Continuum robots for omnidirectional 3D printing and related printing methods

Abstract

Many embodiments are directed to systems and methods for 3D printing. Many embodiments utilize a print head modeled after a concentric tube robot (CTR). Certain embodiments provide a print bed allowing for collaborative printing and can include ports to allow numerous degrees of freedom from a print head without loss of a print bed solution. Further embodiments allow printing within irregular print beds, including printing within an injection mold. Certain embodiments of print heads possess multiple nozzles and / or internal tubes to allow for additional geometries. Certain embodiments are directed to print nozzles allowing for multiple material printing, and optionally on-the-fly material switching. Certain embodiments are directed to uses of bioprinting, including in vivo printing of devices, while additional embodiments allow for pipeline type printing, such that the printed part continually and / or continuously moves through a path during the printing process.

Description

CONTINUUM ROBOTS FOR OMNIDIRECTIONAL 3D PRINTING AND RELATED PRINTING METHODS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The current application claims priority to U.S. Provisional Patent Application No. 63 / 557,208, filed February 23, 2024, entitled “Concentric Tube Robots for Omnidirectional 3d Printing and Related Printing Methods” to Skyler-Scott, et al.; the disclosure of which is hereby incorporated by reference in its entirety. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with Government support under contract AY1AX000002-01 awarded by the Advanced Research Projects Agency - Health. The Government has certain rights in the invention. FIELD OF THE INVENTION

[0003] The present invention relates to three-dimensional (3D) printing, more specifically, systems, and methods of 3D printing that use printing heads modeled after continuum robots to print structures and devices in situ, in vivo, and / or in confined spaces. BACKGROUND

[0004] Embedded 3D printing (E3DP) is transcending the manufacturing capabilities of several fields, such as soft robotics and tissue engineering. At its core, E3DP involves patterning of materials into a viscoelastic support matrix along predefined omnidirectional paths. The support matrices shear thinning property permits smooth movement of printheads within the print bath, while its thixotropic behavior mitigates crevice formation and holds printed structures in place for further crosslinking. Despite these desirable material properties, the viscoelastic nature of the matrix requires a secondary container to hold the support matrix itself in place. This container can limit the accessibility to the workspace for 3D printers, particularly if multiple printheads are introduced, as only the top of the container is penetrable for extruding nozzles. Still, to reduce print times for E3DP, multiple printheads are desirable, especially when considering that increasingmovement rates is limited by an enlarged disruptive region around rapidly translating nozzles.

[0005] Traditional rectilinear 3D printing platforms struggle to take full advantage of the omnidirectional patterning potential of E3DP. That is, as a straight nozzle patterns material within the support matrix, it is impossible to reach points below already printed structures without distorting these structures. Consequently, print paths are usually generated in (i) a layer-by-layer manner or (ii) in a free-form manner where discretized paths are connected by optimization algorithms. Although the latter method allows for omnidirectional printing, it introduces several disruptions to the material extrusion and can cause challenges in connection of printed paths. Additionally, the discretized paths can be far from one another, so lengthy translations between points might are needed, adding to the print time. Print times are further increased when multi-material E3DP is desired, as frequent time-consuming changes of extruders typically are required to switch between materials. Thus, there is a need in the field for 3D printing that allows for printing within confined areas and / or collaborative printing with minimal interference between print heads or nozzles. SUMMARY OF THE INVENTION

[0006] Many embodiments are directed to systems and methods for 3D printing. Many embodiments utilize a print head modeled after a concentric tube robot (CTR). Certain embodiments provide a print bed allowing for collaborative printing and can include ports to allow numerous degrees of freedom from a print head without loss of a print bed solution. Further embodiments allow printing within irregular print beds, including printing within an injection mold. Certain embodiments of print heads possess multiple nozzles and / or internal tubes to allow for additional geometries. Certain embodiments are directed to print nozzles allowing for multiple material printing, and optionally on-the-fly material switching. Certain embodiments are directed to uses of bioprinting, including in vivo printing of devices, while additional embodiments allow for pipeline type printing, such that the printed part continually and / or continuously moves through a path during the printing process.

[0007] Other features and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings which illustrate, by way of example, the principles of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The description and claims will be more fully understood with reference to the following figures and data graphs, which are presented as exemplary embodiments of the invention and should not be construed as a complete recitation of the scope of the invention.

[0009] Figures 1A-1C illustrate examples of radial (Figure 1A), rotational (Figure 1B), and axial (Figure 1C) dimensions, in accordance with various embodiments.

[0010] Figures 1D-1E illustrate the abilities of printing using a Cartesian coordinate system (Figure 1D) and of a cylindrical coordinate system (Figure 1E), in accordance with various embodiments.

[0011] Figure 2A illustrates an example of a telescoping CTR-based printing device in accordance with various embodiments.

[0012] Figure 2B illustrates geometry of combined flexible tubing in accordance with various embodiments.

[0013] Figure 3 illustrates a multi-lumen printhead for multi-material printing in accordance with various embodiments.

[0014] Figure 4 illustrates an exemplary CTR-based system using three curved, internal tubes to allow printing at multiple locations simultaneously in accordance with various embodiments.

[0015] Figures 5A-5B illustrate examples of dendritic printing systems in accordance with various embodiments.

[0016] Figure 5C illustrates a schematic of a 2-layer, 2-tube system, which produces a total of 7 nozzles in accordance with various embodiments.

[0017] Figure 6 illustrates an example embedded print within an injection mold in accordance with various embodiments.

[0018] Figure 7A illustrates an exemplary setup for a moving bath pipeline in accordance with various embodiments.

[0019] Figures 7B-7C illustrate additional components that can be used in a moving bath pipeline in accordance with various embodiments.

[0020] Figure 8A illustrates flow types through a pipeline based on an idealized flow and practical flow types in accordance with various embodiments.

[0021] Figures 8B-8C illustrate exemplary systems that allow printing and merger of precursor components in a moving bath pipeline in accordance with various embodiments.

[0022] Figure 9 provides a photograph of an exemplary setup using six printheads to collaboratively print an object in accordance with various embodiments.

[0023] Figures 10A-10B illustrate various views of an insertion port allowing four degrees of freedom in accordance with various embodiments.

[0024] Figure 11 illustrates an exploded view of an insertion port allowing six degrees of freedom in accordance with various embodiments.

[0025] Figure 12 illustrates an exemplary system for multi-material printing in accordance with various embodiments.

[0026] Figure 13A illustrates an axial view of a tricuspid valve printed by a CTR-based 3D printer in accordance with various embodiments.

[0027] Figures 13B-13C illustrates side and top-down views of a tricuspid valve being printed in accordance with various embodiments.

