Patent Publication Number: US-11383430-B2

Title: Heating system for fiber-reinforced thermoplastic feedstock and workpiece

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The following are hereby incorporated by reference:
         (i) U.S. Pat. No. 10,076,870, entitled “Filament Guide,” issued on Sep. 18, 2018; and   (ii) U.S. patent application Ser. No. 15/959,213, entitled “Variable-Contour Compaction Press,” filed on Apr. 21, 2018; and   (iii) U.S. patent application Ser. No. 15/959,214, entitled “Variable-Contour Compaction Roller,” filed on Apr. 21, 2018; and   (iv) U.S. patent application Ser. No. 15/959,215, entitled “Self-Cleaning Variable-Contour Compaction Press,” filed on Apr. 21, 2018; and   (v) U.S. patent application Ser. No. 16/023,197, entitled “Filament Cutter,” filed on Jun. 29, 2018; and   (vi) U.S. patent application Ser. No. 16/023,210, entitled “Filament Accumulator or Tensioning Assembly,” filed Jun. 29, 2018; and   (vii) U.S. patent application Ser. No. 16/690,765, entitled “Heater for Thermoplastic Filament and Workpiece,” filed Nov. 21, 2019; and   (viii) U.S. patent application Ser. No. 16/792,150, entitled “Thermoplastic Mold with Tunable Adhesion,” filed on Feb. 14, 2020; and   (ix) U.S. patent application Ser. No. 16/792,156, entitled “Thermoplastic Mold with Implicit Registration,” filed on Feb. 14, 2020; and   (x) U.S. Patent Application Ser. No. 63/025,109, entitled “Heating System for Fiber-Reinforced Thermoplastic Feedstock and Workpiece,” filed May 14, 2020, and   (xi) U.S. Patent Application Ser. No. 63/029,172, entitled “Heating System for Fiber-Reinforced Thermoplastic Feedstock and Workpiece,” filed May 22, 2020.       

     For the purposes of this specification, if there is any inconsistency in the language between this specification and the language in one or more of these documents, the language in this specification prevails. 
     FIELD OF THE INVENTION 
     The present invention relates to additive manufacturing in general, and, more particularly, to an additive manufacturing process that uses segments of fiber-reinforced thermoplastic feedstock (e.g., pre-preg tape, filament, etc.) as its elemental unit of fabrication. 
     BACKGROUND OF THE INVENTION 
     In the same way that a building can be constructed by successively depositing bricks on top of one another, it is well known in the field of additive manufacturing that an article of manufacture can be fabricated by successively depositing segments of fiber-reinforced thermoplastic filament on top of one another. 
     In some ways, a segment of thermoplastic filament is similar to a spaghetti noodle. When the temperature of a thermoplastic filament is below its resin softening point, the filament is long, thin, stiff, and not sticky—like a dry spaghetti noodle. In contrast, when the temperature of the filament is above its resin softening point but below its melting point, the filament is long, thin, flexible, and sticky—like a wet spaghetti noodle. 
     There are, however, some key differences between bricks and thermoplastic filament. For example, masonry bricks are not, in and of themselves, self-adhesive, and, therefore an adhesive compound—typically mortar—is used to bind them together. In contrast, segments of thermoplastic filaments are self-adhesive, and they will become bound if they are pressed tightly when they are hot and held together until they are cool. 
     Similarly, it is well known in the field of additive manufacturing that an article of manufacture can be fabricated by successively depositing segments of thermoplastic tape on top of one another. Whereas a segment of thermoplastic filament is similar to spaghetti, a segment of thermoplastic tape is similar to a ribbon pasta or lasagna noodle. When the temperature of the thermoplastic tape is below its resin softening point, the tape is long, thin, wide, stiff, and not tacky—like a dry lasagna noodle. In contrast, when the temperature of the tape is above its resin softening point but below its melting point, the tape is long, thin, wide, flexible, and sticky—like a wet lasagna noodle. And like thermoplastic filament, segments of thermoplastic tape are self-adhesive, and they will become bound if they are pressed tightly when they are hot and held together until they are cool. 
       FIG. 1  depicts an illustration of additive manufacturing system  100  in the prior art, which system fabricates articles of manufacture by successively depositing segments of fiber-reinforced thermoplastic feedstock (e.g., filament, tape, etc.) on top of one another. 
     Additive manufacturing system  100  comprises: platform  101 , robot mount  102 , robot  103 , build plate support  104 , build plate  105 , workpiece  106 , deposition head  107 , tamping tool  108 , controller  109 , feedstock reel  110 , feedstock  111 , accumulator  112 , laser  141 , optical cable  151 , optical instrument  161 , laser beam  171 , laser control cable  191 , irradiated region  271 , nip line segment  281 , pinch line segment  282 , and deposition path  291 , interrelated as shown. 
       FIG. 2 a    depicts a close-up of workpiece  106 , deposition head  107 , tamping tool  108 , feedstock  111 , optical cable  151 , optical instrument  161 , and laser beam  171 , as depicted in  FIG. 1 .  FIG. 2 b    depicts a close-up of workpiece  106 , deposition head  107 , tamping tool  108 , feedstock  111 , irradiated region  271 , and deposition path  291 , along cross-section AA-AA, as depicted in  FIG. 2 a   .  FIG. 3  depicts a schematic diagram of the heating architecture for additive manufacturing system  100 . 
     Platform  101  is a rigid metal structure that ensures that the relative spatial relationship of robot mount  102 , robot  103 , deposition head  107  (including tamping tool  108 ), and optical instrument  161  are maintained and known with respect to build-plate support  104 , build plate  105 , and workpiece  106 . Robot mount  102  is a rigid, massive, and stable support for robot  103  that provides ballast and inertial stability for robot  103 . Robot  103  is a six-axis articulated mechanical arm that holds deposition head  107 , optical instrument  161  and optical cable  151 . The movement of robot  103  (including deposition head  107 ) is under the direction of controller  109 . Robot  103  is capable of depositing feedstock  111  at any location, in anyone-, two-, or three-dimensional curve, and with any angular orientation. 
     Build plate support  104  is a rigid, massive, and stable support for build plate  105  and workpiece  106 . Build plate support  104  comprises a stepper motor—under the direction of controller  109 —that is capable of rotating build plate  105  (and, consequently workpiece  106 ) around an axis that is normal to the X-Y plane. Build plate  105  is a rigid aluminum-alloy support onto which workpiece  106  is steadfastly affixed so that workpiece  106  cannot move in any direction or rotate around any axis independently of build plate  105 . Workpiece  106  comprises one or more segments of feedstock  111  that have been successively deposited and welded together in a desired geometry. Deposition head  107  is the end effector of robot  103  and comprises:
         (i) a feedstock guide that directs feedstock  111  into position for heating, tamping, and welding onto workpiece  106 , and   (ii) tamping tool  108 , which tamps the heated feedstock  111  into the heated workpiece  106 , and   (iii) a feedstock cutter—under the direction of controller  109 —that periodically or sporadically cuts feedstock  111 , and   (iv) optical instrument  161 , which takes laser beam  171  from optical cable  151 , conditions it, and directs it onto irradiated region  271 , and   (v) a structural support for optical instrument  161  that maintains the relative spatial position of the feedstock guide, tamping tool  108 , the cutter, and optical instrument  161 .
 
The feedstock guide, the feedstock cutter, and the structural support for optical instrument  161  are omitted from the figures so that the reader can more clearly understand the functional and spatial relationship of workpiece  106 , deposition head  107 , tamping tool  108 , feedstock  111 , and optical instrument  161 .
       

     Tamping tool  108  comprises a roller-bearing mounted steel cylinder that tamps the heated feedstock  111  into the heated workpiece  106 . 
     Controller  109  comprises the hardware and software necessary to direct robot  103 , build plate support  104 , and deposition head  107  in order to fabricate the article of manufacture. 
     Feedstock reel  110  is a circular reel that stores 1000 meters of feedstock  111  and feeds that feedstock to deposition head  107  and that maintains a constant tension on feedstock  111 . Feedstock  111  is a carbon fiber-reinforced thermoplastic filament or tape, which is commonly called “pre-preg.” Accumulator  112  takes feedstock  111  from feedstock reel  110  and provides it to deposition head  107  with the correct tension for depositing. 
     Optical Instrument  161  is hardware that takes high-energy light from optical cable  151  and outputs laser beam  171 , which illuminates and heats those portions of feedstock  111  and workpiece  106  that are within Irradiated region  271 . Laser  141  is a high-energy laser whose output power is controlled by controller  109 , via laser control cable  191 . Because controller  109  controls robot  103  and the speed at which feedstock  111  is deposited, controller  109  knows how quickly or slowly each unit-length of feedstock  111  must be heated and adjusts laser  141  accordingly. When the feedstock is deposited quickly, laser  141  is set to higher power so that feedstock  111  and workpiece  106  can be heated quickly. In contrast, when feedstock  111  is deposited more slowly, laser  141  is set to lower power, and when deposition stops laser  141  is turned off. Optical cable  151  is a glass fiber for carrying the light from laser  141  to optical instrument  161  with substantially no loss. 
     Nip line segment  281  is that line segment on the circumferential surface of tamping tool  108  where the compressive force on feedstock  111  from tamping tool  108  and workpiece  106  is at a maximum. Pinch line segment  282  is that line segment on the circumferential surface of tamping tool  108  where the compressive force on feedstock  111  from tamping tool  108  and workpiece  106  first substantially constrains any movement of feedstock  111  parallel to the axis of tamping tool  108 . 
     Deposition path  291  depicts the location on workpiece  106  where feedstock  111  is next to be deposited. 
     In this context, the process of fabricating articles of manufacture with segments of fiber-reinforced thermoplastic feedstock presents many challenges. 
     SUMMARY OF THE INVENTION 
     Some embodiments of the present invention art are capable of welding feedstock to a workpiece without some of the costs and disadvantages for doing so in the prior art. The nature of these costs and disadvantages becomes clear upon close examination of additive manufacturing system  100 , as presented above and in  FIGS. 1, 2   a ,  2   b , and  3 . 
     The job of laser beam  171  is to heat each segment of feedstock  111 - and the corresponding portion of workpiece  106  to which it is to be welded—to a very narrow temperature range above their resin softening point. If the temperature of either is too low, then the weld will be defective, and if the temperature of either is too high, then it could burn or melt. 
     In the prior art, laser beam  171  heats both workpiece  106  and feedstock  111  at the same time, in the same manner, and with the beam&#39;s energy evenly split between them. Given that both workpiece  106  and feedstock  111  comprise the same material and must be heated to the same temperature, the use of laser beam  171  to heat them both appears to be reasonable. In practice, however, it fails to produce quality welds, and on close examination, the reason why is clear: the task of heating the workpiece is, in general, far more complex and variable than the task of heating the feedstock. 
     The geometry and composition of each unit-length of feedstock  111  is approximately uniform, and, therefore, each unit-length of feedstock  111  has approximately the same surface area, heat capacity, and thermal conductivity as every other segment. As long as the initial temperature of each segment is the same, then the same amount of heat energy is needed to heat each segment to its resin softening point. 
     In contrast, the geometry and fiber orientation of each portion of workpiece  106  varies, and, therefore, different portions of workpiece  106  have different surface areas, heat capacities, and thermal conductivities. As a result, different portions of workpiece  106  require different amounts of heat energy to heat them to their resin softening point. 
     Furthermore, laser beam  271  needs to heat those portions of workpiece  106  along deposition path  291 . When deposition path  291  is straight, laser beam  271  heats the correct portions, but when deposition path  291  twists and turns—as shown in  FIG. 2 b   -laser beam  271  does not heat the correct portions. 
     And still furthermore, the angle of incidence of laser beam  271  on feedstock  111  is generally consistent, which causes each unit-length of feedstock to absorb the same amount of heat energy per unit-time. In contrast, the angle of incidence of laser beam  271  on workpiece  106  is inconsistent because of variations in the contour of workpiece  106 . This, in turn, causes:
         (i) the irradiance of laser beam  171  at each unit-area on workpiece  106  to vary, and   (ii) the amount of light that is reflected off of workpiece  106  to vary, and   (iii) the amount of light that is refracted into—and absorbed by—workpiece  106  to vary, and   (iv) different unit-areas of workpiece  106  to absorb different amounts of heat energy per unit-time.       

     To address these and other issues, the first illustrative embodiment comprises two lasers. One laser beam is solely dedicated to heating the feedstock, and the other laser beam is solely dedicated to heating the workpiece. This is advantageous because it enables one laser beam to be dedicated to addressing the particular issues associated with heating the feedstock and one laser beam to be dedicated to addressing the particular issues associated with heating the workpiece. Furthermore, the total cost for the two less-powerful lasers can be less than the cost of laser  141  in the prior art. 
     In accordance with the first illustrative embodiment, each laser beam—and its associated optical instrument—is independently-controlled to ensure that each segment of feedstock and each portion of the workpiece are properly heated. For example, and without limitation, the first illustrative embodiment employs feedforward, a variety of sensors, and feedback to continually:
         (i) adjust the average power of each laser during each time-interval, and   (ii) steer the workpiece laser beam along the deposition path, and   (iii) adjust the irradiance and angle of incidence of each laser beam to compensate for changes in the contour of the workpiece and other factors, to ensure that each segment of feedstock and each portion of the workpiece are properly heated, tamped, and welded.       

     The second illustrative embodiment comprises four lasers. Two laser beams are solely dedicated to heating the feedstock, and the other two laser beams are solely dedicated to heating the workpiece. This is advantageous because it enables two laser beams to cooperate in addressing the particular issues associated with heating the feedstock and two laser beams to cooperate in addressing the particular issues associated with heating the workpiece. Furthermore, the total cost for the four lasers can be less than the cost of the two lasers in the first illustrative embodiment. 
     The second illustrative embodiment is advantageous over the first illustrative embodiment because the use of four laser beams enables fine-tuning of the temperature of the feedstock and the workpiece immediately prior to deposition and tamping. Furthermore, the use of four laser beams is advantageous when the rate of deposition is high (e.g., &gt;100 mm/sec), highly non-uniform, and when the deposition path comprises many twists and turns. 
     The second illustrative embodiment uses one optical cable to carry each laser beam from its laser to its associated optical instrument on the deposition head. Because there are four laser beams, there are four optical cables. The third illustrative embodiment adds the means to carry all of the four laser beams to the deposition head via only one optical cable. This is advantageous because it enables the deposition head to be lighter and more compact. 
     These and other advantages of the illustrative embodiments will be apparent in the disclosure below and in the accompanying figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts an illustration of additive manufacturing system  100  in the prior art, which system fabricates articles of manufacture by successively depositing segments of fiber-reinforced thermoplastic feedstock (e.g., filament, tape, etc.) on top of one another. 
         FIG. 2 a    depicts a close-up of workpiece  106 , deposition head  107 , tamping tool  108 , feedstock  111 , optical cable  151 , optical instrument  161 , and laser beam  171 , as depicted in  FIG. 1 . 
         FIG. 2 b    depicts a close-up of workpiece  106 , deposition head  107 , tamping tool  108 , and feedstock  111  along cross-section AA-AA, as depicted in  FIG. 2   a.    
         FIG. 3  depicts a schematic diagram of the heating architecture for additive manufacturing system  100 . 
         FIG. 4  depicts an illustration of additive manufacturing system  400  in accordance with the first illustrative embodiment of the present invention. 
         FIG. 5 a    depicts a close-up of workpiece  406 , deposition head  407 , tamping tool  408 , feedstock  411 , sensor array  415 , optical instrument  461 , optical instrument  462 , optical cable  451 , optical cable  452 , sensor cable  454 , laser beam  471 , laser beam  472 , feedstock region  571 - 1 , feedstock region  571 - 2 , feedstock region  571 - 3 , workpiece region  572 - 1 , workpiece region  572 - 2 , workpiece region  572 - 3 , nip line segment  581 , and pinch line segment  582 , interrelated as shown. 
         FIG. 5 b    depicts a close-up of workpiece  406  in which deposition path  591  curves to the right (from the perspective of deposition head  407 ). 
         FIG. 6  depicts a close-up of workpiece  406  in which deposition path  591  curves to the left (from the perspective of deposition head  407 ). 
         FIG. 7  depicts a schematic diagram of the heating and sensor architecture for additive manufacturing system  400 , which irradiates and heats feedstock  411  and workpiece  406  and measures the temperature of feedstock  411  and workpiece  406 . 
         FIG. 8  depicts a schematic diagram of the sensor and control architecture for that portion of additive manufacturing system  400  that irradiates and heats feedstock  411  and workpiece  406 . 
         FIG. 9  depicts a flowchart of the tasks performed by additive manufacturing system  400 . Because additive manufacturing system  400  concurrently performs tasks on different segments of feedstock  411  and different portions of workpiece  406 , the tasks depicted in  FIG. 9  are concurrent. 
         FIG. 10  depicts a flowchart of the details of task  907 —adjusting optical instrument  461  and optical instrument  462 , as directed by controller  409 . 
         FIG. 11  depicts a flowchart of the relative timing of the tasks performed on segment m of feedstock  411  and on portion n of workpiece  406 , wherein m and n are integers. In accordance with the first illustrative embodiment segment m of feedstock  411  is deposited and tamped onto portion n of workpiece  406 . 
         FIG. 12  depicts an illustration of additive manufacturing system  1200  in accordance with the second illustrative embodiment of the present invention. 
         FIG. 13 a    depicts a close-up of workpiece  1206 , deposition head  1207 , tamping tool  1208 , feedstock  1211 , sensor array  1215 , optical instrument  1260 , optical instrument  1261 , optical instrument  1262 , optical instrument  1263 , optical cable  1250 , optical cable  1251 , optical cable  1252 , optical cable  1253 , sensor cable  1254 , laser beam  1270 , laser beam  1271 , laser beam  1272 , laser beam  1273 , feedstock region  1371 - 1 , feedstock region  1371 - 2 , feedstock region  1371 - 3 , workpiece region  1372 - 1 , workpiece region  1372 - 2 , workpiece region  1372 - 3 , nip line segment  1381 , and pinch line segment  1382 , interrelated as shown. 
         FIG. 13 b    depicts a close-up of workpiece  1206  in which deposition path  1391  curves to the right (from the perspective of deposition head  1207 ). 
         FIG. 14  depicts a close-up of workpiece  1206  in which deposition path  1391  curves to the left (from the perspective of deposition head  1207 ). 
         FIG. 15  depicts a schematic diagram of the heating and sensor architecture for additive manufacturing system  1200 , which irradiates and heats feedstock  1211  and workpiece  1206  and measures the temperature of feedstock  1211 , workpiece  1206 , and tamping tool  1208 . 
         FIG. 16  depicts a schematic diagram of the sensor and control architecture for that portion of additive manufacturing system  1200  that irradiates and heats feedstock  1211  and workpiece  1206 . 
         FIG. 17  depicts a flowchart of the tasks performed by additive manufacturing system  1200 . Because additive manufacturing system  1200  concurrently performs tasks on different segments of feedstock  1211  and different portions of workpiece  1206 , the tasks depicted in  FIG. 17  are concurrent. 
         FIG. 18  depicts a flowchart of the details of task  1707 —adjusting optical instruments as directed by controller  1209 . 
         FIG. 19  depicts a flowchart of the details of task  1801 —adjusting optical instrument  1260 . 
         FIG. 20  depicts a flowchart of the details of task  1802 —adjusting optical instrument  1261 . 
         FIG. 21  depicts a flowchart of the details of task  1803 —adjusting optical instrument  1262 . 
         FIG. 22  depicts a flowchart of the details of task  1804 —adjusting optical instrument  1263 . 
         FIG. 23  depicts a flowchart of the relative timing of the tasks performed on segment m of feedstock  1211  and on portion n of workpiece  1206 , wherein m and n are integers. In accordance with the second illustrative embodiment segment m of feedstock  1211  is deposited and tamped onto portion n of workpiece  1206 . 
         FIG. 24  depicts an illustration of additive manufacturing system  2400  in accordance with the third illustrative embodiment of the present invention. 
         FIG. 25  depicts a close-up of workpiece  1206 , deposition head  1207 , tamping tool  1208 , feedstock  1211 , sensor array  1215 , optical instrument  1260 , optical instrument  1261 , optical instrument  1262 , optical instrument  1263 , optical cable  2454 , sensor cable  1254 , laser beam  1270 , laser beam  1271 , laser beam  1272 , laser beam  1273 , feedstock region  1371 - 1 , feedstock region  1371 - 2 , feedstock region  1371 - 3 , workpiece region  1372 - 1 , workpiece region  1372 - 2 , workpiece region  1372 - 3 , nip line segment  1381 , and pinch line segment  1382 , beam splitter  2461 , beam splitter  2462 , and beam splitter  2463 , interrelated as shown. 
         FIG. 26  depicts a schematic diagram of the heating and sensor architecture for additive manufacturing system  2400 , which irradiates and heats feedstock  1211  and workpiece  1206  and measures the temperature of feedstock  1211 , workpiece  1206 , and tamping tool  1208 . 
     
