d between neighboring nozzles. 
     Referring again to  FIG. 15 , during the process  1500 , the printer  100  may form some arrangements of the extrusion material in the outline around the perimeter of the region with curved shapes. In some printhead embodiments, the nozzles in the printhead extrude the extrusion material at approximately the same rate. The controller  128  optionally identifies the curved portions of the path of movement for the printhead with reference to the printhead path control data  138  and optionally controls the operation of the printhead to maintain a uniform distribution of the extrusion material in both the inner and outer portions of the curve (block  1512 ). In one configuration that is described in more detail in conjunction with  FIG. 7 , the controller  128  operates the Zθ actuator  154  to oscillate the printhead. In another configuration that is described in more detail in conjunction with  FIG. 8 , the controller  128  operates some of the nozzles on the inner portion of the curves with shorter lengths activate and deactivate the nozzle on the inner curve intermittently. 
     The controller  128  adjusts the operation of the printhead  108  for curved paths because each nozzle in the extrusion printhead  108  extrudes the extrusion material at substantially the same volumetric rate (e.g., 0.01 cm 3 /sec). To subtend a given angle of a curve, the controller  128  nominally operates multiple nozzles for a single length of time required for the printhead to move through the full angle, even though the linear distance that is covered by an outer nozzle is often substantially larger than the linear distance covered by an interior nozzle. However, the nozzles that form shorter linear arrangements of the extrusion material extrude the extrusion material at the same rate as the nozzles forming the longer linear arrangements, which potentially produces an uneven surface since the shorter linear arrangements of extrusion material in the inner curves include substantially the same amount of extrusion material as the longer linear arrangements in the outer curves. By contrast, in the linear arrangements described above, the controller  128  operates the nozzles that form inner segments of the outlines for shorter periods of time than the nozzles that form the outer portions of the outlines so parallel linear arrangements of the extrusion material do not encounter the same issue with greater volumes of the extrusion material being formed in the interior arrangements of extrusion material. 
     In the embodiment that is depicted in  FIG. 7 , the controller  128  operates the Zθ actuator  154  to oscillate the printhead  108  about the Z axis to form arrangements of the extrusion material that have uniform densities and surfaces. The Zθ actuator  154  produces the oscillating pattern of movement in the printhead  108  while the X/Y actuators move the printhead  108  in the process direction along the curved path. The oscillation of the printhead  108  increases the linear length of the interior curved arrangement of the extrusion material to have a similar length to the linear length of an outer curved arrangement of the extrusion material.  FIG. 7  illustrates the operation of the printhead  108  with oscillation to form two curved arrangements of the extrusion material  704  and  708 . In  FIG. 7 , the printhead  108  forms the arrangement of extrusion material  704  along a curved path, and the controller  128  identifies a linear length of the curved path for the arrangement  704  with reference to the printhead path control data  138  in the memory  132 . The controller  128  also identifies the linear length of the curve for the inner arrangement of the extrusion material  708  and identifies both a magnitude and frequency of an oscillation for the printhead  108  that increases the total linear length of the inner arrangement  708  to be similar or equal to the linear length of the outer arrangement  708 . For example, in one configuration the controller  128  introduces a sinusoidal waveform onto the curved path for the inner arrangement of the extrusion material  708 . The controller  128  identifies both a magnitude and frequency for the sinusoidal oscillation or other pattern of oscillation that produces an inner curve with this oscillation yielding a linear length that is similar to the length of the outer arrangement of extrusion material  704 . 
     During operation, the controller  128  operates the Zθ actuator  154  to produce the identified shape, amplitude and frequency of oscillation in the printhead  108  to form the arrangements of extrusion material  704  and  708  that are depicted in  FIG. 7 . In the illustrative example of  FIG. 7 , the nozzle  312  is located at or near the axis of rotation for the Zθ actuator  154 , and the oscillation of the printhead  108  produces little or no effect on the outer curved arrangement of the extrusion material  704 . The inner curved arrangement of the extrusion material  708  includes the oscillating pattern that increases the total linear length of the inner arrangement of built material  708  to be similar to the outer arrangement  704 . The inner arrangement of extrusion material  708  has a similar density to the outer arrangement  704  and the oscillation of the printhead  108  enables the printer  100  to form multiple concentric curved arrangements for the extrusion material with uniform density and thickness in each layer of a three-dimensional printed object. 