[0028] Figures 14A-14B illustrate examples of objects printed using dendritic printing devices in accordance with various embodiments.

[0029] Figure 15 illustrates a flow chart of a process for variable shape print layer generation in accordance with various embodiments.

[0030] Figures 16A-16E illustrate exemplary equations and boundary planes that can be used in variable shape print layer generation in accordance with various embodiments.

[0031] Figure 17 illustrates an exemplary equation that can be used to adjust a boundary plane for variable shape print layer generation in accordance with various embodiments.

[0032] Figure 18 illustrates exemplary equations for generating points on a boundary plane in accordance with various embodiments.

[0033] Figure 19 illustrates an exemplary equation that can be used to define a boundary condition for variable shape print layer generation in accordance with various embodiments.

[0034] Figure 20 illustrates an exemplary equation that can be used to determine signed distance for variable shape print layer generation in accordance with various embodiments.

[0035] Figures 21A-21C illustrate exemplary shells that can be generated from a process for variable shape print layer generation in accordance with various embodiments.

[0036] Figure 22 illustrates a flow chart of a process for spiral path planning in accordance with various embodiments.

[0037] Figure 23 illustrates exemplary equations for spiral path planning in accordance with various embodiments.

[0038] Figure 24 illustrates a flow chart of a process for TSP path planning in accordance with various embodiments.

[0039] Figure 25 illustrates exemplary equations for TSP path planning in accordance with various embodiments.

[0040] Figure 26 illustrates a flow chart of a process for contour following path planning in accordance with various embodiments.

[0041] Figures 27A-27B illustrate printing paths to print a full-size human heart and a rabbit structure in accordance with various embodiments.

[0042] Figures 28A-28C illustrate a pipeline printing system printing 3D Benchys in accordance with various embodiments.

[0043] Figure 28D illustrates an elbow bend in a pipeline printing system showing the predictability of distortion within a viscoplastic matrix in accordance with various embodiments.

[0044] Figures 29A-29D illustrate exemplary structures printed from a single dendritic printhead in accordance with various embodiments.

[0045] Figures 30A-30B illustrate printing a sacrificial structure within a biological matrix in accordance with various embodiments.

[0046] Figure 31 illustrates an exemplary system to navigate a printhead or tube into an object by manipulating a position or angle of a keyhole in accordance with various embodiments. DETAILED DESCRIPTION

[0047] The embodiments of the invention described herein are not intended to be exhaustive or to limit the invention to precise forms disclosed. Rather, the embodiments selected for description have been chosen to enable one skilled in the art to practice the invention.

[0048] Turning now to the drawings, many embodiments are directed to systems and methods for 3D printing. Many embodiments utilize a print head modeled after a concentric tube robot (CTR). Certain embodiments provide a print bed allowing for collaborative printing and can include ports to allow numerous degrees of freedom from a print head without loss of a print bed solution. Further embodiments allow printing within irregular print beds, including printing within an injection mold. Certain embodiments of print heads possess multiple nozzles and / or internal tubes to allow for additional geometries. Certain embodiments are directed to print nozzles allowing for multiple material printing, and optionally on-the-fly material switching. Certain embodiments are directed to uses of bioprinting, including in vivo printing of devices, while additional embodiments allow for pipeline type printing, such that the printed part continually and / or continuously moves through a path during the printing process. Definitions

[0049] As used herein, “three dimensional printing,” or “3D printing,” refer to additive manufacturing and methods that deposit material via one or more methods, including (but not limited to) Fused Deposition Modeling (FDM), Stereolithography (SLA), Selective Laser Sintering (SLS), Digital Light Processing (DLP), Binder Jetting, Material Jetting, and combinations thereof.

[0050] As used herein, “viscosity” refers to the measure of a fluid's resistance to flow or deformation. Viscosity is a fundamental property of fluids and describes how easily a fluid moves or deforms under an applied force. Viscosity is typically described in terms ofits resistance to shear stress, which is the force required to make adjacent layers of fluid move with respect to each other. A fluid with high viscosity resists flow and deformation more strongly than a fluid with low viscosity.

[0051] As used herein, “flow” or “fluid flow” describe the pattern of flow (e.g., laminar, turbulent, etc.) of a fluid in different situations. Such flow can be described using the Reynolds number. Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion. Turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities

[0052] As used herein, the terms “rigid” and “flexible” are relative terms to describe how a material responds to external forces. Flexibility is the ability of a material to deform or bend without breaking, while rigidity is the resistance of a material to deformation or bending. Flexibility and rigidity are not mutually exclusive, but rather depend on the type, magnitude, and direction of the applied force, as well as the shape, size, and structure of the material.

[0053] Certain ranges are presented herein with numerical values being preceded by the term “about.” The term “about” is used herein to provide literal support for the exact number that it precedes, as well as a number that is near to or approximately the number that the term precedes. In determining whether a number is near to or approximately a specifically recited number, the near or approximating unrecited number may be a number which, in the context in which it is presented, provides the substantial equivalent of the specifically recited number.

[0054] It is noted that, as used herein and in the appended claims, the singular forms “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise. It is further noted that the claims may be drafted to exclude any optional element. As such, this statement is intended to serve as antecedent basis for use of such exclusive terminology as “solely,” “only” and the like in connection with the recitation of claim elements, or use of a “negative” limitation.

[0055] As used herein, the term “continuum robot” refers to type of robotic system that has a flexible, continuous structure, resembling a soft or snake-like body, rather than using rigid joints and segments.

[0056] As used herein, the term “keyhole” refers to a pore or orifice on a surface that allows entry of an apparatus with limited movement within the plane of the keyhole. A keyhole may have any geometric shape or cross section, such as round, square, triangular, pentagonal, hexagonal, heptagonal, octagonal, nonagonal, etc. A keyhole may be a fixed or static orifice on the surface. In some instances, the keyhole may be created by entry of a robot into the object—for example, the surface may be a constructed of a self-healing material, which can be punctured then resealed upon removal of a robot. Keyhole 3D Printing

[0057] Many embodiments herein utilize one or more types of robot that can enter a small pore—referred to as a keyhole—to print a 3D structure. In many instances, the robot is a continuum robot. As will be described herein, such keyholes may allow entry into a pipeline, a static print bed, and / or any other structure. To perform such keyhole printing, many embodiments are directed to a robotic print heads that include a shaft that is capable of entering the keyhole. Examples include concentric tube robots (CTRs), push- pull shaft type robots, steerable needles, and / or any other type of robotic arm that can enter or feed a material extruder through a keyhole.