    
    
     DEFINITIONS 
     Irradiance—For the purposes of this specification, the term “irradiance” is defined as the radiant flux received by a surface per unit-area. The SI unit of irradiance is the Watt per meter 2 . 
     Nip line segment—For the purposes of this specification, a “nip line segment” on a tamping tool is defined as line segment on the circumferential surface of the tamping tool where the tamping tool exerts the maximum radial force on a feedstock. 
     Pinch line segment—for the purposes of this specification, a “pinch line segment” on a tamping tool is defined as the line segment on the circumferential surface of the tamping tool where the tamping tool first pinches a unit-length of feedstock between the tamping tool and the workpiece so that any movement of the feedstock parallel to the rotational axis of the tamping tool is substantially constrained. 
     Printer—For the purposes of this specification, a “printer” is defined as an additive manufacturing system or an additive and subtractive manufacturing system. 
     Printing—For the purposes of this specification, the infinitive “to print” and its inflected forms is defined as to fabricate. The act of fabrication is widely called “printing” in the field of additive manufacturing. 
     Resin Softening Point—For the purposes of this specification, the phrase “resin softening point” is defined as the temperature at which the resin softens beyond some arbitrary softness. 
     Workpiece—For the purposes of this specification, a “workpiece” is defined as an inchoate article of manufacture. 
     DETAILED DESCRIPTION 
       FIG. 4  depicts an illustration of additive manufacturing system  400  in accordance with the first illustrative embodiment of the present invention. Additive manufacturing system  400  fabricates an article of manufacture by successively depositing segments of fiber-reinforced thermoplastic feedstock (e.g., filament, tape, etc.) onto a workpiece until the article of manufacture is complete. 
     Additive manufacturing system  400  comprises: platform  401 , robot mount  402 , robot  403 , build plate support  404 , build plate  405 , workpiece  406 , deposition head  407 , tamping tool  408 , controller  409 , feedstock reel  410 , feedstock  411 , accumulator  412 , force gauge  413 , sensor array  415 , feedstock laser  441 , workpiece laser  442 , optical cable  451 , optical cable  452 , sensor cable  454 , optical instrument  461 , optical instrument  462 , laser beam  471 , laser beam  472 , feedstock laser control cable  491 , and workpiece laser control cable  492 , interrelated as shown. 
       FIG. 5 a    depicts a close-up of workpiece  406 , deposition head  407 , tamping tool  408 , feedstock  411 , sensor array  415 , optical instrument  461 , optical instrument  462 , optical cable  451 , optical cable  452 , sensor cable  454 , laser beam  471 , laser beam  472 , feedstock region  571 - 1 , feedstock region  571 - 2 , feedstock region  571 - 3 , workpiece region  572 - 1 , workpiece region  572 - 2 , workpiece region  572 - 3 , nip line segment  581 , and pinch line segment  582 , interrelated as shown. 
       FIG. 5 b    depicts a close-up of workpiece  406 , deposition head  407 , tamping tool  408 , feedstock  411 , feedstock region  571 - 1 , feedstock region  571 - 2 , feedstock region  571 - 3 , workpiece region  572 - 1 , workpiece region  572 - 2 , workpiece region  572 - 3 , pinch line segment  582 , and deposition path  591  all as seen along cross-section BB-BB as depicted in  FIG. 5   a.    
       FIG. 6  depicts a close-up of workpiece  406 , deposition head  407 , tamping tool  408 , feedstock  411 , feedstock region  571 - 1 , feedstock region  571 - 2 , feedstock region  571 - 3 , workpiece region  572 - 1 , workpiece region  572 - 2 , workpiece region  572 - 3 , pinch line segment  582 , and deposition path  591 , all as seen along cross-section BB-BB as depicted in  FIG. 5   a.    
       FIG. 6  differs from  FIG. 5 a    in that the curvature of deposition path  591  in  FIG. 5 a    curves to the right (from the perspective of deposition head  407 ) whereas deposition path  591  in  FIG. 6  curves to the left. This is because additive manufacturing system  400  steers laser beam  472 , workpiece region  572 - 1 , workpiece region  572 - 2 , and workpiece region  572 - 3  onto deposition path  591  as deposition path  591  meanders on workpiece  406 . 
     Platform  401  is a rigid metal structure and is identical to platform  101  in the prior art. Platform  401  ensures that the relative spatial relationship of robot mount  402 , robot  403 , deposition head  407 , tamping tool  408 , optical instrument  461 , optical instrument  462 , and sensor array  415  are maintained and known with respect to build-plate support  404 , build plate  405 , workpiece  406 , and deposition path  591 . It will be clear to those skilled in the art how to make and use platform  401 . 
     Robot mount  402  is a rigid, massive, and stable support for robot  403  and is identical to robot mount  102  in the prior art. The purpose of robot mount  402  is to provide ballast and inertial stability for robot  403 . It will be clear to those skilled in the art how to make and use robot mount  402 . 
     Robot  403  is a six-axis articulated mechanical arm that supports deposition head  407 , tamping tool  408 , optical instrument  461 , optical instrument  462 , sensor array  415 , optical cable  451 , optical cable  452 , and sensor cable  454 . Robot  403  is identical to robot  103  in the prior art. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which a different type of robot (e.g., a cartesian robot, a cylindrical robot, a SCARA, a delta robot, etc.) is used. A non-limiting example of robot  403  is the IRB  4600  robot offered by ABB. The motion of robot  403  is under the direction of controller  409 , and robot  403  is capable of depositing feedstock  411  at any location on workpiece  406  and in any one-, two-, or three-dimensional curve. It will be clear to those skilled in the art how to make and use robot  403 . 
     Build plate support  404  is a rigid, massive, and stable support for build plate  405  and workpiece  406  and is identical to build plate support  104  in the prior art. The purpose of build plate support  404  is to provide ballast and inertial stability for build plate  405  and also to provide a mechanism for rotating build plate  405  around an axis that is normal to the X-Y plane. To wit, build plate support  404  comprises a stepper motor—under the direction of controller  409 —that is capable of rotating build plate  405  (and, consequently workpiece  406 ) around an axis that is normal to the X-Y plane. It will be clear to those skilled in the art how to make and use build plate support  404 . 
     Build plate  405  is a rigid aluminum-alloy support and is described in detail in U.S. patent application Ser. No. 16/792,156, entitled “Thermoplastic Mold with Implicit Registration,” filed on Feb. 14, 2020, and incorporated by reference for the purpose of describing build plate  405 . The purpose of build plate  405  is to provide support for workpiece  406  (and a mold with a tunably adhesive surface for workpiece  406 ). U.S. patent application Ser. No. 16/792,150, entitled “Thermoplastic Mold with Tunable Adhesion,” filed on Feb. 14, 2020 is also incorporated by reference for the purpose of describing the interface between build plate  405  and workpiece  4066 . It will be clear to those skilled in the art how to make and use build plate  405  after reading this disclosure and the incorporated patent applications. 
     Workpiece  406  comprises a plurality of segments of feedstock  411  that have been successively deposited and welded together in a desired geometry to form the inchoate article of manufacture. Workpiece  406  is steadfastly affixed to build plate  405  so that workpiece  406  cannot move or rotate independently of build plate  405 . 
     Deposition head  407  is the end effector of robot  403  and comprises:
         (i) a feedstock guide that feeds feedstock  411  into position for heating, tamping, and welding to workpiece  406 . The feedstock guide is omitted from the figures for clarity but is described in U.S. Pat. No. 10,076,870, entitled “Filament Guide,” issued on Sep. 18, 2018, which is incorporated by reference.   (ii) tamping tool  408 , which first pinches and then tamps each segment of feedstock  411  onto the corresponding portion of workpiece  406 .   (iii) force gauge  413  that continually measures the force of tamping tool  408  on feedstock  411  at nip line segment  581  and reports those measurements back to controller  409  via sensor cable  454 .   (iv) a feedstock cutter—under the direction of controller  409 —that periodically or sporadically cuts feedstock  411 . The feedstock cutter is omitted from the figures for clarity but is described in U.S. patent application Ser. No. 16/023,197, entitled “Filament Cutter,” filed on Jun. 29, 2018, which is incorporated by reference.   (v) optical instrument  461 , which takes laser beam  471  from optical cable  451 , and—under the direction of controller  409 —conditions laser beam  471  and directs it onto feedstock region  571 - 2 .   (vi) optical instrument  462 , which takes laser beam  472  from optical cable  452 , and—under the direction of controller  409 —conditions laser beam  472  and directs it onto workpiece region  572 - 2 .   (vii) sensor array  415 , which measures the temperature of feedstock region  571 - 2 , workpiece region  572 - 2 , and tamping tool  408  and reports those measurements to controller  409  via sensor cable  454 .   (viii) structural support for optical instrument  461 , optical instrument  462 , and sensor array  415  and that maintains the relative spatial location and position of the feedstock guide, tamping tool  408 , pinch line segment  582 , the cutter, optical instrument  461 , optical instrument  462 , and sensor array  415 . The structural support is omitted from the figures for clarity but it will be clear to those skilled in the art, after reading this disclosure, how to make and use the structural support.
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use deposition head  407 .
       

     Tamping tool  408  comprises a roller-bearing mounted steel cylinder (roller) whose tangential speed equals the linear speed of the feedstock adjacent to the roller (i.e., tamping tool  408  rotates freely and there is substantially no friction between tamping tool  408  and feedstock  411 . It will be clear to those skilled in the art how to make and use tamping tool  408 . 
     The following patent applications disclose designs for tamping tool  408  which are alternatives to the roller-bearing mounted steel cylinder:
         (i) U.S. patent application Ser. No. 15/959,213, entitled “Variable-Contour Compaction Press,” filed on Apr. 21, 2018; and   (ii) U.S. patent application Ser. No. 15/959,214, entitled “Variable-Contour Compaction Roller,” filed on Apr. 21, 2018; and   (iii) U.S. patent application Ser. No. 15/959,215, entitled “Self-Cleaning Variable-Contour Compaction Press,” filed on Apr. 21, 2018;
 
each of which is incorporated by reference.
       

     Controller  409  comprises the hardware and software necessary to control all aspects of fabricating the article of manufacture, including, but not limited to:
         (i) robot  403  (which includes the location and motion of tamping tool  408 ), and   (ii) build plate support  404 , and   (iii) the feedstock cutter, and   (iv) feedstock laser  441 , and   (v) workpiece laser  442 , and   (vi) optical instrument  461 , and   (vii) optical instrument  462 , and   (viii) accumulator  412 .
 
To accomplish this controller  409  relies on a combination of feedforward and feedback, as described in detail below and in the accompanying drawings. It will be clear to those skilled in the art, after reading this disclosure, how to make and use controller  409 .
       

     Feedstock reel  410  is a circular reel that stores 1000 meters of feedstock  411 . Feedstock real  410  feeds feedstock  411  to accumulator  412 . It will be clear to those skilled in the art how to make and use feedstock reel  410 . 
     Feedstock  411  is a carbon fiber-reinforced thermoplastic filament, which is commonly called “pre-preg.” It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the feedstock is a fiber-reinforced pre-preg tape—woven or uni-directional—that is impregnated with thermoplastic resin. 
     Feedstock  411  comprises cylindrical towpreg of contiguous 12K carbon fiber that is impregnated with thermoplastic resin. The cross-section is circular and has a diameter of 1000 μm. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the cross-section of the filament is a quadrilateral (e.g., a square, a rectangle, a rhombus, a trapezoid, a kite, a parallelogram, etc.). Furthermore, it will be clear to those skilled in the art how to make and use alternative embodiments of the present invention in which feedstock  411  comprises a different number of fibers (e.g., 1K, 3K, 6K, 24K, etc.). And still furthermore, it will be clear to those skilled in the art how to make and use alternative embodiments of the present invention in which the fibers in feedstock  111  are made of a different material (e.g., fiberglass, aramid, carbon nanotubes, etc.). 
     In accordance with the first illustrative embodiment, feedstock  411  comprises continuous carbon fiber, but it will be clear to those skilled in the art how to make and use alternative embodiments of the present invention in which feedstock  411  comprises chopped or milled fiber. 
     In accordance with the first illustrative embodiments, the thermoplastic in feedstock  411  is, in general, a semi-crystalline polymer and, in particular, the polyaryletherketone (PAEK) known as polyetherketone (PEK). In accordance with some alternative embodiments of the present invention, the semi-crystalline material is the polyaryletherketone (PAEK), polyetheretherketone (PEEK), polyetherketoneketone (PEKK), polyetheretherketoneketone (PEEKK), or polyetherketoneetherketoneketone (PEKEKK). As those who are skilled in the art will appreciate after reading this specification, the disclosed annealing process, as it pertains to a semi-crystalline polymer in general, takes place at a temperature that is above the glass transition temperature Tg. 
     In accordance with some alternative embodiments of the present invention, the semi-crystalline polymer is not a polyaryletherketone (PAEK) but another semi-crystalline thermoplastic (e.g., polyamide (PA), polybutylene terephthalate (PBT), poly(p-phenylene sulfide) (PPS), etc.) or a mixture of a semi-crystalline polymer and an amorphous polymer. 
     When feedstock  411  comprises a blend of an amorphous polymer with a semi-crystalline polymer, the semi-crystalline polymer can one of the aforementioned materials and the amorphous polymer can be a polyarylsulfone, such as polysulfone (PSU), polyethersulfone (PESU), polyphenylsulfone (PPSU), polyethersulfone (PES), or polyetherimide (PEI). In some additional embodiments, the amorphous polymer can be, for example and without limitation, polyphenylene oxides (PPOs), acrylonitrile butadiene styrene (ABS), methyl methacrylate acrylonitrile butadiene styrene copolymer (ABSi), polystyrene (PS), or polycarbonate (PC). As those who are skilled in the art will appreciate after reading this specification, the disclosed annealing process, as it pertains to a blend of an amorphous polymer with a semi-crystalline polymer, takes place generally at a lower temperature than a semi-crystalline polymer with the same glass transition temperature; in some cases, the annealing process can take place at a temperature slightly below the glass transition temperature. 
     When the feedstock comprises a blend of an amorphous polymer with a semi-crystalline polymer, the weight ratio of semi-crystalline material to amorphous material can be in the range of about 50:50 to about 95:05, inclusive, or about 50:50 to about 90:10, inclusive. Preferably, the weight ratio of semi-crystalline material to amorphous material in the blend is between 60:40 and 80:20, inclusive. The ratio selected for any particular application may vary primarily as a function of the materials used and the properties desired for the printed article. 
     In some alternative embodiment of the present invention, the feedstock comprises a metal. For example, and without limitation, the feedstock can be a wire comprising stainless steel, Inconel (nickel/chrome), titanium, aluminum, cobalt chrome, copper, bronze, iron, precious metals (e.g., platinum, gold, silver, etc.). 
     In accordance with the first illustrative embodiment, the thermoplastic is infused with carbon nano-particles, the purpose of which is two-fold. First, the carbon nano-particles facilitate the absorption of radiant heat from laser beam  471  and laser beam  472 . Second, the carbon nano-particles effectively change the reactance of the thermoplastic, which makes the completed article of manufacture more conducive to electro-static powder coating. 
     Accumulator  412  takes feedstock  411  from feedstock reel  410  and provides it to deposition head  407  with the correct tension for depositing. Accumulator  112  is described in detail by U.S. patent application Ser. No. 16/023,210, entitled “Filament Accumulator or Tensioning Assembly,” filed Jun. 29, 2018, and which is incorporated by reference. 
     Sensor array  415  is a thermal camera that is capable of simultaneously measuring the temperature of:
         (i) feedstock region  571 - 1 , and   (ii) feedstock region  571 - 2 , and   (iii) feedstock region  571 - 3 , and   (iv) workpiece region  572 - 1 , and   (v) workpiece region  572 - 2 , and   (vi) workpiece region  572 - 3 , and   (vii) tamping tool  408 ,
 
sixty (60) times per second and reporting those measurements to controller  409  via sensor cable  454 . In accordance with the first illustrative embodiment, sensor array  415  is a FLIR A35 thermal camera, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which sensor array  415  comprises different hardware.
       