       FIG. 8  depicts another process for the extrusion printhead  108  during formation of two curved arrangements of the extrusion material including an outer arrangement  804  that is formed by the nozzle  312  and an inner arrangement  812  that is formed by the nozzle  316 . In the process depicted in  FIG. 8 , the controller  128  identifies a first linear length of the outer arrangement of the extrusion material  804  and a second linear length of the inner arrangement of the extrusion material  812 . The controller  128  then identifies a ratio of the second linear length to the first linear length, and operates the nozzle  316  in an intermittent manner with a predetermined frequency and a duty cycle corresponding to the identified ratio. For example, if the arrangement of extrusion material  804  has a length of 30 mm and the arrangement of extrusion material  812  has a length of 27 mm, then the controller  128  identifies the ratio (9/10) for a duty cycle of operation for the nozzle  316  (90%). The controller  128  operates the nozzle  316  over a series of predetermined time intervals (e.g. 0.1 second intervals) with the nozzle  316  being activated to extrude extrusion material during a 90% portion of the interval (e.g. 0.09 seconds) while the nozzle  316  is deactivated and does not extrude extrusion material during another portion of the interval (e.g., 0.01 seconds). Since the nozzle  316  extrudes the extrusion material in a liquid form, the liquid extrusion material fills the gaps formed when the nozzle  316  is deactivated and the inner curved arrangement of extrusion material  812  has substantially the same density and height as the outer arrangement of extrusion material  804 . 
     Process  1500  continues as the controller  128  moves the extrusion printhead along straight-line or curved swath paths within the region formed by the outlines of arrangements of extrusion material (block  1516 ) and operates two or more nozzles in the printhead simultaneously to form swaths of the extrusion material that fill at least a portion of the region with a predetermined pattern of the extrusion material (block  1520 ). During the formation of swaths, the controller  128  activates two or more nozzles in the printhead simultaneously to form the swaths of extruded material within the outline. Additionally, the controller  128  also selectively deactivates a portion of the nozzles that may move to positions overlapping already formed regions of the extruded material or that move to locations outside of the perimeter of the printed extrusion material. For example,  FIG. 4  depicts the printhead  108  applying multiple swaths of the extrusion material to form a pattern of the extrusion material in the region formed by the arrangement of extrusion material  332  including extruded lines  336 ,  338 , and  340  from the nozzles  312 ,  316 , and  320 , respectively. 
       FIG. 10  depicts the printhead  904  forming swaths of extrusion material during a fill operation. In  FIG. 10 , the X/Y actuators  150  move the printhead  904  along straight-line paths to fill in a region within an outline formed by the extrusion material.  FIG. 10  depicts the formation of two swaths of the extrusion material including swath  1012  and swath  1016 .  FIG. 10  depicts all of the extrusion nozzles  1008  in the printhead  904  in an activated configuration to form the swaths, but in some configurations, the controller  128  deactivates some of the nozzles in response to the controller  128  identifying that the nozzles have moved outside of the swath area or the perimeter surrounding the region. In the embodiment of  FIG. 1 , the controller  128  identifies the nozzles that are inside or outside of the region based on the printhead path control data  138  and the predetermined geometry of the nozzles in the multi-nozzle printhead  108 . The controller  128  closes valves in the printhead or halts the supply of extrusion material to individual nozzles to prevent the deactivated nozzles from emitting the extrusion material. In some configurations, the extrusion printhead fills the entire region with extrusion material to form a solid layer, while in other embodiments the printhead forms a grid, honeycomb, or other suitable pattern that partially fills the region. In the printer  100 , the controller  128  controls the activation and deactivation of individual nozzles independently to enable the printhead to form arrangements of extruded materials that start and stop at predetermined locations along the process direction P even if the nozzles are arranged in a staggered configuration. Similarly, the controller  128  selects the timing of operation for each nozzle to start or finish a given swath based on the arrangements of extrusion material that have been formed in previously printed swaths. 
     The printer  100  performs the process  1500  to form one or more regions in a layer of a three-dimensional printed object. For multi-layer objects, the printer  100  performs the process  1500  one or more times for each layer to form a three-dimensional printed object from a plurality of layers of the extrusion material. 
     It will be appreciated that variants of the above-disclosed and other features and functions, or alternatives thereof, may be desirably combined into many other different systems, applications or methods. Various presently unforeseen or unanticipated alternatives, modifications, variations or improvements may be subsequently made by those skilled in the art that are also intended to be encompassed by the following claims.