[0058] CTRs are a type of robotic system composed of multiple tubes arranged concentrically around a common axis. Such tubes can be rigid, flexible, or a combination thereof. Many embodiments of CTRs utilize a rigid outer tube with one or more flexible internal tubes. In certain embodiments, one or more tube may be formed with a predefined shape, such as a curve, spiral, angle, and / or other shape. The tubes can be actuated independently or in coordination to achieve complex movements and manipulations. Articulation and / or actuation of one or more tubes in a CTR can enable navigation in space, such as (but not limited to) confined, complex, and / or difficult-to-reach spaces while maintaining dexterity and / or precision. US 2017 / 0095299 provides additional details and uses of CTRs and is hereby incorporated by reference in its entirety.

[0059] In certain instances, the flexible material is a shape memory metal or shape memory alloy. Examples of shape memory metals or alloys include (but are not limited to) Nickel-Titanium (NiTi or Nitinol), Copper-Aluminum-Nickel (Cu-Al-Ni), Iron- Manganese-Silicon (Fe-Mn-Si), Copper-Zinc-Aluminum (Cu-Zn-Al), and Gold-Cadmium(Au-Cd). Additional shape memory alloys include (but are not limited to) copper-based alloys, nickel-titanium-based alloys with additives, titanium-bases alloys, and platinum- based alloys. In some preferred embodiments, the internal tube is NiTi.

[0060] Using an internal tube having a curve, certain embodiments are capable of moving according to cylindrical coordinates, rather than cartesian coordinates. Cartesian coordinates describes a point in three dimensional space based on a distance from a reference point in three planes (i.e., x, y, and z positions). In contrast, cylindrical coordinates describe a point in three dimensional space based on radial, rotational, and axial dimensions. Figures 1A-1C illustrate examples of radial, rotational, and axial dimensions, respectively. Specifically, Figure 1A demonstrates the radial position of a tip of a curved, internal tube, as it extends from a rigid outer tube. For example, as the internal tube extends from the outer tube, the radial position increases, such as from r1 to r2. Figure 1B demonstrates a rotational position, as defined as an angle with the rigid, outer tube as a central axis. The axial position is demonstrated in Figure 1C, as the linear position of a device (e.g., CTR). In traditional CTRs, rotational motion (e.g., Figure 1B) is made by rotating inner and outer tubes relative to each other. This motion creates torque within the robot which can cause the distal tip to be at a position different from expectation. Many of the describe embodiments mitigate and obviate the torque issue by rotating the inner and outer tubes simultaneously. By mitigating the torque, such embodiments ensure that the distal end is positioned where expected based on the degree of rotation.

[0061] Additionally, embodiments using a cylindrical system illustrated in Figures 1A-1C allows for actions that are not possible in traditional, Cartesian systems. Figure 1D illustrates printing of a spiral using a Cartesian system. Such a system requires a fully open side of a print bed. In contrast, Figure 1E illustrates a cylindrical system, which allows entry of the printhead via a keyhole on one face. Additionally, this cylindrical system can allow for embedding or insertion of subsequently printed components. This later-added print can be embedded or inserted into previously printed structures.

[0062] Additional dimensions may be produced using one or more additional tubes arranged in a telescopic fashion, such that an additional tube may extend from the curved, internal tube—e.g., additional tubes, that can be rotated or extended from within preceding internal tube. Such embodiments with one or more additional tubes can include2, 3, 4, 5, 6, or more flexible, internal tubes. Additional internal tubes can allow a larger dexterous workspace and more flexibility of moving within a print bath. As described previously, each tube may have a predefined shape, such as a curve, angle, or other shape that allows additional geometries. Certain of such embodiments include co-rotating bearings between tubes to minimize torsional buildup between the internal tubes. Figure 2A illustrates an exemplary CTR-based system using three curved, internal tubes (201, 202, 203) to allow a greater freedom of printing within a print bed.

[0063] The curvature of the internal tubes may interfere with each other due to the curvature (and orientation of the curvature) and stiffness (e.g., rigidity, flexibility) of such tubes. The interference can affect the resultant curvature of the tubes. This combined curvature can be used as an additional method for augmenting position or angle of ink delivery, such as through rotation of an internal tube. For example, Figure 2B illustrates internal (inner) tubes and outer tubes aligned in the different directions. The characteristics of each tube (stiffness, curvature, orientation, etc.) combine, such that the combined tube (i.e., when the internal tube is retracted within the outer tube) has a resultant orientation and curvature that is different either the internal and outer tubes.

[0064] While the foregoing paragraphs describe the use of CTRs, additional embodiments are directed to other continuum robots, including push-pull type robots, tendon driven robots, steerable needles, and others.

[0065] Push-pull type robots (also known as antagonistic actuation robots) possess concentric tubes that are joined at its distal end—i.e., the end furthest from the main part of the robotic device and the point from which print material (e.g., “ink”) is emitted. Each tube of these concentric tubs includes a plurality of slits or cuts that allow flexibility within the tubes. The pattern of cuts within each tube allows actions such as pushing, pulling, or twisting one or more of the tubes, which bends or deforms the robot into a particular conformation or angle. Multiple actions (e.g., pushing and twisting, pulling and twisting, etc.) can be combined to generate additional conformations. Additional details regarding push-pull type robots can be found in US 2023 / 0363843; the disclosure of which is hereby incorporated by reference in its entirety. In many instances, the tubes of the push-pull type robots are constructed of a flexible material, such as a shape-memory metal (suchas described below) or a plastic or polymeric material. In some instances a plastic or polymeric material can be fiber-reinforced, which can increase strength and / or resiliency.

[0066] Additional embodiments are directed toward tendon-driven continuum robots (also referred to as a tendon-driven robot). Tendon-driven robots include robots that utilize cables or flexible rods (referred to as “tendons”) to control the motion of the robot. The tendons are actuated to create bending or curving motions along the robot’s body, allowing it to achieve highly flexible and precise movements. This design combines the flexibility of continuum robots with the control precision that tendon-driven systems offer. In a tendon-driven robot, The robot consists of a flexible body or backbone, which can bend in multiple directions, the body is typically a soft, flexible material that can conform to the environment. Tendons are threaded through the structure and can be pulled or released to create specific deformations. By controlling the tension in the tendons, the robot's shape and movement can be precisely controlled. The tendons often run along different parts of the robot, allowing for multi-directional control.

[0067] Certain embodiments are directed to steerable needles. A steerable needle is a type of needle designed to be controlled and guided through tissue with greater precision than a traditional needle. It features mechanisms that allow it to be steered or bent in real-time, enabling it to navigate around obstacles and reach specific, targeted areas inside of an object. Steerable needles often have a flexible shaft or a segmented design, which allows it to curve or bend when manipulated. The steering mechanism may utilize a tendon-driven mechanism, a shape-memory material, and / or a push-pull type mechanism, such as those described herein.