     Force Gauge  413 —is a mechanical strain gauge that continually measures the force of tamping tool  408  on feedstock  411  at nip line segment  581  and reports those measurements back to controller  409  via sensor cable  454 . It will be clear to those skilled in the art how to make and use force gauge  413 . 
     Feedstock laser  441  is a variable-power continuous-wave laser that generates laser beam  471  and conveys it to optical instrument  461  via optical cable  451 . In accordance with the first illustrative embodiment, feedstock laser  441  is directed by controller  409  to generate laser beam  471  with a specific average power over a given time-interval. In accordance with the first illustrative embodiment, laser beam  471  is characterized by a wavelength λ=980 nm and has a maximum power output of 400 Watts. 
     In accordance with the illustrative embodiment, feedstock laser  441  is a continuous-wave laser. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use a pulsed laser. In any case, it will be clear to those skilled in the art how to make and use feedstock laser  441 . 
     Workpiece laser  442  is a variable-power continuous-wave laser that generates laser beam  472  and conveys it to optical instrument  462  via optical cable  452 . In accordance with the first illustrative embodiment, workpiece laser  442  is directed by controller  409  to generate laser beam  472  with a specific average power over a given time-interval. In accordance with the first illustrative embodiment, laser beam  472  is characterized by a wavelength λ=980 nm and has a maximum power output of 400 Watts. 
     In accordance with the illustrative embodiment, workpiece laser  442  is a continuous-wave laser. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use a pulsed laser. In any case, it will be clear to those skilled in the art how to make and use workpiece laser  442 . 
     In accordance with the first illustrative embodiment, feedstock laser  441  and workpiece laser  442  are identical and generate laser beams characterized by the same wavelength. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the lasers:
         (i) are not identical, or   (i) generate laser beams characterized by different wavelengths, or   (iii) have different maximum power output, or   (iv) any combination of i, ii, and iii.       

     Optical cable  451  is a glass fiber, in well-known fashion, that carries laser beam  471  from feedstock laser  441  to optical instrument  461  with substantially no loss. It will be clear to those skilled in the art how to make and use optical cable  451 . 
     Optical cable  452  is a glass fiber, in well-known fashion, that carries the laser beam  472  from workpiece laser  442  to optical instrument  462  with substantially no loss. It will be clear to those skilled in the art how to make and use optical cable  452 . 
     Sensor cable  454  is an electrical cable, in well-known fashion, that carries the measurements from sensor array  415  to controller  409 . It will be clear to those skilled in the art how to make and use sensor cable  454 . 
     Optical Instrument  461  is an optomechanical machine that comprises optics and actuators that receive laser beam  471  from feedstock laser  441 , via optical cable  451 , conditions it under the direction of controller  409 , and directs it onto the segment of feedstock  411  that is within feedstock region  571 - 2 . In accordance with the first illustrative embodiment, optical instrument  461  comprises:
         (i) an actuator and an optic that, under the direction of controller  409 , adjusts the length of the segment of feedstock  411  that is irradiated and heated by laser beam  471  (i.e., adjusts the length of feedstock region  571 - 2 ), and   (ii) an actuator and an optic that, under the direction of controller  409 , adjusts the distance between pinch line segment  582  and laser beam  471  (i.e., adjusts the distance between pinch line segment  582  and feedstock region  571 - 2 ), and   (iii) an actuator and an optic that, under the direction of controller  409 , adjusts the irradiance within each unit-area of laser beam  471  on feedstock  411 , and   (iv) an actuator and an optic that, under the direction of controller  409 , adjusts the angle of incidence of laser beam  471  on feedstock  411 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use optical instrument  461 .
       

     Optical Instrument  462  is an optomechanical machine that comprises optics and actuators that receive laser beam  472  from workpiece laser  442 , via optical cable  452 , conditions it, and directs it onto the portion of workpiece  406  that is within workpiece region  572 - 2 , all under the direction of controller  409 . In accordance with the first illustrative embodiment, optical instrument  461  comprises:
         (i) an actuator and an optic that, under the direction of controller  409 , adjusts the length of the portion of workpiece  406  that is irradiated and heated by laser beam  472  (i.e., adjusts the length of workpiece region  572 - 2 ), and   (ii) an actuator and an optic that, under the direction of controller  409 , adjusts the distance between pinch line segment  582  and laser beam  472  (i.e., adjusts the distance between pinch line segment  582  and workpiece region  572 - 2 ), and   (iii) an actuator and an optic that, under the direction of controller  409 , adjusts the irradiance within each unit-area of laser beam  472  on workpiece  406 , and   (iv) an actuator and an optic that, under the direction of controller  409 , adjusts the angle of incidence of laser beam  472  on workpiece  406 , and   (v) an actuator that steers laser beam  472  onto deposition path  591 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use optical instrument  462 .
       

     Feedstock laser control cable  491  is an electrical cable, in well-known fashion, that carries instructions from controller  409  to feedstock laser  441 , which instructions control all aspects (e.g., power, etc.) of feedstock laser  441 . It will be clear to those skilled in the art how to make and use feedstock laser control cable  491 . 
     Workpiece laser control cable  492  is an electrical cable, in well-known fashion, that carries instructions from controller  409  to workpiece laser  442 , which instructions control all aspects (e.g., power, etc.) of workpiece laser  442 . It will be clear to those skilled in the art how to make and use feedstock laser control cable  492 . 
     Feedstock region  571 - 1 , feedstock region  571 - 2 , and feedstock region  571 - 3  are three volumes in space through which feedstock  411  passes. 
     The length of feedstock region  571 - 1  is defined as the length of feedstock  411  within feedstock region  571 - 1 . In accordance with the first illustrative embodiment, the length of feedstock region  571 - 1  is 15 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the length of feedstock region  571 - 1  is different. 
     The length of feedstock region  571 - 2  is defined as the length of feedstock  411  being irradiated by laser beam  471 . In accordance with the first illustrative embodiment, the length of feedstock region  571 - 2  is continually adjusted by optical instrument  461 , all under the direction of controller  409 . In accordance with the first illustrative embodiment, the minimum length of feedstock region  571 - 2  is 5 mm and the maximum length is 15 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the minimum and maximum lengths are different. 
     The length of feedstock region  571 - 3  is defined as the length of feedstock  411  within feedstock region  571 - 3 . In accordance with the first illustrative embodiment, the length of feedstock region  571 - 3  is 10 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the length of the feedstock region  571 - 3  is different. 
     In accordance with the first illustrative embodiment, the distance of feedstock region  571 - 1  from pinch line segment  582  (as measured along the length of feedstock  411 ) is 55 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the distance is different. 
     In accordance with the first illustrative embodiment, the distance of feedstock region  571 - 2  from pinch line segment  582  (as measured along the length of feedstock  411 ) is continually adjusted by optical instrument  461 , all under the direction of controller  409 . In accordance with the first illustrative embodiment, the minimum distance of feedstock region  571 - 2  from pinch line segment  582  is 25 mm and the maximum distance is 35 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the minimum and maximum lengths are different. 
     In accordance with the first illustrative embodiment, the distance of feedstock region  571 - 3  from pinch line segment  582  (as measured along the length of feedstock  411 ) is 5 mm but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the distance is different. 
     Workpiece region  572 - 1 , workpiece region  572 - 2 , and workpiece region  572 - 3  are three volumes in space through which deposition path  591  passes. 
     The length of workpiece region  572 - 1  is defined as the length of deposition path  591  within workpiece region  572 - 1 . In accordance with the first illustrative embodiment, the length of workpiece region  572 - 1  is 15 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the length of workpiece region  572 - 1  is different. 
     The length of workpiece region  572 - 2  is defined as the length of deposition path  591  being irradiated by laser beam  472 . In accordance with the first illustrative embodiment, the length of workpiece region  572 - 2  is continually adjusted by optical instrument  462 , all under the direction of controller  409 . In accordance with the first illustrative embodiment, the minimum length of workpiece region  572 - 2  is 5 mm and the maximum length is 15 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the minimum and maximum lengths are different. 
     The length of workpiece region  572 - 3  is defined as the length of deposition path  591  within workpiece region  572 - 3 . In accordance with the first illustrative embodiment, the length of workpiece region  572 - 3  is 10 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the length of the workpiece region  572 - 3  is different. 
     In accordance with the first illustrative embodiment, the distance of workpiece region  572 - 1  from pinch line segment  582  (as measured along the length of deposition path  591 ) is 55 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the distance is different. 
     In accordance with the first illustrative embodiment, the distance of workpiece region  572 - 2  from pinch line segment  582  (as measured along the length of deposition path  591 ) is continually adjusted by optical instrument  462 , all under the direction of controller  409 . In accordance with the first illustrative embodiment, the minimum distance of workpiece region  572 - 2  from pinch line segment  582  is 25 mm and the maximum distance is 35 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the minimum and maximum lengths are different. 
     Nip line segment  581  is the line segment on the circumferential surface of tamping tool  408  where tamping tool  408  exerts the maximum radial force on feedstock  411 . 
     Pinch line segment  582  is the line segment on the circumferential surface of tamping tool  408  where tamping tool  408  first pinches a unit-length of feedstock  411  between tamping tool  408  and workpiece  406  so that any movement of feedstock  411  parallel to the rotational axis of tamping tool  408  is substantially constrained. 
     Deposition path  591  is a line on the surface of workpiece  406  where feedstock  411  is to be deposited and tamped. In  FIG. 5 b   , deposition path  591  curves to the left. In contrast, in  FIG. 6 , deposition path  591  curves to the right. 
       FIG. 7  depicts a schematic diagram of the heating and sensor architecture for additive manufacturing system  400 , which irradiates and heats feedstock  411  and workpiece  406  and measures the temperature of feedstock  411 , workpiece  406 , and tamping tool  408 . 
     As shown in  FIG. 7 , feedstock laser  441  provides laser beam  471  to optical instrument  461  via optical cable  451  in well-known fashion, and workpiece laser  442  provides laser beam  472  to optical instrument  462  via optical cable  452 . 
     Under the direction of controller  409 , optical instrument  461  irradiates and heats the segment of feedstock that is within feedstock region  571 - 2 , and optical instrument  462  irradiates and heats the portion of workpiece  406  that is within workpiece region  572 - 2 . 
     Thermal sensor  771 - 1  periodically measures the temperature of the segment of feedstock that is within feedstock region  571 - 1  and reports those measurements back to controller  409 . Thermal sensor  771 - 2  periodically measures the temperature of the segment of feedstock that is within feedstock region  571 - 2  and reports those measurements back to controller  409 . Thermal sensor  771 - 3  periodically measures the temperature of the segment of feedstock that is within feedstock region  571 - 3  and reports those measurements back to controller  409 . 
     Thermal sensor  772 - 1  periodically measures the temperature of that portion of workpiece  406  that is within workpiece region  572 - 1  and reports those measurements back to controller  409 . Thermal sensor  772 - 2  periodically measures the temperature of that portion of workpiece  406  that is within workpiece region  572 - 2  and reports those measurements back to controller  409 . Thermal sensor  772 - 3  periodically measures the temperature of that portion of workpiece  406  that is within workpiece region  572 - 3  and reports those measurements back to controller  409 . 
     Thermal sensor  773  periodically measures the temperature of tamping tool  408  and reports those measurements back to controller  409 . 
     Although the first illustrative embodiment measures the temperature of three segments of feedstock  411 , it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that measure any number (e.g., four, five, six, eight, ten, twelve, etc.) of segments. Although the first illustrative embodiment measures the temperature of three portions of workpiece  406 , it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that measure any number (e.g., four, five, six, eight, ten, twelve, etc.) of portions. 
     In accordance with the first illustrative embodiment, the temperature measurements are made periodically at sixty (60) times per second, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that make periodic measurements at a different rate or that make measurements aperiodically or sporadically. 
       FIG. 8  depicts a schematic diagram of the sensor and control architecture for that portion of additive manufacturing system  400  that irradiates and heats feedstock  411  and workpiece  406 . 
     In accordance with the first illustrative embodiment, controller  409  uses a combination of feedforward and feedback to continually direct:
         (i) feedstock laser  441  to adjust the average power of laser beam  471  on the segment of feedstock that is within feedstock region  571 - 2 , and   (ii) optical instrument  461  to adjust the length of feedstock region  571 - 2 , and   (iii) optical instrument  461  to adjust the distance between pinch line segment  582  and feedstock region  571 - 2 , and   (iv) optical instrument  461  to adjust the irradiance of laser beam  471  on the segment of feedstock  411  within feedstock region  571 - 2 , and   (v) optical instrument  461  to adjust the angle of incidence of laser beam  471  on the segment of feedstock  411  within feedstock region  571 - 2 , and   (vi) workpiece laser  442  to adjust the average power of laser beam  472  on the portion of workpiece that is within workpiece region  572 - 2 , and   (vii) optical instrument  462  to adjust the length of workpiece region  572 - 2 , and   (viii) optical instrument  462  to adjust the distance between pinch line segment  582  and workpiece region  572 - 2 , and   (ix) optical instrument  462  to adjust the irradiance of laser beam  472  on the portion of workpiece  406  within workpiece region  572 - 2 , and   (x) optical instrument  462  to adjust the angle of incidence of laser beam  472  on the portion of workpiece  406  within workpiece region  572 - 2 , and   (xi) optical instrument  462  to steer laser beam  472  onto deposition path  591 , and (xii) accumulator  412  to feed feedstock  411  to deposition head  407 , and   (xiii) robot  403  to advance tamping tool  408  to deposit and tamp feedstock  411  onto workpiece  406 , and
 
based on:
   (i) knowledge of the toolpath (e.g., G-code, etc.) for the article of manufacture to be printed (and the geometry of the workpiece at each time-interval, which can be derived from that toolpath), and   (ii) a thermal model of the feedstock  411 , and   (iii) a location-specific thermal model of each portion on workpiece  406  onto which feedstock  411  will be deposited and tamped (which can be derived from the thermal model of the feedstock  411  and the geometry of the workpiece at each instant during fabrication), and   (iv) periodic measurements of the temperature of the segment of feedstock  411  that is within feedstock region  571 - 1 , and   (v) periodic measurements of the temperature of the segment of feedstock  411  that is within feedstock region  571 - 2 , and   (vi) periodic measurements of the temperature of the segment of feedstock  411  that is within feedstock region  571 - 3 , and   (vii) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  572 - 1 , and   (viii) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  572 - 2 , and   (ix) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  572 - 3 , and   (x) periodic measurements of the temperature of tamping tool  408 , and   (xi) periodic measurements of the force of tamping tool  408  on feedstock  411  at nip line segment  581 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that accomplish this, whether with traditional imperative programming or with an artificial neural network.
       