[0068] Another type of robot or navigation within the scope of this disclosure includes devices where the print nozzle or shaft is guided using the keyhole itself. For example, a keyhole may be movable within a plane (e.g., X-Y plane). Additionally or alternatively, a keyhole may be tilted or rotated within a plane allowing for slanted access to a portions of an object absent flexibility of the print nozzle itself. Figure 31 illustrates a possible mechanism for keyhole-driven navigation, where one or more rotary motors (e.g., stepper motors, servo motors, brushed motors, brushless motors, etc.) which allow additional dimensions of navigability to a tube or shaft.

[0069] Using combinations of inks, complex mechanisms or devices can be printed in a single process. Such printing may be performed using embodiments including two or more lumens or conduits in parallel—including (but not limited to) 2, 3, 4, 5, 6, or more lumens. With multiple lumens, such embodiments allow for multiple inks or materials to be swapped or changed “on-the-fly” or with minimal delay during a printing process. Figure 3 illustrates a schematic of a multi-lumen internal tube possessing three lumens to allow multiple inks to be printed during a single procedure. These lumens may be separate internal tubes residing within the outer tube or these lumens may be separate (and / or flexible) lumens residing within an internal tube. In Figure 3, these lumens coalesce at a single printing nozzle, such that inks are changed with minimal delay or division in printing materials. The printed filament can allow for the material to change easily.

[0070] The individual lumens can have the same cross sectional areas, such that linear displacement is the same volume regardless of ink-type. Alternatively, lumen cross sectional area can be different, such that certain lumens possess a larger cross sectional area and some have a lower cross sectional area. Different cross sectional areas may lower forces used to deposit or extrude an ink—e.g., a larger cross sectional area may benefit more viscous inks, while a lower cross sectional area may be beneficial for lower viscosity inks. Printing systems can be adjusted to compensate for cross sectional area, such that known volumes are deposited based on the linear displacement. Additionally, these geometries may prevent or mitigate backflow of one ink into another lumen. To assist with joining or fusing different materials, two or more materials can be extruded simultaneously to allow some amount of mixing or fusion, as appropriate. By allowing on- the-fly material switching, a single process can print complex devices, such as robots (e.g., soft robots).

[0071] Additional embodiments possess multiple internal tubes in parallel. Such instances enable printing at multiple locations simultaneously and can include 2, 3, 4, 5, 6, or more internal tubes that are parallel within a rigid, outer tube. The individual internal tubes may be at equal angels from each other (e.g., radially symmetric)—such that 2 internal tubes may be 180° from each other, 3 internal tubes may be 120° from each other, 4 internal tubes may be 90° from each other, etc. Alternatively, each tube may beangled individually or independently to allow for additional geometries. Figure 4 illustrates an exemplary CTR-based system using three curved, internal tubes to allow printing at multiple locations simultaneously. The system of Figure 4 shows three internal tubes extending axially from the outer tube. To control the navigation, positioning, and / or deployment of the internal tube, the system includes a lead screw, a material inlet, a tube alignment mechanism, and a spur gear. One of ordinary skill in the art will appreciate the mechanical linkages or connections that would allow this movement and actuation.

[0072] The foregoing demonstration of parallel, internal tubes can be further extended to a “dendritic” system, where the foregoing parallel tubes can further include additional parallel internal tubes. As with the rigid outer tubes describe above, each internal tube may include 2, 3, 4, 5, 6, or more internal tubes. This embedding can occur for multiple layers of embedding. For example, 3 internal tubes, each with 3 internal tubes would produce a printhead with 9 nozzles for printing. Figures 5A-5B illustrate examples of these dendritic systems, where Figure 5A illustrates a 9 nozzle system, where the rigid outer tube includes 3 internal tubes, each with 3 internal tubes. Figure 5B illustrates an 8-nozzle system, where the rigid outer tube includes 2 internal tubes, each with 2 internal tubes, each of which have 2 more internal tubes. These systems possess one or more of the following: shaft alignment devices, linear rails, linear stages, lead screws, and stepper motors to control the movement, deployment, printing, etc. of the systems and printheads.

[0073] In some embodiments of dendritic systems, ink or printing materials are deposited from only the most distal nozzles. In some embodiments, the distal tip of each layer can also be used to print or deposit an ink. Figure 5C illustrates a schematic of a 2- layer, 2-tube system, which produces a total of 7 nozzles (e.g., 1 nozzle / lumen from the outermost tube, 2 lumens from the intermediate or first layer, and 4 lumens from the second layer tubes). Extending to a third layer, a total of 15 lumens / nozzles are possible. Extending to a 2 layer, 3 tube system produces a total of 9 Lumens / nozzles in the 2nd layer, 3 lumens / nozzles in the 1st layer, and 1 lumen / nozzle in the outermost. So a total of 13 lumens / nozzles are also possible. These foregoing descriptions of dendritic systems are merely exemplary and one of ordinary skill in the art will understand how to modify a dendritic system to include additional lumens or nozzles at additional layers.

[0074] In some instances one or more of the foregoing robots or robotic systems may incorporate a flexible or pliable outer tube. Such a tube may overlay a robot describe above, such as (but not limited to) a tendon-driven system, a push-pull type system, etc. In some instances, this flexible outer tube can form a conduit for printing. Such a conduit may be in addition to or instead of an internal conduit running through one or more of the systems described above. In some instances, using multiple lumens in this manner allows for concentric printing—e.g., printing one material inside of a second material. An exemplary and non-limiting application of concentric printing may be for printing a vasculature or other conduit within a print bed. In such instances, the desired material for the conduit may need support during curing or hardening. Thus, a sacrificial material may be printed internally to the wall material to provide the support. The sacrificial material may then be removed by melting, dissolving, or other applicable mechanism. As noted, this example is used solely for illustrative or demonstrative purposes, and additional possibilities for concentric printing exist. Additionally, such concentric printing is not limited to two materials and may be expanded to allow for 3 layers, 4 layers, 5 layers, or more. A person of ordinary skill in the art will understand how to modify such systems to increase the print layers within a concentric system.

[0075] As mentioned previously, continuum robots can be used for 3D printing. In such instances, one or more of the tubes described above can be used as a conduit for printing materials, including (but not limited to) polymeric, biologic, metallic, and / or any other form of material for constructing or building an object via 3D printing. These materials, or “inks,” can have different properties for different uses, including rigidity, resiliency, biocompatibility, absorbability, decomposability, and / or any other desirable property. Biologic inks may be used for medical purposes, including in vivo, in situ, and / or other forms of printing devices or tissues (e.g., vascular valves, skin grafts, tissue replacement, etc.) Such inks can include cells (e.g., endothelial, dermal, etc.), support materials (e.g., collagen) into a position.