     With regard to feedforward, controller  409  takes as input:
         (i) the toolpath (e.g., G-code, etc.) for the article of manufacture to be printed, in well-known fashion, and   (ii) a thermal model of the feedstock, which itself is based on, among other things, the thermal properties of the resin, the mass of resin per unit-length of feedstock, the profile of the feedstock (e.g., filament, tape, circular, rectangular, etc.), the thermal properties of the reinforcing fibers, the number of fibers per unit-length of feedstock, the mass of the fibers per unit-length of feedstock, and the length and orientation of the fibers in the feedstock (e.g., continuous, chopped, medium, ball milled, etc.),
 
and generates therefrom:
   (i) a prediction of whether feedstock  411  will be deposited at a uniform or non-uniform rate at each instant during the printing of the article of manufacture (because, for example and without limitation, the deposition starts and stops, accelerates, decelerates and occurs uniformly because of turns, contours, cuts, etc.), and   (ii) a prediction of the speed (e.g., in millimeters per second, etc.) at which feedstock  411  will be deposited at each instant during the printing of the article of manufacture, and   (iii) a prediction of the interval of time between when each segment of feedstock  411  is irradiated and heated and when the segment is deposited and tamped, and   (iv) a prediction of the interval of time between when each portion of workpiece  406  is irradiated and heated and when feedstock  411  is deposited and tamped onto that portion of workpiece  406 , and   (v) a location-specific thermal model of each portion on workpiece  406  onto which feedstock  411  will be deposited and tamped, which itself is based on, among other things, the thermal model of the feedstock and the shape and mass of the workpiece in the vicinity of each portion to be irradiated and heated, which is derived from a model of the nascent article of manufacture (i.e., workpiece) at each step of printing, which is derived from the toolpath.       

     With regard to feedback, controller  409  takes as input:
         (i) the thermal model of the feedstock, and   (ii) the location-specific thermal model of each portion on workpiece  406  onto which feedstock  411  will be deposited and tamped, and   (iii) periodic measurements of the temperature of the segment of feedstock  411  that is within feedstock region  571 - 1 , and   (iv) periodic measurements of the temperature of the segment of feedstock  411  that is within feedstock region  571 - 2 , and   (v) periodic measurements of the temperature of the segment of feedstock  411  that is within feedstock region  571 - 3 , and   (vi) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  572 - 1 , and   (vii) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  572 - 2 , and   (viii) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  572 - 3 , and   (ix) the periodic measurements of the temperature of tamping tool  408 , and   (x) periodic measurements of the force of tamping tool  408  on feedstock  411  at nip line segment  581 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use a thermal model of the feedstock, a location-specific thermal model of each portion on workpiece  406  onto which feedstock  411  will be deposited and tamped, a prediction of whether the feedstock will be deposited at a uniform or non-uniform rate, a prediction of the speed at which the feedstock is deposited, and a prediction of the interval between when each segment of feedstock and each portion of the workpiece is irradiated and heated and when the segment is deposited and tamped onto the portion of the workpiece.
       

       FIG. 9  depicts a flowchart of the tasks performed by additive manufacturing system  400 . Because additive manufacturing system  400  concurrently performs tasks on different segments of feedstock  411  and different portions of workpiece  406 , the tasks depicted in  FIG. 9  are concurrent. 
     At task  901 :
         (i) feedstock laser  441  generates laser beam  471  with an average power during each time-interval, and   (ii) workpiece laser  442  generates laser beam  472  with an average power during each time-interval, and
 
both as directed by controller  409 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  901 .
       

     At task  902 , thermal sensor  771 - 1  periodically measures the temperature of the segment of feedstock  411  that is within feedstock region  571 - 1  and reports those measurements to controller  409 . Additionally, thermal sensor  771 - 2  periodically measures the temperature of the segment of feedstock  411  that is within feedstock region  571 - 2  and reports those measurements to controller  409 . And furthermore, thermal sensor  771 - 3  periodically measures the temperature of the segment of feedstock  411  that is within feedstock region  571 - 3  and reports those measurements to controller  409 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  901 . 
     At task  903 , thermal sensor  772 - 1  periodically measures the temperature of that portion of workpiece  406  that is within workpiece region  572 - 1  and reports those measurements to controller  409 . Additionally, thermal sensor  772 - 2  periodically measures the temperature of that portion of workpiece  406  that is within workpiece region  572 - 2  and reports those measurements to controller  409 . And furthermore, thermal sensor  772 - 3  periodically measures the temperature of that portion of workpiece  406  that is within workpiece region  572 - 3  and reports those measurements to controller  409 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  901 . 
     At task  904 , thermal sensor  773  periodically measures the temperature of tamping tool  408  and reports those measurements back to controller  409 . Additionally, force gauge  413  periodically measures the force of tamping tool  408  on feedstock  411  at nip line segment  581  and reports those measurements back to controller  409 . 
     At task  905 , optical instrument  461  irradiates and heats the segment of feedstock  411  that is within feedstock region  571 - 2  as directed by controller  409 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  905 . 
     At task  906 , optical instrument  462  irradiates and heats the portion of workpiece  406  that is within workpiece region  572 - 2  as directed by controller  409 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  906 . 
     At task  907 :
         (i) optical instrument  461  adjusts a trait of laser beam  471  and/or the relationship of laser beam  471  to the segment of feedstock  411  within feedstock region  571 - 2 , and   (ii) optical instrument  462  adjusts a trait of laser beam  472  and/or the relationship of laser beam  472  to the portion of workpiece  406  within workpiece region  572 - 2 , and
 
both as directed by controller  409 . Task  907  is described in detail in  FIG. 10  and in the accompanying text.
       

     At task  908 , additive manufacturing system  400  deposits a segment of feedstock  411  onto a portion of workpiece  406  and tamps the segment onto the workpiece with tamping tool  408 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  908 . 
       FIG. 10  depicts a flowchart of the details of task  907 —adjusting optical instrument  461  and optical instrument  462 , as directed by controller  409 . Controller  409  continually directs optical instrument  461  and optical instrument  462  to make adjustments, and, therefore, the tasks depicted in  FIG. 10  are concurrent. 
     At task  1001 , controller  409  directs optical instrument  461  to adjust—lengthen or shorten—the length of feedstock region  571 - 2  (i.e., the length of feedstock  411  being irradiated by laser beam  471 ). This provides controller  409  with a mechanism for adjusting the temperature of each unit-length of feedstock  411  when it is deposited and tamped. For example—and assuming that everything else is constant—increasing the length of feedstock region  571 - 2  spreads the heat energy of laser beam  471  over a greater length of feedstock, which decreases the rate at which each unit-length of feedstock is heated. Conversely, decreasing the length of feedstock region  571 - 2  concentrates the heat energy, which increases the rate at which each unit-length of feedstock is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the length of feedstock region  571 - 2  is advantageous for, among other things, compensating for variations in the rate at which feedstock  411  is deposited and tamped. 
     At task  1002 , controller  409  directs optical instrument  461  to adjust—increase or decrease—the distance between pinch line segment  582  and feedstock region  571 - 2 . This provides controller  409  with a mechanism for adjusting the temperature of each unit-length of feedstock  411  when it is deposited and tamped. For example—and assuming everything else is constant—increasing the distance gives each unit-length of feedstock more time to cool before it is deposited and tamped. Conversely, decreasing the distance gives each unit segment of feedstock less time to cool before it is deposited and tamped. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the distance between pinch line segment  582  and feedstock region  571 - 2  is advantageous for, among other things, fine tuning the temperature of each unit-length of feedstock  411  at the time that it is deposited and tamped. 
     At task  1003 , controller  409  directs optical instrument  461  to adjust the irradiance of laser beam  471  on each unit-length of feedstock  411  within feedstock region  571 - 2 . This provides controller  409  with a mechanism for adjusting the temperature of each unit-length of feedstock  411  when it is deposited and tamped. For example—and assuming everything else is constant—increasing the irradiance on a unit-length of feedstock  411  increases the rate at which it is heated. Conversely, decreasing the irradiance on a unit-length of feedstock  411  decreases the rate at which it is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the irradiance of laser beam  471  on feedstock  411  is advantageous for, among other things, compensating for variations in the angle of incidence of laser beam  471  on feedstock  411  caused by changes in the relative position of optical instrument  461  to feedstock  411 . These changes are often caused by changes in the contour of workpiece  406 . 
     At task  1004 , controller  409  directs optical instrument  461  to adjust the angle of incidence of laser beam  471  on feedstock  411  within feedstock region  571 - 2 . This provides controller  409  with another mechanism for adjusting the temperature of each unit-length of feedstock  411  when it is deposited and tamped. For example—and assuming everything else is constant—adjusting the angle of incidence of laser beam  471  on feedstock  411  changes the effective irradiance on each unit-length of feedstock  411 . It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the angle of incidence of laser beam  471  on feedstock  411  is advantageous for, among other things, compensating for changes in the relative position of optical instrument  461  to feedstock  411 . These changes are often caused by changes in the contour of workpiece  406 . 
     At task  1005 , controller  409  directs optical instrument  462  to adjust—lengthen or shorten—the length of workpiece region  572 - 2  (i.e., the portion of workpiece  406  being irradiated by laser beam  472 ). This provides controller  409  with a mechanism for adjusting the temperature of each unit portion of workpiece  406  when it is deposited and tamped. For example—and assuming that everything else is constant—increasing the length of workpiece region  572 - 2  spreads the heat energy of laser beam  472  over a greater portion of workpiece  406 , which decreases the rate at which each unit portion of workpiece  406  is heated. Conversely, decreasing the length of workpiece region  572 - 2  concentrates the heat energy, which increases the rate at which each unit portion of workpiece  406  is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the length of workpiece region  572 - 2  is advantageous for, among other things, compensating for variations in the rate at which feedstock  411  is deposited and tamped. 
     At task  1006 , controller  409  directs optical instrument  462  to adjust—increase or decrease—the distance between pinch line  582  and workpiece region  572 - 2 . This provides controller  409  with a mechanism for adjusting the temperature of each unit portion of workpiece  406  when it is deposited and tamped. For example—and assuming everything else is constant—increasing the distance gives each unit portion of workpiece  406  more time to cool before it is deposited and tamped. Conversely, decreasing the distance gives each unit segment of feedstock less time to cool before it is deposited and tamped. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the distance between pinch line segment  582  and workpiece region  572 - 2  is advantageous for, among other things, fine tuning the temperature of each unit portion of workpiece  406  at the time that the corresponding segment of feedstock  411  is deposited and tamped. 
     At task  1007 , controller  409  directs optical instrument  462  to adjust the irradiance of laser beam  472  on each unit portion of workpiece  406  within workpiece region  572 - 2 . This provides controller  409  with a mechanism for adjusting the temperature of each unit portion of workpiece  406  at the time that the corresponding segment of feedstock  411  is deposited and tamped. For example—and assuming everything else is constant—increasing the irradiance on a unit portion of workpiece  406  increases the rate at which it is heated. Conversely, decreasing the irradiance on a unit-area of workpiece  406  decreases the rate at which it is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the irradiance of laser beam  472  on is advantageous for, among other things, compensating for variations in the angle of incidence of laser beam  472  on caused by changes in the relative position of optical instrument  462  to. These changes are often caused by changes in the contour of workpiece  406 . 
     At task  1008 , controller  409  directs optical instrument  462  to adjust the angle of incidence of laser beam  472  on workpiece  406  within workpiece region  572 - 2 . This provides controller  409  with another mechanism for adjusting the temperature of each unit portion of workpiece  406  when it is deposited and tamped. For example—and assuming everything else is constant—adjusting the angle of incidence of laser beam  472  on workpiece  406  changes the effective irradiance on each unit portion of workpiece  406 . It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the angle of incidence of laser beam  472  on workpiece  406  is advantageous for, among other things, compensating for changes in the relative position of optical instrument  462  to workpiece  406 . These changes are often caused by changes in the contour of workpiece  406 . 
     At task  1009 , controller  409  directs optical instrument  462  to steer workpiece laser beam  472  onto deposition path  591 . 
     In accordance with the first illustrative embodiment, sensor array  415  is not mechanically steered onto workpiece region  572 - 1 , workpiece region  572 - 2 , or workpiece region  572 - 3 . Instead, controller  409  picks the temperature measurements for workpiece region  572 - 1 , workpiece region  572 - 2 , or workpiece region  572 - 3  out of the thermal image from sensor array  415  based on the location of deposition path  591  in that image. It will be clear to those skilled in the art, after reading this disclosure, how to accomplish this. 
       FIG. 11  depicts a flowchart of the relative timing of the tasks performed on segment m of feedstock  411  and on portion n of workpiece  406 , wherein m and n are integers. In accordance with the first illustrative embodiment segment m of feedstock  411  is deposited and tamped onto portion n of workpiece  406 . 
     During time-Interval Δt=m−3, the temperature of segment m of feedstock  411  is measured by thermal sensor  771 - 1  and reported to controller  409 . 
     During time-Interval Δt=n−3, the temperature of portion n of workpiece  406  is measured by thermal sensor  772 - 1  and reported to controller  409 . 
     In accordance with the first illustrative embodiment, the duration of time-interval Δt=m−3 equals the duration of time-interval Δt=n−3, and time-interval Δt=m−3 is contemporaneous with time-interval Δt=n−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−3 does not equal the duration of time-interval Δt=n−3. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−3 is not contemporaneous with time-interval Δt=n−3. And still furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−3 overlaps, immediately precedes, immediately succeeds, precedes but not immediately, or succeeds but not immediately time-interval Δt=n−3. 
     During time-Interval Δt=m−2:
         (i) controller  409  directs feedstock laser  441  to generate laser beam  471  with a given average power, and   (ii) controller  409  directs optical instrument  461  to adjust a trait of laser beam  471  and/or the relationship of laser beam  471  to feedstock  411 , and   (iii) optical instrument  461  irradiates and heats segment m of feedstock  411 , and   (iv) the temperature of segment m of feedstock  411  is measured by thermal sensor  771 - 2  and reported to controller  409 .       

     In accordance with the first illustrative embodiment, the duration of time-interval Δt=m−2 equals the duration of Δt=m−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−2 does not equal the duration of time interval Δt=m−3. Furthermore, in accordance with the first illustrative embodiment, time-interval Δt=m−2 is after, and is mutually-exclusive of, time-interval Δt=m−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−2 overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=m−3. 
     During time-Interval Δt=n−2:
         (i) controller  409  directs workpiece laser  442  to generate laser beam  472  with a given average power, and   (ii) controller  409  directs optical instrument  462  to adjust a trait of laser beam  472  and/or the relationship of laser beam  472  to workpiece  406 , and   (iii) controller  409  directs optical instrument  462  to steer laser beam  472  onto deposition path  591 , and   (iv) optical instrument  462  irradiates and heats portion n of workpiece  406 , and   (v) the temperature of portion n of workpiece  406  is measured by thermal sensor  772 - 2  and reported to controller  409 .       

     In accordance with the first illustrative embodiment, the duration of time-interval Δt=n−2 equals the duration of Δt=n−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=n−2 does not equal the duration of time interval Δt=n−3. Furthermore, in accordance with the first illustrative embodiment, time-interval Δt=n−2 is after, and is mutually-exclusive of, time-interval Δt=n−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=n−2 overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=n−3. 
     In accordance with the first illustrative embodiment, the duration of time-interval Δt=m−2 equals the duration of time-interval Δt=n−2, and time-interval Δt=m−2 is contemporaneous with time-interval Δt=n−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−2 does not equal the duration of time-interval Δt=n−2. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−2 is not contemporaneous with time-interval Δt=n−2. And still furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−2 overlaps, immediately precedes, immediately succeeds, precedes but not immediately, or succeeds but not immediately time-interval Δt=n−2. 
     During time-Interval Δt=m−1, the temperature of segment m of feedstock  411  is measured by thermal sensor  771 - 3  and reported to controller  409 . 
     In accordance with the first illustrative embodiment, the duration of time-interval Δt=m−1 equals the duration of Δt=m−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−1 does not equal the duration of time interval Δt=m−2. Furthermore, in accordance with the first illustrative embodiment, time-interval Δt=m−1 is after, and is mutually-exclusive of, time-interval Δt=m−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−1 overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=m−2. 
     During time-Interval Δt=n−1, the temperature of portion n of workpiece  406  is measured by thermal sensor  772 - 3  and reported to controller  409 . 
     In accordance with the first illustrative embodiment, the duration of time-interval Δt=n−1 equals the duration of Δt=n−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=n−1 does not equal the duration of time interval Δt=n−2. Furthermore, in accordance with the first illustrative embodiment, time-interval Δt=n−1 is after, and is mutually-exclusive of, time-interval Δt=n−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=n−1 overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=n−2. 
     In accordance with the first illustrative embodiment, the duration of time-interval Δt=m−1 equals the duration of time-interval Δt=n−1, and time-interval Δt=m−1 is contemporaneous with time-interval Δt=n−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−1 does not equal the duration of time-interval Δt=n−1. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−1 is not contemporaneous with time-interval Δt=n−1. And still furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−1 overlaps, immediately precedes, immediately succeeds, precedes but not immediately, or succeeds but not immediately time-interval Δt=n−1. 
     During time-Interval Δt=m=n, segment m of feedstock  411  is deposited and tamped onto portion n of workpiece  406 . 
     In accordance with the first illustrative embodiment, the duration of time-interval Δt=m equals the duration of Δt=m−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m does not equal the duration of time interval Δt=m−1. Furthermore, in accordance with the first illustrative embodiment, time-interval Δt=m is after, and is mutually-exclusive of, time-interval Δt=m−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=m−1. 
     In accordance with the first illustrative embodiment, the duration of time-interval Δt=n equals the duration of Δt=n−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=n does not equal the duration of time interval Δt=n−1. Furthermore, in accordance with the first illustrative embodiment, time-interval Δt=n is after, and is mutually-exclusive of, time-interval Δt=n−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=n overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=n−1. 
     In accordance with the first illustrative embodiment, feedstock laser  441  and workpiece laser  442  are not mounted on deposition head  107  because they are too heavy. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use a plurality—perhaps tens or hundreds—of relatively-low-power lightweight lasers that are mounted on the deposition head to provide the laser beams to heat the feedstock and/or the workpiece. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to convey the laser beams from their lasers to the deposition head via free-space optics (i.e., without using an optical cable). 
       FIG. 12  depicts an illustration of additive manufacturing system  1200  in accordance with the second illustrative embodiment of the present invention. Additive manufacturing system  1200  fabricates an article of manufacture by successively depositing segments of fiber-reinforced thermoplastic feedstock (e.g., filament, tape, etc.) onto a workpiece until the article of manufacture is complete. 
     Additive manufacturing system  1200  is similar to additive manufacturing system  400  fabricates in that they both fabricate an article of manufacture by successively depositing segments of fiber-reinforced thermoplastic feedstock (e.g., filament, tape, etc.) onto a workpiece until the article of manufacture is complete. In contrast, additive manufacturing system  1200  is unlike additive manufacturing system  400  in that system  1200  uses:
         (i) a two-stage heating system that comprises two laser beams and two optical instruments to irradiate and heat the feedstock, and   (ii) a two-stage heating system that comprises two lasers beams and two optical instruments to irradiate and heat the workpiece.
 