[0076] Non-biological ink types include (but are not limited to) viscoelastic elastomeric, conductive, and fugitive ink types. Viscoelastic elastomeric inks can include (but are not limited to) Polydimethylsiloxane (PDMS) Inks, Polyurethane (PU) Inks, Elastomeric Silicone Inks, Hydrogel Inks, Acrylate-based Elastomeric Inks, Thermoplastic Elastomer(TPE) Inks, Natural Rubber-based Inks, Composite Elastomeric Inks, Gelatin-based Inks, and Polyethylene Glycol (PEG) Inks. Conductive ink types can include (but are not limited to) Graphene-Based Inks, Carbon Nanotube (CNT) Inks, Silver Nanoparticle Inks, Copper Nanoparticle Inks, Silver Flake or Flake-Based Inks, Conductive Polymer Composites, Metal-Based Inks, Conductive Carbon Grease, and certain Hybrid Inks. Fugitive inks can include sacrificial inks or inks that disappear under certain conditions or circumstances. Fugitive inks can include (but are not limited to) Polyvinyl alcohol (PVA), Sodium Alginate, Polycaprolactone (PCL), and High-Impact Polystyrene (HIPS).

[0077] Various materials may be cured or hardened using an external stimulus or signal, such as heat, electricity, radiation (e.g., ultraviolet), and / or any other stimulus that can be used to harden or cure the printed material. The source of the stimulus may be installed within a distal tip or tip cover and can be activated by a signal from a user or controlling software. Multi-Modal Printing

[0078] As noted above and illustrated by Figures 1A-1C, a CTR-based system of many embodiments can access difficult to reach and / or confined spaces. As the printhead extends from a single rigid tube, such embodiments allow for printing within a larger mold, such as an injection mold. Thus, certain embodiments are capable of manufacturing objects via multiple methods or modes. Injection molding is a traditional method of mass producing plastic products, where a molten material is injected into a defined mold, which is typically comprised of two or more parts. Once a part cures or hardens, the mold is separated into its component parts to release the created part.

[0079] Some embodiments are thus used to print components within an injection mold. Such embodiments can be used to print a skeleton, electronics, and / or any other component within an injection mold, which can assist with mass production of certain devices. Figure 6 illustrates an example embedded print within an injection mold. As illustrated, the mold has two parts (Side A and Side B), which form a spatial negative for an injection molded component. The molten material for the injection mold can be input through the molding material port. A keyhole can be used for a CTR nozzle to enter to print within the device, as described previously. When the printing process is completeand the injection molded component is cured or hardened, a mold can open to allow ejection of the completed object. Excess material from the injection mold can be mechanically removed and / or polished as appropriate.

[0080] As with any injection molded process or object, the injection molded component can be constructed of any appropriate material, including moldable, pliant, rigid, and / or flexible materials, including (but not limited to) thermoplastics, thermoset plastics, elastomers, composites, and bioplastics). Exemplary materials include (but are not limited to) Polyethylene (PE), Polypropylene (PP), Polyvinyl Chloride (PVC), Polystyrene (PS), Acrylonitrile Butadiene Styrene (ABS), Polycarbonate (PC), Polyethylene Terephthalate (PET), Nylon (Polyamide), Polyurethane (PU), Epoxy Resins, Phenolic Resins, Styrene- Butadiene Rubber (SBR), Ethylene Propylene Diene Monomer (EPDM), Silicone Rubber, Thermoplastic Elastomers (TPE), Glass-Fiber Reinforced Polymers (GRP), Carbon-Fiber Reinforced Polymers (CFRP), Polylactic Acid (PLA), and Starch-Based Plastics. 3D Bioprinting

[0081] Another possible print bed is directly into biological cavities. Such printing can occur via a transcatheter system, where the printhead / nozzle is placed into the cavity via a catheter, then printing occurs as described above. Such cavities can include chambers within the heart (e.g., left and right atria and ventricles), sinus cavities (e.g., maxillary, sphenoid, ethmoid, and / or frontal), nasal cavity, vasculature, within organs (e.g., stomach, bladder, etc.), and / or any other applicable body part. Printing within such areas can be permanent or temporary. Such uses can be to replace or repair anatomical structures (e.g., valves), remodel anatomical structures (e.g., to increase or decrease size), and / or any other purpose for which an in vitro printed device may be beneficial for medical intervention or treatment.

[0082] In embodiments used for in vivo printing, the rigid outer tube can form a catheter body. Such catheter bodies can include certain features to assist with navigation, insertion, placement, and / or any other convenience in use. Such features may include a lubricous covering or coating disposed on the catheter body (or outer tube) during positioning of the catheter. In some embodiments, a lubricous or low-friction sleeve / sheath covers the catheter body, while certain embodiments bond a coating ormaterial directly to the catheter body. The lubricous or low-friction sleeve / sheath or coating can be a hydrophilic material and / or a hydrogel.

[0083] Additional embodiments include a tip on the distal end of the catheter body, which can be manufactured of a soft and / or atraumatic material that can prevent damage to native tissue, including a vascular walls.

[0084] In further embodiments of catheters for bioprinting, the ink, the catheter, and / or tip can include a radiopaque material for visualization under fluoroscopy or radiography. In certain embodiments, the radiopaque material can be selected from one or more salts, compounds, or nanoparticles containing iodine, barium, tantalum, bismuth, or gold. In some embodiments, the radiopaque material is a tantalum powder. Printing Pipeline

[0085] Certain embodiments utilize a moving print bath to print objects, rather than utilizing a stationary bath. As embedded printing typically uses a viscoplastic support matrix, these properties may be utilized to move the bath along a pipeline with periodic keyholes for a CTR-based printhead as described herein. Moving print baths of various embodiments thus allow multiple objects to be printed simultaneously along the length of a pipeline. Figure 7A illustrates an exemplary setup 700 for a moving bath pipeline. Such systems include a conduit 702 to move a support matrix through the conduit. Within the conduit, an object 704 is printed. As the object 704 reaches various positions, one or more printheads 706 or nozzles can perform its portion of the print. In the illustrated example, the pipeline possesses multiple insertion ports, each to allow entry from a printhead 706. The different printheads 706 can be used to print different aspects of the object 704. While the foregoing describes these printing as different locations, it should be noted that the process may be continuous, rather than at defined positions, such that the gross construct may occur as the object passes through a first region, and the vascularization begins as the object passes into a second region, etc.

[0086] Additional embodiments may include a light sheet, light gate, scanner, or other device 708 to image or identify a position of an object 704. Such embodiments of a light sheet, light gate, or scanner 708 may be used for quality control, such that the methodmay identify if the completed object 704 is within tolerances. In some instances, the light gate or scanner 708 may be used to assess the flow of the support matrix 702.