A two-stage heating system is advantageous over a single-stage heating system in that it provides finer control of the temperature of the feedstock and the workpiece and does so with less-expensive lasers.
       

     Additive manufacturing system  1200  comprises: platform  1201 , robot mount  1202 , robot  1203 , build plate support  1204 , build plate  1205 , workpiece  1206 , deposition head  1207 , tamping tool  1208 , controller  1209 , feedstock reel  1210 , feedstock  1211 , accumulator  1212 , sensor array  1215 , feedstock laser  1240 , feedstock laser  1241 , workpiece laser  1242 , workpiece laser  1243 , optical cable  1250 , optical cable  1251 , optical cable  1252 , optical cable  1253 , sensor cable  1254 , optical instrument  1260 , optical instrument  1261 , optical instrument  1262 , optical instrument  1263 , laser beam  1270 , laser beam  1271 , laser beam  1272 , laser beam  1273 , feedstock laser control cable  1291 , and workpiece laser control cable  1292 , interrelated as shown. 
       FIG. 13 a    depicts a close-up of workpiece  1206 , deposition head  1207 , tamping tool  1208 , feedstock  1211 , sensor array  1215 , optical instrument  1260 , optical instrument  1261 , optical instrument  1262 , optical instrument  1263 , optical cable  1250 , optical cable  1251 , optical cable  1252 , optical cable  1253 , sensor cable  1254 , laser beam  1270 , laser beam  1271 , laser beam  1272 , laser beam  1273 , feedstock region  1371 - 1 , feedstock region  1371 - 2 , feedstock region  1371 - 3 , workpiece region  1372 - 1 , workpiece region  1372 - 2 , workpiece region  1372 - 3 , nip line segment  1381 , and pinch line segment  1382 , interrelated as shown. 
       FIG. 13 b    depicts a close-up of workpiece  1206 , deposition head  1207 , tamping tool  1208 , feedstock  1211 , feedstock region  1371 - 1 , feedstock region  1371 - 2 , feedstock region  1371 - 3 , workpiece region  1372 - 1 , workpiece region  1372 - 2 , workpiece region  1372 - 3 , pinch line segment  1382 , and deposition path  1391  all as seen along cross-section CC-CC as depicted in  FIG. 13   a.    
       FIG. 14  depicts a close-up of workpiece  1206 , deposition head  1207 , tamping tool  1208 , feedstock  1211 , feedstock region  1371 - 1 , feedstock region  1371 - 2 , feedstock region  1371 - 3 , workpiece region  1372 - 1 , workpiece region  1372 - 2 , workpiece region  1372 - 3 , pinch line segment  1382 , and deposition path  1391 , all as seen along cross-section CC-CC as depicted in  FIG. 13   a.    
       FIG. 14  differs from  FIG. 13 a    in that the curvature of deposition path  1391  in  FIG. 13 a    curves to the right (from the perspective of deposition head  1207 ) whereas deposition path  1391  in  FIG. 14  curves to the left. This is because additive manufacturing system  1200  steers laser beam  1272 , workpiece region  1372 - 1 , workpiece region  1372 - 2 , and workpiece region  1372 - 3  onto deposition path  1391  as deposition path  1391  meanders on workpiece  1206 . 
     Although the second illustrative embodiment comprises a total of four lasers, it will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that use any number of lasers (e.g., three lasers, five lasers, six lasers, seven lasers, eight lasers, ten lasers, twenty lasers, one-hundred lasers, etc.). 
     Although the second illustrative embodiment apportions its four lasers evenly between the feedstock and the workpiece, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that apportion its lasers to the feedstock and workpiece in any combination (e.g., one laser dedicated to the feedstock and three lasers dedicated to the workpiece, three lasers dedicated to the feedstock and one laser dedicated to the workpiece, etc.). 
     Although the second illustrative embodiment dedicates two lasers to heating the feedstock and two lasers to heating the workpiece, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that do not dedicate each laser to either the feedstock of the workpiece. As a consequence, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which one or more lasers switch, as needed, between heating the feedstock and heating the laser. For example, one laser is dedicated to heating the feedstock, a second laser is dedicated to heating the workpiece, and a third laser heats whichever—the feedstock or the workpiece—needs heating at any given moment. 
     Platform  1201  is identical to platform  401  in the first illustrative embodiment and performs the same function in exactly the same way. It will be clear to those skilled in the art how to make and use platform  1201 . 
     Robot mount  1202  is identical to robot mount  402  in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use robot mount  1202 . 
     Robot  1203  is identical to robot  103  in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use robot  1203 . 
     Build plate support  1204  is identical to build plate support  404  in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use build plate support  1204 . 
     Build plate  1205  is identical to build plate  405  in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use build plate  1205 . 
     Workpiece  1206  is identical to workpiece  406  in the first illustrative embodiment and performs exactly the same function in exactly the same way. 
     Deposition head  1207  is the end effector of robot  1203  and comprises:
         (i) a feedstock guide that is identical to the feedstock guide in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use the feedstock guide.   (ii) tamping tool  1208 , which first pinches and then tamps each segment of feedstock  1211  onto the corresponding portion of workpiece  1206 .   (iii) a feedstock cutter—under the direction of controller  1209 —is identical to feedstock cutter in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use the feedstock cutter.   (iv) optical instrument  1260 , which takes laser beam  1270  from optical cable  1250 , and—under the direction of controller  1209 —conditions laser beam  1270  and directs it onto feedstock region  1371 - 2 .   (v) optical instrument  1261 , which takes laser beam  1271  from optical cable  1251 , and—under the direction of controller  1209 —conditions laser beam  1271  and directs it onto feedstock region  1371 - 1 .   (vi) optical instrument  1262 , which takes laser beam  1272  from optical cable  1252 , and—under the direction of controller  1209 —conditions laser beam  1272  and directs it onto workpiece region  1372 - 2 .   (vii) optical instrument  1263 , which takes laser beam  1273  from optical cable  1253 , and—under the direction of controller  1209 —conditions laser beam  1273  and directs it onto workpiece region  1372 - 3 .   (viii) sensor array  1215 , which measures the temperature of feedstock region  1371 - 2 , workpiece region  1372 - 2 , and tamping tool  1208  and reports those measurements to controller  1209  via sensor cable  1254     (ix) force gauge  1213  that continually measures the force of tamping tool  1208  on feedstock  1211  at nip line segment  1381  and reports those measurements back to controller  1209  via sensor cable  1254 .   (x) structural support, which is similar to the structural support in the first illustrative embodiment except that is also supports optical instrument  1260  and optical instrument  1263  in addition to optical instrument  1261 , optical instrument  1262 , and sensor array  1215 . Otherwise, the structural support performs exactly the same function in exactly the same way. It will be clear to those skilled in the art, after reading this disclosure, how to make and use the structural support.
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use deposition head  1207 .
       

     Tamping tool  1208  is identical to tamping tool  1208  in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use tamping tool  1208 . 
     Controller  1209  comprises the hardware and software necessary to control all aspects of fabricating the article of manufacture, including, but not limited to:
         (i) robot  1203  (which includes the location and motion of deposition head  1207  and tamping tool  1208 ), and   (ii) build plate support  1204 , and   (iii) the feedstock cutter, and   (iv) feedstock laser  1240 , and   (v) feedstock laser  1241 , and   (vi) workpiece laser  1242 , and   (vii) workpiece laser  1243 , and   (viii) optical instrument  1260 , and   (ix) optical instrument  1261 , and   (x) optical instrument  1262 , and   (xi) optical instrument  1263 , and   (xii) accumulator  1212 .
 
To accomplish this controller  1209  relies on a combination of feedforward and feedback, as described in detail below and in the accompanying drawings. It will be clear to those skilled in the art, after reading this disclosure, how to make and use controller  1209 .
       

     Feedstock reel  1210  is identical to feedstock reel  410  in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use feedstock reel  1210 . 
     Feedstock  1211  is identical to feedstock  411  in the first illustrative embodiment and performs exactly same function in exactly the same way. It will be clear to those skilled in the art how to make and use feedstock  1211 . 
     Accumulator  1212  is identical to accumulator  412  in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use accumulator  1212 . 
     Force Gauge  1213 —is a mechanical strain gauge that continually measures the force of tamping tool  1208  on feedstock  1211  at nip line segment  1381  and reports those measurements back to controller  1209  via sensor cable  1254 . It will be clear to those skilled in the art how to make and use force gauge  1213 . 
     Sensor array  1215  is identical to sensor array  415  in the first illustrative embodiment and performs exactly the same function in exactly the same way. It will be clear to those skilled in the art how to make and use sensor array  1215 . 
     Feedstock laser  1240  is a variable-power laser that generates laser beam  1270  and conveys it to optical instrument  1260  via optical cable  1250 . In accordance with the second illustrative embodiment, feedstock laser  1240  is directed by controller  1209  to generate laser beam  1270  with a specific average power over a given time-interval. In accordance with the second illustrative embodiment, laser beam  1270  is characterized by a wavelength λ=980 nm and has a maximum power output of 200 Watts. 
     In accordance with the illustrative embodiment, feedstock laser  1240  is a continuous-wave laser. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use a pulsed laser. In any case, it will be clear to those skilled in the art how to make and use feedstock laser  1240 . 
     Feedstock laser  1241  is a variable-power laser that generates laser beam  1271  and conveys it to optical instrument  1261  via optical cable  1251 . In accordance with the second illustrative embodiment, feedstock laser  1241  is directed by controller  1209  to generate laser beam  1271  with a specific average power over a given time-interval. In accordance with the second illustrative embodiment, laser beam  1271  is characterized by a wavelength λ=980 nm and has a maximum power output of 200 Watts. 
     In accordance with the illustrative embodiment, feedstock laser  1241  is a continuous-wave laser. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use a pulsed laser. In any case, it will be clear to those skilled in the art how to make and use feedstock laser  1241 . 
     Workpiece laser  1242  is a variable-power laser that generates laser beam  1272  and conveys it to optical instrument  1262  via optical cable  1252 . In accordance with the second illustrative embodiment, workpiece laser  1242  is directed by controller  1209  to generate laser beam  1272  with a specific average power over a given time-interval. In accordance with the second illustrative embodiment, laser beam  1272  is characterized by a wavelength λ=980 nm and has a maximum power output of 200 Watts. 
     In accordance with the illustrative embodiment, workpiece laser  1242  is a continuous-wave laser. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use a pulsed laser. In any case, it will be clear to those skilled in the art how to make and use workpiece laser  1242 . 
     Workpiece laser  1243  is a variable-power laser that generates laser beam  1273  and conveys it to optical instrument  1263  via optical cable  1253 . In accordance with the second illustrative embodiment, workpiece laser  1243  is directed by controller  1209  to generate laser beam  1273  with a specific average power over a given time-interval. In accordance with the second illustrative embodiment, laser beam  1273  is characterized by a wavelength λ=980 nm and has a maximum power output of 200 Watts. 
     In accordance with the illustrative embodiment, workpiece laser  1243  is a continuous-wave laser. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use a pulsed laser. In any case, it will be clear to those skilled in the art how to make and use workpiece laser  1243 . 
     In accordance with the second illustrative embodiment, feedstock laser  1240 , feedstock laser  1241 , workpiece laser  1242 , and workpiece laser  1243  are identical and generate laser beams characterized by the same wavelength. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which one or more of the lasers:
         (i) are not identical, or   (i) generate laser beams characterized by different wavelengths, or   (iii) have different maximum power output, or   (iv) any combination of i, ii, and iii.       

     Optical cable  1250  is identical to optical cable  451  in the first illustrative embodiment. It will be clear to those skilled in the art how to make and use optical cable  1250 . 
     Optical cable  1251  is identical to optical cable  451  in the first illustrative embodiment. It will be clear to those skilled in the art how to make and use optical cable  1251 . 
     Optical cable  1252  is identical to optical cable  451  in the first illustrative embodiment. It will be clear to those skilled in the art how to make and use optical cable  1252 . 
     Optical cable  1253  is identical to optical cable  451  in the first illustrative embodiment. It will be clear to those skilled in the art how to make and use optical cable  1253 . 
     Sensor cable  1254  is identical to sensor cable  454  in the first illustrative embodiment. It will be clear to those skilled in the art how to make and use sensor cable  1254 . 
     Optical Instrument  1260  is identical to optical instrument  461  in the first illustrative embodiment and performs a similar function on the segment of feedstock  1211  in feedstock region  1371 - 3 . In particular, optical instrument  1260  is an optomechanical machine that comprises optics and actuators that receive laser beam  1270  from feedstock laser  1240 , via optical cable  1250 , conditions it under the direction of controller  1209 , and directs it onto the segment of feedstock  1211  that is within feedstock region  1371 - 3 . In accordance with the second illustrative embodiment, optical instrument  1261  comprises:
         (i) an actuator and an optic that, under the direction of controller  1209 , adjusts the length of the segment of feedstock  1211  that is irradiated and heated by laser beam  1270  (i.e., adjusts the length of feedstock region  1371 - 3 ), and   (ii) an actuator and an optic that, under the direction of controller  1209 , adjusts the distance between pinch line segment  1382  and laser beam  1270  (i.e., adjusts the distance between pinch line segment  1382  and feedstock region  1371 - 3 ), and   (iii) an actuator and an optic that, under the direction of controller  1209 , adjusts the irradiance within each unit-area of laser beam  1270  on feedstock  1211 , and   (iv) an actuator and an optic that, under the direction of controller  1209 , adjusts the angle of incidence of laser beam  1270  on feedstock  1211 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use optical instrument  1260 .
       

     Optical Instrument  1261  is identical to optical instrument  461  in the first illustrative embodiment and performs exactly the same function in exactly the same way. In particular, optical instrument  1261  is an optomechanical machine that comprises optics and actuators that receive laser beam  1271  from feedstock laser  1241 , via optical cable  1251 , conditions it under the direction of controller  1209 , and directs it onto the segment of feedstock  1211  that is within feedstock region  1371 - 2 . In accordance with the second illustrative embodiment, optical instrument  1261  comprises:
         (i) an actuator and an optic that, under the direction of controller  1209 , adjusts the length of the segment of feedstock  1211  that is irradiated and heated by laser beam  1271  (i.e., adjusts the length of feedstock region  1371 - 2 ), and   (ii) an actuator and an optic that, under the direction of controller  1209 , adjusts the distance between pinch line segment  1382  and laser beam  1271  (i.e., adjusts the distance between pinch line segment  1382  and feedstock region  1371 - 2 ), and   (iii) an actuator and an optic that, under the direction of controller  1209 , adjusts the irradiance within each unit-area of laser beam  1271  on feedstock  1211 , and   (iv) an actuator and an optic that, under the direction of controller  1209 , adjusts the angle of incidence of laser beam  1271  on feedstock  1211 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use optical instrument  1261 .
       

     Optical Instrument  1262  is identical to optical instrument  462  in the first illustrative embodiment and performs exactly the same function in exactly the same way. In particular, optical instrument  1262  is an optomechanical machine that comprises optics and actuators that receive laser beam  1272  from workpiece laser  1242 , via optical cable  1252 , conditions it, and directs it onto the portion of workpiece  1206  that is within workpiece region  1372 - 2  under the direction of controller  1209 . In accordance with the second illustrative embodiment, optical instrument  1261  comprises:
         (i) an actuator and an optic that, under the direction of controller  1209 , adjusts the length of the portion of workpiece  1206  that is irradiated and heated by laser beam  1272  (i.e., adjusts the length of workpiece region  1372 - 2 ), and   (ii) an actuator and an optic that, under the direction of controller  1209 , adjusts the distance between pinch line segment  1382  and laser beam  1272  (i.e., adjusts the distance between pinch line segment  1382  and workpiece region  1372 - 2 ), and   (iii) an actuator and an optic that, under the direction of controller  1209 , adjusts the irradiance within each unit-area of laser beam  1272  on workpiece  1206 , and   (iv) an actuator and an optic that, under the direction of controller  1209 , adjusts the angle of incidence of laser beam  1272  on workpiece  1206 , and   (v) an actuator that steers laser beam  1272  onto deposition path  1391 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use optical instrument  1262 .
       