[0087] Additionally, while Figure 7A illustrates three print heads 706 printing from an upper position within the system 700, various embodiments may include additional print heads 706 positioned axially around the conduit 702. Figure 7B illustrates an object 704 being printed at two positions, where each position includes six printheads 706 to simultaneously print a portion of object 704.

[0088] Additional and / or alternative embodiments can include a rotational pipeline section 710, such as illustrated in Figure 7C, which allows a single printhead to access multiple positions of an object without moving a printhead. Such rotational pipelines 710 can include two tubes that are concentrically aligned with bearings at each end. The inner tube may be sealed using any applicable valve, such as a circular duckbill valve, which allows access to a printhead (e.g., CTR). It should be noted that a person of ordinary skill in the art will understand that additional types of valves may be used for this sealing process. The tubes may be freely moved concentrically within each other to rotate the support matrix to allow access by a printhead through any desired angle, while not moving the printhead.

[0089] One challenge of such a print is the flow of the support matrix through the pipeline. Figure 8A illustrates flow types through a pipeline based on an idealized flow and practical flow types. Specifically, in an idealized situation, the entire column of the support matrix would move uniformly as a “plug” type flow. However, such plug type flow is unlikely, given the realities and physics of fluids, including viscosity and inertia. Newtonian fluids typically flow as illustrated, where the flow may be mostly laminar. While laminar flow provides a calm and stable media, the central portion of the fluid moves faster than outer flow. Such forces may tear and / or distort an object being printed. A viscoplastic material may create a boundary layer with turbulent flow (i.e., a yielded region). Under this regime, a central portion of the viscoplastic support material’s flow allows a plug flow type regime that may be suitable for printing without distortion.

[0090] The flow from the viscoplastic matrix allows for predictable shearing or movement of an object within the matrix. Such predictability allows for a system (e.g., system 700 of Figures 7A-7B) to include bends, merges, etc. Figures 8B and 8C illustrateembodiments that print three (Figure 8B) or four (Figure 8C) precursor components, which are then merged into a central line for joining or finishing a larger object. As such mergers require angles or bends within the conduit, the precursor components may be printed, such that they are in their desired form, once they have undergone any deformation from the bends. Cooperative Printing

[0091] Many embodiments of CTR-based printing devices allow for cooperative printing between multiple printheads operating in a print bed. The multiple printheads can enter the print bath from a single face or from multiple faces. For example, multiple printheads can collaboratively print an object from an upper surface, while other embodiments can use printheads approaching from different faces or angles. Such faces can be specific for differently shaped print beads, including prismatic shapes (e.g., rectangular prisms, pentagonal prisms, hexagonal prisms, heptagonal prisms, octagonal prisms, etc.). For a rectangular prism with one printhead per face, up to six printheads could be used. Figure 9 provides a photograph of an exemplary setup using six printheads to collaboratively print an object.

[0092] In some instances, a printhead entering from a bottom or vertical face may cause problems, where a viscoelastic support matrix could leak from a keyhole. To solve such a problem Certain embodiments are directed to and / or include an insertion port with multi-gate design (e.g., 2 gates, 3 gates, 4 gates, 5 gates, 6 gates, or more).

[0093] Turning to Figures 10A-10B, an example of a 2 gate design is illustrated. In this insertion port, a seal, such as (but not limited to) an O-ring, is used to prevent leakage while a tube reciprocates within a print bath. A secondary valve can be used to prevent leakage or backflow once a tube is removed from the print bed—in the present example, a duckbill valve is illustrated, however additional valve types may be used by one of ordinary skill in the art. The exemplary valves of Figures 10A-10B allow for up to four degrees of freedom, including rotational and reciprocating movements.

[0094] In certain embodiments, additional degrees of freedom may be beneficial for additional adjustment and / or printing geometries. Figure 11 provides an exploded view of an insertion port that allows for six degrees of freedom, including lateral and verticalmotion of a tube within the print bed. In such embodiments, a seal may be clamped to a rubber sheet, which prevents leakage while enabling the lateral and vertical motion of a tube. A second valve can be used to block backflow of the support matrix when the printhead or tube is removed. While Figure 11 illustrates the sue of a sleeve bearing for the seal and a rubber sheet for the valve, one of ordinary skill in the art will understand that that other components known in the art may fulfill these purposes. Systems for Embedded 3D Printing

[0095] Several embodiments implement a printhead or nozzle described herein into a system. In many instances, an actuating mechanism may be utilized to move a printing material, or ink, through the tubes. Additional embodiments can include one or more motors, gears, drive screws etc. to maneuver, actuate, and / or position a printhead in the proper location (e.g., to its radial, axial, and / or rotational position).

[0096] Such a multi-lumen system can be operated by a system for regulating and actuating which ink is being deposited. Figure 12 illustrates such an exemplary system, with individual syringes for each lumen. One or more pressure sources can be used to actuate the syringes, where the pressure source can be mechanical, pneumatic, hydraulic, and / or any other mechanism to apply a pressure. In certain instances, a solenoid valve or other type of valve can be used to regulate which syringe is being actuated. Motors, gears, and / or screws can be used to maneuver the printhead and / or nozzle.

[0097] Components (e.g., gears, motors, etc.) may be driven by a controller (e.g., microcontroller), computer, and / or other device. Such a controller / computer can include a processor and memory (e.g., volatile, non-volatile, read-only, random access, etc.). In many instances, the computer system may contain instructions to control printing, including the position, flow of the ink, which ink to print, etc. Path Planning

[0098] Additional embodiments are directed to methods (including computerized methods) to design path planning and printhead control. Such methods can identify and / or optimize paths for printing. Further instances can account for collaborative printing,such as collision avoidance. Various embodiments include instructions to change ink, flow, speed, and / or other parameters to assist in printing. Variable Shape Print Layer Generation

[0099] Turning to Figure 15, a process 1500 for path planning in accordance with many embodiments is illustrated. Specifically, process 1500 illustrates a method for variable shape print layer generation.

[0100] In many embodiments, the path planning process begins with obtaining a mesh file at 1502. A mesh file describes a 3D object. Common formats of mesh files include (but are not limited to) STL files, OBJ files, PLY files, 3MF files, STEP files, IGES files, Parasolid files, SolidWorks files, GLTF / GLB files, FBX files, and AMF files. Many embodiments use an STL file, which describes a raw, unstructured triangulated surface by the unit normal and vertices (ordered by the right-hand rule) of the triangles using a three-dimensional Cartesian coordinate system. Certain embodiments utilize a mesh file following cylindrical coordinates (e.g., using axial, radial, and rotational positions) as described herein and / or may convert a file in a Cartesian coordinate system to a cylindrical coordinate system.