     Optical Instrument  1263  is identical to optical instrument  462  in the first illustrative embodiment and performs a similar function on the portion of workpiece  1206  in workpiece region  1372 - 3 . In particular, optical instrument  1263  is an optomechanical machine that comprises optics and actuators that receive laser beam  1273  from workpiece laser  1243 , via optical cable  1253 , conditions it, and directs it onto the portion of workpiece  1206  that is within workpiece region  1372 - 3  under the direction of controller  1209 . In accordance with the second illustrative embodiment, optical instrument  1263  comprises:
         (i) an actuator and an optic that, under the direction of controller  1209 , adjusts the length of the portion of workpiece  1206  that is irradiated and heated by laser beam  1273  (i.e., adjusts the length of workpiece region  1372 - 3 ), and   (ii) an actuator and an optic that, under the direction of controller  1209 , adjusts the distance between pinch line segment  1382  and laser beam  1273  (i.e., adjusts the distance between pinch line segment  1382  and workpiece region  1372 - 3 ), and   (iii) an actuator and an optic that, under the direction of controller  1209 , adjusts the irradiance within each unit-area of laser beam  1273  on workpiece  1206 , and   (iv) an actuator and an optic that, under the direction of controller  1209 , adjusts the angle of incidence of laser beam  1273  on workpiece  1206 , and   (v) an actuator that steers laser beam  1273  onto deposition path  1391 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use optical instrument  1263 .
       

     Feedstock laser control cable  1290  is an electrical cable, in well-known fashion, that carries instructions from controller  1209  to feedstock laser  1240 , which instructions control all aspects (e.g., power, etc.) of feedstock laser  1240 . It will be clear to those skilled in the art how to make and use feedstock laser control cable  1290 . 
     Feedstock laser control cable  1291  is an electrical cable, in well-known fashion, that carries instructions from controller  1209  to feedstock laser  1241 , which instructions control all aspects (e.g., power, etc.) of feedstock laser  1241 . It will be clear to those skilled in the art how to make and use feedstock laser control cable  1291 . 
     Workpiece laser control cable  1292  is an electrical cable, in well-known fashion, that carries instructions from controller  1209  to workpiece laser  1242 , which instructions control all aspects (e.g., power, etc.) of workpiece laser  1242 . It will be clear to those skilled in the art how to make and use feedstock laser control cable  1292 . 
     Workpiece laser control cable  1293  is an electrical cable, in well-known fashion, that carries instructions from controller  1209  to workpiece laser  1243 , which instructions control all aspects (e.g., power, etc.) of workpiece laser  1243 . It will be clear to those skilled in the art how to make and use feedstock laser control cable  1293 . 
     Feedstock region  1371 - 1 , feedstock region  1371 - 2 , and feedstock region  1371 - 3  are three volumes in space through which feedstock  1211  passes. 
     The length of feedstock region  1371 - 1  is defined as the length of feedstock  1211  within feedstock region  1371 - 1 . In accordance with the second illustrative embodiment, the length of feedstock region  1371 - 1  is 15 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the length of feedstock region  1371 - 1  is different. 
     The length of feedstock region  1371 - 2  is defined as the length of feedstock  1211  being irradiated by laser beam  1271 . In accordance with the second illustrative embodiment, the length of feedstock region  1371 - 2  is continually adjusted by optical instrument  1261  under the direction of controller  1209 . In accordance with the second illustrative embodiment, the minimum length of feedstock region  1371 - 2  is 5 mm and the maximum length is 15 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the minimum and maximum lengths are different. 
     The length of feedstock region  1371 - 3  is defined as the length of feedstock  1211  within feedstock region  1371 - 3 . In accordance with the second illustrative embodiment, the length of feedstock region  1371 - 3  is 10 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the length of the feedstock region  1373 - 3  is different. 
     In accordance with the second illustrative embodiment, the distance of feedstock region  1371 - 1  from pinch line segment  1382  (as measured along the length of feedstock  1211 ) is 55 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the distance is different. 
     In accordance with the second illustrative embodiment, the distance of feedstock region  1371 - 2  from pinch line segment  1382  (as measured along the length of feedstock  1211 ) is continually adjusted by optical instrument  1261  under the direction of controller  1209 . In accordance with the second illustrative embodiment, the minimum distance of feedstock region  1371 - 2  from pinch line segment  1382  is 25 mm and the maximum distance is 35 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the minimum and maximum lengths are different. 
     In accordance with the second illustrative embodiment, the distance of feedstock region  1371 - 3  from pinch line segment  1382  (as measured along the length of feedstock  1211 ) is 5 mm but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the distance is different. 
     Workpiece region  1372 - 1 , workpiece region  1372 - 2 , and workpiece region  1372 - 3  are three volumes in space through which deposition path  1391  passes. 
     The length of workpiece region  1372 - 1  is defined as the length of deposition path  1391  within workpiece region  1372 - 1 . In accordance with the second illustrative embodiment, the length of workpiece region  1372 - 1  is 15 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the length of workpiece region  1372 - 1  is different. 
     The length of workpiece region  1372 - 2  is defined as the length of deposition path  1391  being irradiated by laser beam  1271 . In accordance with the second illustrative embodiment, the length of feedstock region  1372 - 2  is continually adjusted by optical instrument  1262  under the direction of controller  1209 . In accordance with the second illustrative embodiment, the minimum length of workpiece region  1372 - 2  is 5 mm and the maximum length is 15 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the minimum and maximum lengths are different. 
     The length of workpiece region  1372 - 3  is defined as the length of deposition path  1391  within workpiece region  1372 - 3 . In accordance with the second illustrative embodiment, the length of workpiece region  1372 - 3  is 10 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the length of the workpiece region  1373 - 3  is different. 
     In accordance with the second illustrative embodiment, the distance of workpiece region  1372 - 1  from pinch line segment  1382  (as measured along the length of deposition path  1391 ) is 55 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments in which the distance is different. 
     In accordance with the second illustrative embodiment, the distance of workpiece region  1372 - 2  from pinch line segment  1382  (as measured along the length of deposition path  1391 ) is continually adjusted by optical instrument  1262  under the direction of controller  1209 . In accordance with the second illustrative embodiment, the minimum distance of workpiece region  1372 - 2  from pinch line segment  1382  is 25 mm and the maximum distance is 35 mm, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the minimum and maximum lengths are different. 
     Nip line segment  1381  is the line segment on the circumferential surface of tamping tool  1208  where tamping tool  1208  exerts the maximum radial force on feedstock  1211 . 
     Pinch line segment  1382  is the line segment on the circumferential surface of tamping tool  1208  where tamping tool  1208  first pinches a unit-length of feedstock  1211  between tamping tool  1208  and workpiece  1206  so that any movement of feedstock  1211  parallel to the rotational axis of tamping tool  1208  is substantially constrained. 
     Deposition path  1391  is a line on the surface of workpiece  1206  where feedstock  1211  is to be deposited and tamped. In  FIG. 13 b   , deposition path  1391  curves to the left. In contrast, in  FIG. 14 , deposition path  1391  curves to the right. 
       FIG. 15  depicts a schematic diagram of the heating and sensor architecture for additive manufacturing system  1200 , which irradiates and heats feedstock  1211  and workpiece  1206  and measures the temperature of feedstock  1211 , workpiece  1206 , and tamping tool  1208 . 
     As shown in  FIG. 15 :
         (i) feedstock laser  1240  provides laser beam  1270  to optical instrument  1260  via optical cable  1250 , and   (ii) feedstock laser  1241  provides laser beam  1271  to optical instrument  1261  via optical cable  1251 , and   (iii) workpiece laser  1242  provides laser beam  1272  to optical instrument  1262  via optical cable  1252 , and   (iii) workpiece laser  1243  provides laser beam  1273  to optical instrument  1263  via optical cable  1253 .       

     Under the direction of controller  1209 :
         (i) optical instrument  1260  irradiates and heats the segment of feedstock that is within feedstock region  1371 - 3 , and   (ii) optical instrument  1261  irradiates and heats the segment of feedstock that is within feedstock region  1371 - 2 , and   (iii) optical instrument  1262  irradiates and heats the portion of workpiece  1206  that is within workpiece region  1372 - 2 , and   (iv) optical instrument  1263  irradiates and heats the portion of workpiece  1206  that is within workpiece region  1372 - 3 .       

     Thermal sensor  1571 - 1  periodically measures the temperature of the segment of feedstock that is within feedstock region  1371 - 1  and reports those measurements back to controller  1209 . Thermal sensor  1571 - 2  periodically measures the temperature of the segment of feedstock that is within feedstock region  1371 - 2  and reports those measurements back to controller  1209 . Thermal sensor  1571 - 3  periodically measures the temperature of the segment of feedstock that is within feedstock region  1371 - 3  and reports those measurements back to controller  1209 . 
     Thermal sensor  1572 - 1  periodically measures the temperature of that portion of workpiece  1206  that is within workpiece region  1372 - 1  and reports those measurements back to controller  1209 . Thermal sensor  1572 - 2  periodically measures the temperature of that portion of workpiece  1206  that is within workpiece region  1372 - 2  and reports those measurements back to controller  1209 . Thermal sensor  1572 - 3  periodically measures the temperature of that portion of workpiece  1206  that is within workpiece region  1372 - 3  and reports those measurements back to controller  1209 . 
     Thermal sensor  773  periodically measures the temperature of tamping tool  1208  and reports those measurements back to controller  1209 . 
     In accordance with the second illustrative embodiment, the temperature measurements are made periodically at sixty (60) times per second, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that make periodic measurements at a different rate or that make measurements aperiodically or sporadically. 
       FIG. 16  depicts a schematic diagram of the sensor and control architecture for that portion of additive manufacturing system  1200  that irradiates and heats feedstock  1211  and workpiece  1206 . 
     In accordance with the second illustrative embodiment, controller  1209  uses a combination of feedforward and feedback to continually direct:
         (i) feedstock laser  1240  to adjust the average power of laser beam  1270  on the segment of feedstock that is within feedstock region  1371 - 3 , and   (ii) optical instrument  1260  to adjust the length of feedstock region  1371 - 3 , and   (iii) optical instrument  1260  to adjust the distance between pinch line segment  1382  and feedstock region  1371 - 3 , and   (iv) optical instrument  1260  to adjust the irradiance of laser beam  1270  on the segment of feedstock  1211  within feedstock region  1371 - 3 , and   (v) optical instrument  1260  to adjust the angle of incidence of laser beam  1270  on the segment of feedstock  1211  within feedstock region  1371 - 3 , and   (vi) feedstock laser  1241  to adjust the average power of laser beam  1271  on the segment of feedstock that is within feedstock region  1371 - 2 , and   (vii) optical instrument  1261  to adjust the length of feedstock region  1371 - 2 , and   (viii) optical instrument  1261  to adjust the distance between pinch line segment  1382  and feedstock region  1371 - 2 , and   (ix) optical instrument  1261  to adjust the irradiance of laser beam  1271  on the segment of feedstock  1211  within feedstock region  1371 - 2 , and   (x) optical instrument  1261  to adjust the angle of incidence of laser beam  1271  on the segment of feedstock  1211  within feedstock region  1371 - 2 , and   (xi) workpiece laser  1242  to adjust the average power of laser beam  1272  on the portion of workpiece that is within workpiece region  1372 - 2 , and   (xii) optical instrument  1262  to adjust the length of workpiece region  1372 - 2 , and (xiii) optical instrument  1262  to adjust the distance between pinch line segment  1382  and workpiece region  1372 - 2 , and   (xiv) optical instrument  1262  to adjust the irradiance of laser beam  1272  on the portion of workpiece  1206  within workpiece region  1372 - 2 , and   (xv) optical instrument  1262  to adjust the angle of incidence of laser beam  1272  on the portion of workpiece  1206  within workpiece region  1372 - 2 , and   (xvi) optical instrument  1262  to steer laser beam  1272  onto deposition path, and   (xvii) workpiece laser  1243  to adjust the average power of laser beam  1273  on the portion of workpiece that is within workpiece region  1372 - 3 , and   (xviii) optical instrument  1263  to adjust the length of workpiece region  1372 - 3 , and   (xix) optical instrument  1263  to adjust the distance between pinch line segment  1383  and workpiece region  1372 - 3 , and   (xx) optical instrument  1263  to adjust the irradiance of laser beam  1273  on the portion of workpiece  1206  within workpiece region  1372 - 3 , and   (xxi) optical instrument  1263  to adjust the angle of incidence of laser beam  1273  on the portion of workpiece  1206  within workpiece region  1372 - 3 , and   (xxii) optical instrument  1263  to steer laser beam  1273  onto deposition path  1391 , and   (xxiii) accumulator  1212  to feed feedstock  1211  to deposition head  1207 , and   (xxiv) robot  1203  to advance tamping tool  1208  to deposit and tamp feedstock  1211  onto workpiece  1206 , and
 
based on:
   (i) knowledge of the toolpath (e.g., G-code, etc.) for the article of manufacture to be printed (and the geometry of the workpiece at each time-interval, which can be derived from that toolpath), and   (ii) a thermal model of the feedstock  1211 , and   (iii) a location-specific thermal model of each portion on workpiece  1206  onto which feedstock  1211  will be deposited and tamped (which can be derived from the thermal model of the feedstock  1211  and the geometry of the workpiece at each instant during fabrication), and   (iv) periodic measurements of the temperature of the segment of feedstock  1211  that is within feedstock region  1371 - 1 , and   (v) periodic measurements of the temperature of the segment of feedstock  1211  that is within feedstock region  1371 - 2 , and   (vi) periodic measurements of the temperature of the segment of feedstock  1211  that is within feedstock region  1371 - 3 , and   (vii) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  1372 - 1 , and   (viii) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  1372 - 2 , and   (ix) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  1372 - 3 , and   (x) periodic measurements of the temperature of tamping tool  1208 , and   (xi) periodic measurements of the force of tamping tool  1208  on feedstock  1211  at nip line segment  1381 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that accomplish this, whether with traditional imperative programming or with an artificial neural network.
       

     With regard to feedforward, controller  1209  takes as input:
         (i) the toolpath (e.g., G-code, etc.) for the article of manufacture to be printed, in well-known fashion, and   (ii) a thermal model of the feedstock, which itself is based on, among other things, the thermal properties of the resin, the mass of resin per unit-length of feedstock, the profile of the feedstock (e.g., filament, tape, circular, rectangular, etc.), the thermal properties of the reinforcing fibers, the number of fibers per unit-length of feedstock, the mass of the fibers per unit-length of feedstock, and the length and orientation of the fibers in the feedstock (e.g., continuous, chopped, medium, ball milled, etc.),
 
and generates therefrom:
   (i) a prediction of whether feedstock  1211  will be deposited at a uniform or non-uniform rate at each instant during the printing of the article of manufacture (because, for example and without limitation, the deposition starts and stops, accelerates, decelerates and occurs uniformly because of turns, contours, cuts, etc.), and   (ii) a prediction of the speed (e.g., in millimeters per second, etc.) at which feedstock  1211  will be deposited at each instant during the printing of the article of manufacture, and   (iii) a prediction of the interval of time between when each segment of feedstock  1211  is irradiated and heated and when the segment is deposited and tamped, and   (iv) a prediction of the interval of time between when each portion of workpiece  1206  is irradiated and heated and when feedstock  1211  is deposited and tamped onto that portion of workpiece  1206 , and   (v) a location-specific thermal model of each portion on workpiece  1206  onto which feedstock  1211  will be deposited and tamped, which itself is based on, among other things, the thermal model of the feedstock and the shape and mass of the workpiece in the vicinity of each portion to be irradiated and heated, which is derived from a model of the nascent article of manufacture (i.e., workpiece) at each step of printing, which is derived from the toolpath.       

     With regard to feedback, controller  1209  takes as input:
         (i) the thermal model of the feedstock, and   (ii) the location-specific thermal model of each portion on workpiece  1206  onto which feedstock  1211  will be deposited and tamped, and   (iii) periodic measurements of the temperature of the segment of feedstock  1211  that is within feedstock region  1371 - 1 , and   (iv) periodic measurements of the temperature of the segment of feedstock  1211  that is within feedstock region  1371 - 2 , and   (v) periodic measurements of the temperature of the segment of feedstock  1211  that is within feedstock region  1371 - 3 , and   (vi) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  1372 - 1 , and   (vii) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  1372 - 2 , and   (viii) periodic measurements of the temperature of that portion of workpiece that is within workpiece region  1372 - 3 , and   (ix) periodic measurements of the temperature of tamping tool  1208 , and   (x) periodic measurements of the force of tamping tool  1208  on feedstock  1211  at nip line segment  1381 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use a thermal model of the feedstock, a location-specific thermal model of each portion on workpiece  1206  onto which feedstock  1211  will be deposited and tamped, a prediction of whether the feedstock will be deposited at a uniform or non-uniform rate, a prediction of the speed at which the feedstock is deposited, and a prediction of the interval between when each segment of feedstock and each portion of workpiece is irradiated and heated and when the segment of feedstock is deposited and tamped onto the portion of the workpiece.
       

       FIG. 17  depicts a flowchart of the tasks performed by additive manufacturing system  1200 . Because additive manufacturing system  1200  concurrently performs tasks on different segments of feedstock  1211  and different portions of workpiece  1206 , the tasks depicted in  FIG. 17  are concurrent. 
     At task  1701 :
         (i) feedstock laser  1240  generates laser beam  1270  with an average power during each time-interval, and   (ii) feedstock laser  1241  generates laser beam  1271  with an average power during each time-interval, and   (iii) workpiece laser  1242  generates laser beam  1272  with an average power during each time-interval, and   (iv) workpiece laser  1243  generates laser beam  1273  with an average power during each time-interval,
 
all as directed by controller  1209 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  1701 .
       

     At task  1702 , thermal sensor  1571 - 1  periodically measures the temperature of the segment of feedstock  1211  that is within feedstock region  1371 - 1  and reports those measurements to controller  1209 . Additionally, thermal sensor  1571 - 2  periodically measures the temperature of the segment of feedstock  1211  that is within feedstock region  1371 - 2  and reports those measurements to controller  1209 . And furthermore, thermal sensor  1571 - 3  periodically measures the temperature of the segment of feedstock  1211  that is within feedstock region  1371 - 3  and reports those measurements to controller  1209 . Task  1702  is identical to task  902  in the first illustrative embodiment, and it will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  1701 . 
     At task  1703 , thermal sensor  1572 - 1  periodically measures the temperature of that portion of workpiece  1206  that is within workpiece region  1372 - 1  and reports those measurements to controller  1209 . Additionally, thermal sensor  1572 - 2  periodically measures the temperature of that portion of workpiece  1206  that is within workpiece region  1372 - 2  and reports those measurements to controller  1209 . And furthermore, thermal sensor  1572 - 3  periodically measures the temperature of that portion of workpiece  1206  that is within workpiece region  1372 - 3  and reports those measurements to controller  1209 . Task  1703  is identical to task  903  in the first illustrative embodiment, and it will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  1701 . 
     At task  1704 , thermal sensor  1373  periodically measures the temperature of tamping tool  1208  and reports those measurements back to controller  1209 . Additionally, force gauge  1213  periodically measures the force of tamping tool  1208  on feedstock  1211  at nip line segment  1381  and reports those measurements back to controller  1209 . 
     At task  1705 :
         (i) optical instrument  1260  irradiates and heats the segment of feedstock  1211  that is within feedstock region  1371 - 3 , and   (ii) optical instrument  1261  irradiates and heats the segment of feedstock  1211  that is within feedstock region  1371 - 2 ,
 
all as directed by controller  1209 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  1705 .
       

     At task  1706 :
         (i) optical instrument  1262  irradiates and heats the portion of workpiece  1206  that is within workpiece region  1372 - 2 , and   (ii) optical instrument  1263  irradiates and heats the portion of workpiece  1206  that is within workpiece region  1372 - 3 ,
 
all as directed by controller  1209 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  1706 .
       

     At task  1707 :
         (i) optical instrument  1260  adjusts a trait of laser beam  1270  and/or the relationship of laser beam  1270  to the segment of feedstock  1211  within feedstock region  1371 - 3 , and   (ii) optical instrument  1261  adjusts a trait of laser beam  1271  and/or the relationship of laser beam  1271  to the segment of feedstock  1211  within feedstock region  1371 - 2 , and   (iii) optical instrument  1262  adjusts a trait of laser beam  1272  and/or the relationship of laser beam  1272  to the portion of workpiece  1206  within workpiece region  1372 - 2 , and   (iv) optical instrument  1263  adjusts a trait of laser beam  1273  and/or the relationship of laser beam  1273  to the portion of workpiece  1206  within workpiece region  1372 - 3 ,
 
all as directed by controller  1209 . Task  1707  is described in detail in  FIGS. 18, 19, 20, 21, 22 , and in the accompanying text.
       

     At task  1708 , additive manufacturing system  1200  deposits a segment of feedstock  1211  onto a portion of workpiece  1206  and tamps the segment onto the workpiece with tamping tool  1208 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  1708 . 
       FIG. 18  depicts a flowchart of the details of task  1707 —adjusting optical instruments as directed by controller  1209 . Optical instrument  1260 , optical instrument  1261 , optical instrument  1262 , and optical instrument  1263  continually make adjustments, as directed by controller  1209 , and, therefore, the tasks depicted in  FIG. 18  are concurrent. 
     At task  1801 , optical instrument  1260  continually adjusts a trait of laser beam  1270  and/or the relationship of laser beam  1270  to the segment of feedstock  1211  within feedstock region  1371 - 3 . Task  1801  is described in detail in  FIG. 19  and in the accompanying text. 
     At task  1802 , optical instrument  1261  continually adjusts a trait of laser beam  1271  and/or the relationship of laser beam  1271  to the segment of feedstock  1211  within feedstock region  1371 - 2 . Task  1802  is described in detail in  FIG. 20  and in the accompanying text. 
     At task  1803 , optical instrument  1262  continually adjusts a trait of laser beam  1272  and/or the relationship of laser beam  1272  to the portion of workpiece  1206  within workpiece region  1372 - 2 . Task  1803  is described in detail in  FIG. 21  and in the accompanying text. 
     At task  1804 , optical instrument  1263  continually adjusts a trait of laser beam  1273  and/or the relationship of laser beam  1273  to the portion of workpiece  1206  within workpiece region  1372 - 3 . Task  1804  is described in detail in  FIG. 22  and in the accompanying text. 
       FIG. 19  depicts a flowchart of the details of task  1801 —adjusting optical instrument  1260 . Controller  1209  continually directs optical instrument  1260  to make adjustments, and, therefore, the tasks depicted in  FIG. 19  are concurrent. 
     At task  1901 , controller  1209  directs optical instrument  1260  to adjust—lengthen or shorten—the length of feedstock region  1371 - 3  (i.e., the length of feedstock  1211  being irradiated by laser beam  1270 ). This provides controller  1209  with a mechanism for adjusting the temperature of each unit-length of feedstock  1211  when it is deposited and tamped. For example—and assuming that everything else is constant—increasing the length of feedstock region  1371 - 3  spreads the heat energy of laser beam  1270  over a greater length of feedstock, which decreases the rate at which each unit-length of feedstock is heated. Conversely, decreasing the length of feedstock region  1371 - 3  concentrates the heat energy, which increases the rate at which each unit-length of feedstock is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the length of feedstock region  1371 - 3  is advantageous for, among other things, compensating for variations in the rate at which feedstock  1211  is deposited and tamped. 
     At task  1902 , controller  1209  directs optical instrument  1260  to adjust—increase or decrease—the distance between pinch line segment  1382  and feedstock region  1371 - 3 . This provides controller  1209  with a mechanism for adjusting the temperature of each unit-length of feedstock  1211  when it is deposited and tamped. For example—and assuming everything else is constant—increasing the distance gives each unit-length of feedstock more time to cool before it is deposited and tamped. Conversely, decreasing the distance gives each unit segment of feedstock less time to cool before it is deposited and tamped. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the distance between pinch line segment  1382  and feedstock region  1371 - 3  is advantageous for, among other things, fine tuning the temperature of each unit-length of feedstock  1211  at the time that it is deposited and tamped. 
     At task  1903 , controller  1209  directs optical instrument  1260  to adjust the irradiance of laser beam  1270  on each unit-length of feedstock  1211  within feedstock region  1371 - 3 . This provides controller  1209  with a mechanism for adjusting the temperature of each unit-length of feedstock  1211  when it is deposited and tamped. For example—and assuming everything else is constant—increasing the irradiance on a unit-length of feedstock  1211  increases the rate at which it is heated. Conversely, decreasing the irradiance on a unit-length of feedstock  1211  decreases the rate at which it is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the irradiance of laser beam  1270  on feedstock  1211  is advantageous for, among other things, compensating for variations in the angle of incidence of laser beam  1270  on feedstock  1211  caused by changes in the relative position of optical instrument  1260  to feedstock  1211 . These changes are often caused by changes in the contour of workpiece  1206 . 
     At task  1904 , controller  1209  directs optical instrument  1260  to adjust the angle of incidence of laser beam  1270  on feedstock  1211  within feedstock region  1371 - 3 . This provides controller  1209  with another mechanism for adjusting the temperature of each unit-length of feedstock  1211  when it is deposited and tamped. For example—and assuming everything else is constant—adjusting the angle of incidence of laser beam  1270  on feedstock  1211  changes the effective irradiance on each unit-length of feedstock  1211 . It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the angle of incidence of laser beam  1270  on feedstock  1211  is advantageous for, among other things, compensating for changes in the relative position of optical instrument  1260  to feedstock  1211 . These changes are often caused by changes in the contour of workpiece  1206 . 
       FIG. 20  depicts a flowchart of the details of task  1802 —adjusting optical instrument  1261 . Controller  1209  continually directs optical instrument  1261  to make adjustments, and, therefore, the tasks depicted in  FIG. 20  are concurrent. 
     At task  2001 , controller  1209  directs optical instrument  1261  to adjust—lengthen or shorten—the length of feedstock region  1371 - 2  (i.e., the length of feedstock  1211  being irradiated by laser beam  1271 ). This provides controller  1209  with a mechanism for adjusting the temperature of each unit-length of feedstock  1211  when it is deposited and tamped. For example—and assuming that everything else is constant—increasing the length of feedstock region  1371 - 2  spreads the heat energy of laser beam  1271  over a greater length of feedstock, which decreases the rate at which each unit-length of feedstock is heated. Conversely, decreasing the length of feedstock region  1371 - 2  concentrates the heat energy, which increases the rate at which each unit-length of feedstock is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the length of feedstock region  1371 - 2  is advantageous for, among other things, compensating for variations in the rate at which feedstock  1211  is deposited and tamped. 
     At task  2002 , controller  1209  directs optical instrument  1261  to adjust—increase or decrease—the distance between pinch line segment  1382  and feedstock region  1371 - 2 . This provides controller  1209  with a mechanism for adjusting the temperature of each unit-length of feedstock  1211  when it is deposited and tamped. For example—and assuming everything else is constant—increasing the distance gives each unit-length of feedstock more time to cool before it is deposited and tamped. Conversely, decreasing the distance gives each unit segment of feedstock less time to cool before it is deposited and tamped. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the distance between pinch line segment  1382  and feedstock region  1371 - 2  is advantageous for, among other things, fine tuning the temperature of each unit-length of feedstock  1211  at the time that it is deposited and tamped. 
     At task  2003 , controller  1209  directs optical instrument  1261  to adjust the irradiance of laser beam  1271  on each unit-length of feedstock  1211  within feedstock region  1371 - 2 . This provides controller  1209  with a mechanism for adjusting the temperature of each unit-length of feedstock  1211  when it is deposited and tamped. For example—and assuming everything else is constant—increasing the irradiance on a unit-length of feedstock  1211  increases the rate at which it is heated. Conversely, decreasing the irradiance on a unit-length of feedstock  1211  decreases the rate at which it is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the irradiance of laser beam  1271  on feedstock  1211  is advantageous for, among other things, compensating for variations in the angle of incidence of laser beam  1271  on feedstock  1211  caused by changes in the relative position of optical instrument  1261  to feedstock  1211 . These changes are often caused by changes in the contour of workpiece  1206 . 
     At task  2004 , controller  1209  directs optical instrument  1261  to adjust the angle of incidence of laser beam  1271  on feedstock  1211  within feedstock region  1371 - 2 . This provides controller  1209  with another mechanism for adjusting the temperature of each unit-length of feedstock  1211  when it is deposited and tamped. For example—and assuming everything else is constant—adjusting the angle of incidence of laser beam  1271  on feedstock  1211  changes the effective irradiance on each unit-length of feedstock  1211 . It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the angle of incidence of laser beam  1271  on feedstock  1211  is advantageous for, among other things, compensating for changes in the relative position of optical instrument  1261  to feedstock  1211 . These changes are often caused by changes in the contour of workpiece  1206 . 
       FIG. 21  depicts a flowchart of the details of task  1803 —adjusting optical instrument  1262 . Controller  1209  continually directs optical instrument  1262  to make adjustments, and, therefore, the tasks depicted in  FIG. 21  are concurrent. 
     At task  2101 , controller  1209  directs optical instrument  1262  to adjust—lengthen or shorten—the length of workpiece region  1372 - 2  (i.e., the portion of workpiece  1206  being irradiated by laser beam  1272 ). This provides controller  1209  with a mechanism for adjusting the temperature of each unit portion of workpiece  1206  when it is deposited and tamped. For example—and assuming that everything else is constant—increasing the length of workpiece region  1372 - 2  spreads the heat energy of laser beam  1272  over a greater portion of workpiece  1206 , which decreases the rate at which each unit portion of workpiece  1206  is heated. Conversely, decreasing the length of workpiece region  1372 - 2  concentrates the heat energy, which increases the rate at which each unit portion of workpiece  1206  is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the length of workpiece region  1372 - 2  is advantageous for, among other things, compensating for variations in the rate at which feedstock  1211  is deposited and tamped. 
     At task  2102 , controller  1209  directs optical instrument  1262  to adjust—increase or decrease—the distance between pinch line  1382  and workpiece region  1372 - 2 . This provides controller  1209  with a mechanism for adjusting the temperature of each unit portion of workpiece  1206  when it is deposited and tamped. For example—and assuming everything else is constant—increasing the distance gives each unit portion of workpiece  1206  more time to cool before it is deposited and tamped. Conversely, decreasing the distance gives each unit segment of feedstock less time to cool before it is deposited and tamped. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the distance between pinch line segment  1382  and workpiece region  1372 - 2  is advantageous for, among other things, fine tuning the temperature of each unit portion of workpiece  1206  at the time that the corresponding segment of feedstock  1211  is deposited and tamped. 
     At task  2103 , controller  1209  directs optical instrument  1262  to adjust the irradiance of laser beam  1272  on each unit portion of workpiece  1206  within workpiece region  1372 - 2 . This provides controller  1209  with a mechanism for adjusting the temperature of each unit portion of workpiece  1206  at the time that the corresponding segment of feedstock  1211  is deposited and tamped. For example—and assuming everything else is constant—increasing the irradiance on a unit portion of workpiece  1206  increases the rate at which it is heated. Conversely, decreasing the irradiance on a unit-area of workpiece  1206  decreases the rate at which it is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the irradiance of laser beam  1272  on workpiece  1206  is advantageous for, among other things, compensating for variations in the angle of incidence of laser beam  1272  on workpiece  1206  caused by changes in the relative position of optical instrument  1262  to workpiece  1206 . These changes are often caused by changes in the contour of workpiece  1206 . 
     At task  2104 , controller  1209  directs optical instrument  1262  to adjust the angle of incidence of laser beam  1272  on workpiece  1206  within workpiece region  1372 - 2 . This provides controller  1209  with another mechanism for adjusting the temperature of each unit portion of workpiece  1206  when it is deposited and tamped. For example—and assuming everything else is constant—adjusting the angle of incidence of laser beam  1272  on workpiece  1206  changes the effective irradiance on each unit portion of workpiece  1206 . It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the angle of incidence of laser beam  1272  on workpiece  1206  is advantageous for, among other things, compensating for changes in the relative position of optical instrument  1262  to workpiece  1206 . These changes are often caused by changes in the contour of workpiece  1206 . 
     At task  2105 , controller  1209  directs optical instrument  1262  to steer laser beam  1272  onto deposition path  1391 . 
     In accordance with the second illustrative, sensor array  1215  is not mechanically steered onto workpiece region  1372 - 1 , workpiece region  1372 - 2 , or workpiece region  1372 - 3 . Instead, controller  1209  picks the temperature measurements for workpiece region  1372 - 1 , workpiece region  1372 - 2 , or workpiece region  1372 - 3  out of the thermal image from sensor array  1215  based on the location of deposition path  1391  in that image. It will be clear to those skilled in the art, after reading this disclosure, how to accomplish this. 
       FIG. 22  depicts a flowchart of the details of task  1804 —adjusting optical instrument  1263 . Controller  1209  continually directs optical instrument  1263  to make adjustments, and, therefore, the tasks depicted in  FIG. 22  are concurrent. 
     At task  2201 , controller  1209  directs optical instrument  1263  to adjust—lengthen or shorten—the length of workpiece region  1372 - 3  (i.e., the portion of workpiece  1206  being irradiated by laser beam  1273 ). This provides controller  1209  with a mechanism for adjusting the temperature of each unit portion of workpiece  1206  when it is deposited and tamped. For example—and assuming that everything else is constant—increasing the length of workpiece region  1372 - 3  spreads the heat energy of laser beam  1273  over a greater portion of workpiece  1206 , which decreases the rate at which each unit portion of workpiece  1206  is heated. Conversely, decreasing the length of workpiece region  1372 - 3  concentrates the heat energy, which increases the rate at which each unit portion of workpiece  1206  is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the length of workpiece region  1372 - 3  is advantageous for, among other things, compensating for variations in the rate at which feedstock  1211  is deposited and tamped. 
     At task  2202 , controller  1209  directs optical instrument  1263  to adjust—increase or decrease—the distance between pinch line  1382  and workpiece region  1372 - 3 . This provides controller  1209  with a mechanism for adjusting the temperature of each unit portion of workpiece  1206  when it is deposited and tamped. For example—and assuming everything else is constant—increasing the distance gives each unit portion of workpiece  1206  more time to cool before it is deposited and tamped. Conversely, decreasing the distance gives each unit segment of feedstock less time to cool before it is deposited and tamped. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the distance between pinch line segment  1382  and workpiece region  1372 - 3  is advantageous for, among other things, fine tuning the temperature of each unit portion of workpiece  1206  at the time that the corresponding segment of feedstock  1211  is deposited and tamped. 
     At task  2203 , controller  1209  directs optical instrument  1263  to adjust the irradiance of laser beam  1273  on each unit portion of workpiece  1206  within workpiece region  1372 - 3 . This provides controller  1209  with a mechanism for adjusting the temperature of each unit portion of workpiece  1206  at the time that the corresponding segment of feedstock  1211  is deposited and tamped. For example—and assuming everything else is constant—increasing the irradiance on a unit portion of workpiece  1206  increases the rate at which it is heated. Conversely, decreasing the irradiance on a unit-area of workpiece  1206  decreases the rate at which it is heated. It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the irradiance of laser beam  1273  on workpiece  1206  is advantageous for, among other things, compensating for variations in the angle of incidence of laser beam  1273  on workpiece  1206  caused by changes in the relative position of optical instrument  1263  to workpiece  1206 . These changes are often caused by changes in the contour of workpiece  1206 . 
     At task  2204 , controller  1209  directs optical instrument  1263  to adjust the angle of incidence of laser beam  1273  on workpiece  1206  within workpiece region  1372 - 3 . This provides controller  1209  with another mechanism for adjusting the temperature of each unit portion of workpiece  1206  when it is deposited and tamped. For example—and assuming everything else is constant—adjusting the angle of incidence of laser beam  1273  on workpiece  1206  changes the effective irradiance on each unit portion of workpiece  1206 . It will be clear to those skilled in the art, after reading this disclosure, that being able to adjust the angle of incidence of laser beam  1273  on workpiece  1206  is advantageous for, among other things, compensating for changes in the relative position of optical instrument  1263  to workpiece  1206 . These changes are often caused by changes in the contour of workpiece  1206 . 
     At task  2205 , controller  1209  directs optical instrument  1263  to steer laser beam  1273  onto deposition path  1391 . 
       FIG. 23  depicts a flowchart of the relative timing of the tasks performed on segment m of feedstock  1211  and on portion n of workpiece  1206 , wherein m and n are integers. In accordance with the second illustrative embodiment segment m of feedstock  1211  is deposited and tamped onto portion n of workpiece  1206 . 
     During time-Interval Δt=m−3, the temperature of segment m of feedstock  1211  is measured by thermal sensor  1571 - 1  and reported to controller  1209 . 
     During time-Interval Δt=n−3, the temperature of portion n of workpiece  1206  is measured by thermal sensor  1572 - 1  and reported to controller  1209 . 
     In accordance with the second illustrative embodiment, the duration of time-interval Δt=m−3 equals the duration of time-interval Δt=n−3, and time-interval Δt=m−3 is contemporaneous with time-interval Δt=n−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−3 does not equal the duration of time-interval Δt=n−3. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−3 is not contemporaneous with time-interval Δt=n−3. And still furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−3 overlaps, immediately precedes, immediately succeeds, precedes but not immediately, or succeeds but not immediately time-interval Δt=n−3. 
     During time-Interval Δt=m−2:
         (i) controller  1209  directs feedstock laser  1241  to generate laser beam  1271  with a given average power, and   (ii) controller  1209  directs optical instrument  1261  to adjust a trait of laser beam  1271  and/or the relationship of laser beam  1271  to feedstock  1211 , and   (iii) optical instrument  1261  irradiates and heats segment m of feedstock  1211 , and   (iv) the temperature of segment m of feedstock  1211  is measured by thermal sensor  1571 - 2  and reported to controller  1209 .
 