[0101] At 1504, many embodiments generate boundary planes for each printer nozzle. As described above, systems can include multiple printer nozzles, including 1, 2, 3, 4, 5, 6, or more print nozzles. A boundary plane divides the 3D object described in the mesh file into subparts, where each subpart is printed by a unique printer nozzle. Such boundarylayers can be generated based on an origin and a normal (^⃗, ^^⃗ ) Boundary planegeneration can begin with defining the initial print volume (e.g., print bed). The print bed may be a regular shape (e.g., cube, rectangular prism, pyramidal, etc.) or may be an irregular shape, such as printing within an injection mold. As a non-limiting example, a print bath formed as a cube or other rectangular prism has six sides, thus such embodiments define six boundary planes to define the print volume. To prevent collisions between printer nozzles, two boundary planes can be defined for each printer nozzle pair. Figure 16A illustrates the equations used to define the boundary planes for a printer i, and a printer j. Figure 16B demonstrates a two dimensional (2D) representation of boundary planes between 2, 3, and 4 printers. Figures 16C-16E illustrate 3D versions ofboundary planes defined in accordance with 1504, where Figure 16C illustrates the six, initial boundary planes defining the print bed and print volume. Figure 16D illustrates a boundary layer defining the print volumes for a 2-printer nozzle system that bifurcates the six-sided print volume. As noted herein, some systems may provide a printer nozzle on each face of the print bead—e.g., for a six-sided bed, there can be six printer nozzles. Figure 16E illustrates the various boundary layers to define a print volume for single printer nozzle in a six-nozzle system.

[0102] Returning to Figure 15, as extruded ink or material possess a volume or thickness, a volumeless boundary plane can lead to too much material deposited at the interface between two printing nozzles. To compensate for the reality of 3D printing, boundary planes are shifted inwards (i.e., toward the print nozzle origin) based on printing scale at 1506. Figure 17 illustrates the equations and parameters that can be used to shift a boundary plane, in accordance with many embodiments.

[0103] At 1508 in Figure 15, many embodiments generate evenly distributed points on each boundary plane for each nozzle. On a per-nozzle basis, generating these points can include one or more of: a) bounding a printing plane with print volume boundary planes using plane-plane intersection conditions; b) generating minimum and maximum box vertices using line-line intersection conditions; c) generating 2D points within the boundary box; and d) transforming the points from a 2D plane into a 3D volume. The various equations or parameters used for the foregoing processes are provided in Figure 18, including plane-plane intersection, line-line intersection, and the printing point

[0104] At 1510 in Figure 15, further embodiments remove any points generated in where the plane boundary condition is violated. Figure 19 illustrates a parameter for defining a boundary condition.

[0105] Signed distance values for the remaining points are then computed to determine which points are inside the desired object at 1512. In many instances, this computation utilizes the equation illustrated in Figure 20. Any points that reside outside of the desired object may be removed at 1514.

[0106] In many embodiments, items 1502-1514 are repeated until an object is fully captured. Exemplary and non-limiting shells generated in accordance with process 1500 are illustrated in Figures 21A-21C, which illustrate a shell from a single print nozzle (Figure 21A), three print nozzles (Figure 21B), and six print nozzles (Figure 21C).

[0107] Once shells are generated a path can be planned according to various processes or methodologies. Spiral Path Planning Algorithm

[0108] Figure 22 provides an illustration of process 2200 for spiral path planning. In process 2200, candidate printing points for a shell can be generated at 2202. If these points are based on Cartesian coordinates, the Cartesian coordinates can be converted to cylindrical coordinates (e.g., as described herein) at 2204.

[0109] Once the points have been established in cylindrical coordinates, they can then be sorted at 2206. Sorting can includes shoring based on one or more of the cylindrical coordinates—e.g., height, radius, and angle. In some instances, the sorting is in ascending order. In certain instances, the sorting is in descending order. In some instances, one or more coordinates may be sorted in ascending order, while the remaining parameter(s) are sorted in descending order (or vice versa). The individual coordinates may be prioritized in a method that allows avoidance of conflict between a nozzle and a deposited material. In some instances, the parameters are sorted first by height, then radius, then angle.

[0110] At 2208 of many embodiments, a first point is identified in the set of points, where the first point is closest to the printer origin. At 2210 of some embodiments, this first point is added to a path and it and all points before it can be removed from the candidate list of points. The candidate list can then be resorted based on the smallest relative distance from the previous point at 2212. This next closest point can then be added to the path at 2214. This point-to-point process can then be iterated until all points in the candidate list have been checked.

[0111] Exemplary equations that can be used for the items of process 2200 are illustrated in Figure 23.TSP Path Planning Algorithm

[0112] Figure 24 provides an illustration of process 2400 for TSP path planning. In process 2400, candidate printing points for a shell can be generated at 2402. At 2404, various embodiments create a graph by connecting each point to all neighboring points within the chosen printing scale. Additional embodiments generate a set of subgraphs at 2406. Such subgraphs can be generated using one or more of the processes described above, including process 1500 of Figure 15 and / or process 2200 of Figure 22.

[0113] At 2408, various embodiments find an initial path using a depth first greedy algorithm. Using a depth first exploration, some embodiments search for any disconnected paths created by the depth first algorithm at 2410. Further embodiments attempt to merge disconnected paths with a main path at 2412. Items 2410 and 2412 can be repeated until all disconnected paths are merged into the main path and / or until a time limit is reached. The time limit can be a matter of time (e.g., days, hours, minutes, seconds, etc.) and / or a matter of processing cycles, iterations, and / or any other computational aspect.

[0114] Exemplary equations that can be used for the items of process 2400 are illustrated in Figure 25. Contour Following Path Planning Algorithm

[0115] Figure 26 provides an illustration of process 2600 for contour following path planning. In process 2600, many embodiments generate an evenly sampled cylindrical SDF slice from the mesh (e.g., the obtained mesh from 1502 of Figure 15). At 2604, many embodiments unwrap the slice into a 2D binary images. Once in a binary image, a contours filter may be applied to the binary image at 2606. In various embodiments, the contour filter is an Open-cv counter filter. Once the contour filter is applied to the binary image, the contours can be drawn on an empty image at 2308.