In accordance with the second illustrative embodiment, the duration of time-interval Δt=m−2 equals the duration of Δt=m−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−2 does not equal the duration of time interval Δt=m−3. Furthermore, in accordance with the second illustrative embodiment, time-interval Δt=m−2 is after, and is mutually-exclusive of, time-interval Δt=m−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−2 overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=m−3.
       

     During time-Interval Δt=n−2:
         (i) controller  1209  directs workpiece laser  1242  to generate laser beam  1272  with a given average power, and   (ii) controller  1209  directs optical instrument  1262  to adjust a trait of laser beam  1272  and/or the relationship of laser beam  1272  to workpiece  1206 , and   (iii) controller  1209  directs optical instrument  1262  to steer laser beam  1272  onto deposition path  1391 , and   (iv) optical instrument  1262  irradiates and heats portion n of workpiece  1206 , and   (v) the temperature of portion n of workpiece  1206  is measured by thermal sensor  1572 - 2  and reported to controller  1209 .       

     In accordance with the second illustrative embodiment, the duration of time-interval Δt=n−2 equals the duration of Δt=n−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=n−2 does not equal the duration of time interval Δt=n−3. Furthermore, in accordance with the second illustrative embodiment, time-interval Δt=n−2 is after, and is mutually-exclusive of, time-interval Δt=n−3. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=n−2 overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=n−3. 
     In accordance with the second illustrative embodiment, the duration of time-interval Δt=m−2 equals the duration of time-interval Δt=n−2, and time-interval Δt=m−2 is contemporaneous with time-interval Δt=n−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−2 does not equal the duration of time-interval Δt=n−2. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−2 is not contemporaneous with time-interval Δt=n−2. And still furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−2 overlaps, immediately precedes, immediately succeeds, precedes but not immediately, or succeeds but not immediately time-interval Δt=n−2. 
     During time-Interval Δt=m−1:
         (i) controller  1209  directs feedstock laser  1240  to generate laser beam  1270  with a given average power, and   (ii) controller  1209  directs optical instrument  1260  to adjust a trait of laser beam  1270  and/or the relationship of laser beam  1270  to feedstock  1211 , and   (iii) optical instrument  1260  irradiates and heats segment m of feedstock  1211 , and   (iv) the temperature of segment m of feedstock  1211  is measured by thermal sensor  1571 - 3  and reported to controller  1209 .       

     In accordance with the second illustrative embodiment, the duration of time-interval Δt=m−1 equals the duration of Δt=m−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−1 does not equal the duration of time interval Δt=m−2. Furthermore, in accordance with the second illustrative embodiment, time-interval Δt=m−1 is after, and is mutually-exclusive of, time-interval Δt=m−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−1 overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=m−2. 
     During time-Interval Δt=n−1:
         (i) controller  1209  directs workpiece laser  1243  to generate laser beam  1273  with a given average power, and   (ii) controller  1209  directs optical instrument  1263  to adjust a trait of laser beam  1273  and/or the relationship of laser beam  1273  to workpiece  1206 , and   (iii) controller  1209  directs optical instrument  1263  to steer laser beam  1273  onto deposition path  1391 , and   (iv) optical instrument  1263  irradiates and heats portion n of workpiece  1206 , and   (v) the temperature of portion n of workpiece  1206  is measured by thermal sensor  1572 - 3  and reported to controller  1209 .       

     In accordance with the second illustrative embodiment, the duration of time-interval Δt=n−1 equals the duration of Δt=n−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=n−1 does not equal the duration of time interval Δt=n−2. Furthermore, in accordance with the second illustrative embodiment, time-interval Δt=n−1 is after, and is mutually-exclusive of, time-interval Δt=n−2. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=n−1 overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=n−2. 
     In accordance with the second illustrative embodiment, the duration of time-interval Δt=m−1 equals the duration of time-interval Δt=n−1, and time-interval Δt=m−1 is contemporaneous with time-interval Δt=n−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m−1 does not equal the duration of time-interval Δt=n−1. Furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−1 is not contemporaneous with time-interval Δt=n−1. And still furthermore, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m−1 overlaps, immediately precedes, immediately succeeds, precedes but not immediately, or succeeds but not immediately time-interval Δt=n−1. 
     During time-Interval Δt=m=n, segment m of feedstock  1211  is deposited and tamped onto portion n of workpiece  1206 . 
     In accordance with the second illustrative embodiment, the duration of time-interval Δt=m equals the duration of Δt=m−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=m does not equal the duration of time interval Δt=m−1. Furthermore, in accordance with the second illustrative embodiment, time-interval Δt=m is after, and is mutually-exclusive of, time-interval Δt=m−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=m overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=m−1. 
     In accordance with the second illustrative embodiment, the duration of time-interval Δt=n equals the duration of Δt=n−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the duration of time-interval Δt=n does not equal the duration of time interval Δt=n−1. Furthermore, in accordance with the second illustrative embodiment, time-interval Δt=n is after, and is mutually-exclusive of, time-interval Δt=n−1. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which time-interval Δt=n overlaps, immediately succeeds, or succeeds but not immediately, time-interval Δt=n−1. 
       FIG. 24  depicts an illustration of additive manufacturing system  2400  in accordance with the third illustrative embodiment of the present invention. Additive manufacturing system  2400  fabricates an article of manufacture by successively depositing segments of fiber-reinforced thermoplastic feedstock (e.g., filament, tape, etc.) onto a workpiece until the article of manufacture is complete. 
     Additive manufacturing system  2400  is identical to additive manufacturing system  1200  fabricates in that they both fabricate an article of manufacture by successively depositing segments of fiber-reinforced thermoplastic feedstock (e.g., filament, tape, etc.) onto a workpiece until the article of manufacture is complete. Furthermore, most of the components of system  2400  are identical to their counterparts in system  1200  and perform exactly the same function in exactly the same way. 
     For example, the heating and sensor architecture for additive manufacturing system  2400  is identical to that for additive manufacturing system  1200  as described in  FIG. 15  and the accompanying text. The sensor and control architecture for that portion of additive manufacturing system  2400  is identical to that for additive manufacturing system  1200  as described in  FIG. 16  and the accompanying text. A flowchart of the tasks performed by additive manufacturing system  2400  is identical to that for additive manufacturing system  1200  as described in  FIGS. 17, 18, 19, 20, and 21 . And a flowchart of the relative timing of the tasks performed by additive manufacturing system  2400  is identical to that for additive manufacturing system  1200  as described in  FIG. 22 . 
     In contrast, additive manufacturing system  2400  is unlike additive manufacturing system  1200  in that system  2400 :
         (i) multiplexes the laser beams onto a single optical cable for transport between the lasers and deposition head  1207 , and   (ii) employs lasers whose laser beams are characterized by different wavelengths to facilitate the multiplexing and demultiplexing of the laser beams.
 
U.S. patent application Ser. No. 16/690,765, entitled “Heater for Thermoplastic Filament and Workpiece,” filed Nov. 21, 2019 is incorporated by reference for the purpose of disclosing:
   (i) multi-beam heating systems for additive manufacturing of fiber-reinforced thermoplastics, and   (ii) one- and two-stage laser heating systems for fiber-reinforced thermoplastic feedstock (e.g., filament, tape, etc), and   (iii) one- and two-stage laser heating system for fiber-reinforced thermoplastic workpieces, and   (iv) multiplexing laser beams for use in the heating of fiber-reinforced feedstock and workpieces.       

     Additive manufacturing system  2400  comprises: platform  1201 , robot mount  1202 , robot  1203 , build plate support  1204 , build plate  1205 , workpiece  1206 , deposition head  2407 , tamping tool  1208 , controller  1209 , feedstock reel  1210 , feedstock  1211 , accumulator  1212 , force gauge  1213 , sensor array  1215 , feedstock laser  2440 , feedstock laser  2441 , workpiece laser  2442 , feedstock laser  2443 , optical cable  2454 , sensor cable  1254 , optical instrument  1260 , optical instrument  1261 , optical instrument  1262 , optical instrument  1263 , laser beam  1270 , laser beam  1271 , laser beam  1272 , laser beam  1273 , feedstock laser control cable  1291 , workpiece laser control cable  1292 , beam combiner  2451 , beam combiner  2452 , beam combiner  2453 , beam splitter  2461 , beam splitter  2462 , and beam splitter  2463 , interrelated as shown. 
       FIG. 25  depicts a close-up of workpiece  1206 , deposition head  2407 , tamping tool  1208 , feedstock  1211 , sensor array  1215 , optical instrument  1260 , optical instrument  1261 , optical instrument,  1262 , optical instrument  1263 , optical cable  2454 , sensor cable  1254 , laser beam  1270 , laser beam  1271 , laser beam  1272 , laser beam  1273 , feedstock region  1371 - 1 , feedstock region  1371 - 2 , feedstock region  1371 - 3 , workpiece region  1372 - 1 , workpiece region  1372 - 2 , workpiece region  1372 - 3 , nip line segment  1381 , and pinch line segment  1382 , beam splitter  2461 , beam splitter  2462 , and beam splitter  2463 , interrelated as shown. 
     Deposition head  2407  is identical to deposition head  1207  except that is also comprises beam splitter  2461 , beam splitter  2462 , and beam splitter  2463 , and structural support for beam splitter  2461 , beam splitter  2462 , and beam splitter  2463 . 
     Feedstock laser  2440  is identical to feedstock laser  1240  in that it generates laser beam  1270  for optical instrument  1260 . It will be clear to those skilled in the art how to make and use feedstock laser  2440 . 
     Feedstock laser  2441  is identical to feedstock laser  1241  in that it generates laser beam  1271  for optical instrument  1261  except that it is characterized by a wavelength λ=905 nm. It will be clear to those skilled in the art how to make and use feedstock laser  2441 . 
     Workpiece laser  2442  is identical to workpiece laser  1242  in that it generates laser beam  1272  for optical instrument  1262  except that it is characterized by a wavelength λ=955 nm. It will be clear to those skilled in the art how to make and use workpiece laser  2441 . 
     Workpiece laser  2443  is identical to workpiece laser  1243  in that it generates laser beam  1273  for optical instrument  1263  except that it is characterized by a wavelength λ=930 nm. It will be clear to those skilled in the art how to make and use workpiece laser  2442 . 
     Optical cable  2454  is a glass fiber, in well-known fashion, that carries laser beam  1270 , laser beam  1271 , laser beam  1272 , and laser beam  1273  from feedstock laser  2441  from beam combiner  2453  to beam splitter  2462  with substantially no loss. It will be clear to those skilled in the art how to make and use optical cable  2454 . 
     Beam combiner  2451  is a dichroic beam combiner, in well-known fashion, that combines laser beam  1270  and laser beam  1271 . It will be clear to those skilled in the art how to make and use beam combiner  2451 . 
     Beam combiner  2452  is a dichroic beam combiner, in well-known fashion, that combines laser beam  1272  to the combination of laser beam  1270  and laser beam  1271 . It will be clear to those skilled in the art how to make and use beam combiner  2452 . 
     Beam combiner  2453  is a dichroic beam combiner, in well-known fashion, that combines laser beam  1273  to the combination of laser beam  1270 , laser beam  1271 , and laser beam  1272 . It will be clear to those skilled in the art how to make and use beam combiner  2453 . 
     Beam splitter  2462  is a dichroic beam splitter, in well-known fashion, that splits laser beam  1272  from the combination of laser beam  1270 , laser beam  1271 , laser beam  1272 , and laser beam  1273 . It will be clear to those skilled in the art how to make and use beam splitter  2462 . 
     Beam splitter  2463  is a dichroic beam splitter, in well-known fashion, that splits laser beam  1273  from the combination of laser beam  1270 , laser beam  1271 , and laser beam  1273 . It will be clear to those skilled in the art how to make and use beam splitter  2463 . 
     Beam splitter  2461  is a dichroic beam splitter, in well-known fashion, that splits laser beam  1270  and laser beam  1271  from the combination of laser beam  1270  and laser beam  1271 . It will be clear to those skilled in the art how to make and use beam splitter  2461 . 
     The sensor and control architecture for that portion of additive manufacturing system  2400  is identical to that for additive manufacturing system  1200  as described in  FIG. 16  and the accompanying text. 
     A flowchart of the tasks performed by additive manufacturing system  2400  is identical to that for additive manufacturing system  1200  as described in  FIGS. 17, 18, 19, 20 , and 
     A flowchart of the relative timing of the tasks performed by additive manufacturing system  2400  is identical to that for additive manufacturing system  1200  as described in  FIG. 22 . 
       FIG. 26  depicts a schematic diagram of the heating and sensor architecture for additive manufacturing system  2400 , which irradiates and heats feedstock  1211  and workpiece  1206  and measures the temperature of feedstock  1211 , workpiece  1206 , and tamping tool  1208 . In most respects, the heating and sensor architecture for additive manufacturing system  2400  is identical to that for system  1200 , except for the addition of the multiplexing of laser beams. To wit, and as shown in  FIG. 26 :
         (i) feedstock laser  1240  provides laser beam  1270  to optical instrument  1260  via beam combiner  2451 , optical cable  2454 , and beam splitter  2461 , and   (ii) feedstock laser  1241  provides laser beam  1271  to optical instrument  1261  via beam combiner  2451 , optical cable  2454 , and beam splitter  2461 , and   (iii) workpiece laser  1242  provides laser beam  1272  to optical instrument  1262  via beam combiner  2452 , optical cable  2454 , and beam splitter  2462 , and   (iv) workpiece laser  1243  provides laser beam  1273  to optical instrument  1263  via beam combiner  2452 , optical cable  2454 , and beam splitter  2463 .
 
In all other respects, the heating and sensor system  2400  is identical to that for system  1200 .
       

     Although the third illustrative embodiment employs 4:1 multiplexing, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that employ N:1 multiplexing, where N is a positive integer greater than 1 (e.g., 2, 3, 5, 6, 7, 8, 10, 20, 500, 100, 500, etc.).