[0116] Once the contours are drawn, a path can be generated at 2610. The path generation of many embodiments can follow the following method for each contour: a) Start at top left most non-zero pixel and add this pixel to the path.b) Rotate the contour until the next adjacent non-zero pixel is found. In various instances, the contour is rotated clockwise (e.g., rightward), while in other instances, the contour is rotated counterclockwise (e.g., leftward). c) The pointer may be shifted to the found pixel, and it is added to the path. d) The previous non-zero pixel may be erased. e) Repeat b) through d) until all pixels in the contour have been checked. Once a path has been identified for a contour, items 2602 through 2610 may be repeated until no contours remain (i.e., all contours have been checked). Safety Radii

[0117] To prevent a collision or error caused by a collision between a printhead and printed material, some embodiments define a safety radius. Such a safety radius generates a safety margin to prevent collision between a printhead or CTR with printed materials. For example, the safety radius may be 1.5X, 2X, 3X, 4X the radius of the printhead—e.g., if a CTR printhead has an outer diameter of 0.1 mm, the safety radius could be set to 0.15 mm, 0.2 mm, 0.3 mm, 0.4 mm, etc. Within the safety radius, the printing dimensions may be converted into Z-axis printing.

[0118] If a point is located within a safety radius of the keyhole, the path may converted to a Z-axis type printing, rather than using the cylindrical coordinates and paths. Outside of the safety radius, the path and printing can follow the cylindrical coordinates and path. Additional Printing Devices

[0119] While the foregoing descriptions have focused on CTR-based systems, the concepts described are equally applicable to additional types of robots, including (but not limited to) concentric agonist / antagonist actuators, tendon-driven bending tubes, steerable need.es, soft growing robots, concentric precurved bellows, and / or any other long, slender continuum robot.

[0120] Furthermore, the examples of multi-modal printing, multi-nozzle printing, multi- ink printing, etc. are not mutually exclusive devices and may be combined in any combination (e.g., multi-modal with multi-nozzle, multi-ink with multi-nozzle, all printing modalities, etc.) and still be within the scope of this disclosure.For purposes of completeness, various aspects of the present disclosure are set out in the following numbered Aspects. Aspect 1. A device for embedded three dimensional printing, comprising: an outer tube; and an internal tube constructed of a flexible material disposed within the outer tube and forming a curve; wherein extension of the internal tube determines a radial position of a distal tip of the device, rotation of the inner tube and the outer tube determines a rotational position of the device, and a linear position of the inner tube and the outer tube determines an axial position of the device. Aspect 2. The device of Aspect 1, wherein the internal tube is constructed from a shape-memory metal. Aspect 3. The device of Aspect 1 or 2, wherein the internal tube is constructed from one or more of the alloys selected from: Nickel-Titanium (NiTi or Nitinol), Copper- Aluminum-Nickel (Cu-Al-Ni), Iron-Manganese-Silicon (Fe-Mn-Si), Copper-Zinc- Aluminum (Cu-Zn-Al), and Gold-Cadmium (Au-Cd). Aspect 4. The device of any one of Aspects 1-3, further comprising a second internal tube constructed of a flexible material disposed within the outer tube and forming a curve. Aspect 5. The device of Aspect 4, further comprising a third internal tube constructed of a flexible material disposed within the outer tube and forming a curve. Aspect 6. The device of Aspect 4 or 5, wherein each of the internal tubes comprise at least two additional internal tubes each constructed of a flexible material and each disposed within each of the internal tubes. Aspect 7. The device of Aspect 6, wherein each of the at least two additional internal tubes disposed with each of the internal tubes comprise at least two additional internal tubes each constructed of a flexible material and each disposed within each of the at least two additional internal tubes. Aspect 8. The device of Aspect 4, wherein the internal tube and the second internaltube each comprise two additional internal tubes, each of which comprise two additional internal tubes. Aspect 9. The device of Aspect 5, wherein the internal tube, the second internal tube, and the third internal tube each comprise three additional internal tubes. Aspect 10. The device of any one of Aspects 1-3, wherein the internal tube defines at least two lumens that coalesce at a tip. Aspect 11. The device of any one of Aspects 1-10, further comprising a radiopaque material embedded within one or more component. Aspect 12. The device of any one of Aspects 1-3, further comprising a second internal tube constructed of a flexible material disposed within the internal tube and forming a curve. Aspect 13. The device of Aspect 12, further comprising co-rotating bearings between the internal tube and the second internal tube to minimize torsional buildup between the internal tube and the second internal tube. Aspect 14. A system for embedded three dimensional printing, comprising: the device of any one of Aspects 1-13; and a print bed defined by a plurality of surfaces and containing a viscoelastic support matrix; wherein the device can be inserted into the viscoelastic support matrix to deposit one or more materials. Aspect 15. The system of Aspect 14, further comprising a second device of any one of Aspects 1-10, wherein the second device is positioned to be inserted into the viscoelastic support matrix at a different position and / or angle from the first device. Aspect 16. The system of Aspect 14 or 15, further comprising one or more of a motor, gear, and drive screw configured to move and / or position the device. Aspect 17. The system of any one of Aspects 14-16, wherein the print bed comprises an insertion port to allow printing and minimizing leakage of the viscoelastic support matrix. Aspect 18. The system of Aspect 17, wherein the insertion port comprises an O-ring and a duckbill valve. Aspect 19. The system of Aspect 17, wherein the insertion port comprises a sleevebearing clamped to a rubber sheet and a strip brush. Aspect 20. The system of any one of Aspects 14-19, wherein the print bed is defined by an injection mold, wherein the injection mold is comprised of at least two parts and defines a port for injection of the molded material and a key hole for insertion of the device. Aspect 21. The system of any one of Aspects 14-19, wherein the print bed is defined as a pipeline, such that the viscoelastic support matrix can move linearly through the print bed, and wherein the print bed defines multiple keyholes for insertion of the device. Aspect 22. A method of printing a vascular valve, comprising: accessing a vein or anatomical mimic; inserting a device of any one of Aspects 1-13 into the vein; and printing a valve within the vein using the device. Aspect 23. The method of Aspect 22, wherein printing comprises depositing fibroblast cellularized fibrinogen within the vein. Aspect 24. A method for printing a 3D structure, comprising: inserting a printing device into a print bed via a keyhole; and printing a structure within the print head using the device. Aspect 25. The method of Aspect 24, wherein a distal end of the device in manipulated in cylindrical coordinates. Aspect 26. The method of Aspect 24 or 25, wherein the cylindrical coordinates include radial, rotational, and axial coordinates. Aspect 27. The method of any one of Aspects 24-26, wherein the device is selected from a cylindrical tube robot or a push-pull type robot. Aspect 28. The method of any one of Aspects 24-27, wherein the device is a device selected from one or more of Aspects 1-13. Aspect 29. A device for embedded three dimensional printing, comprising: an external tube comprising a plurality of cuts made into the tube; and an internal tube comprising a plurality of cuts made into the tube; wherein pushing, pulling, and / or twisting one of the external or internal tube deforms the combination of the inner and outer tube into a particularconformation. Aspect 30. The device of Aspect 29, wherein one or both of the external tube and the internal tube is constructed from a shape-memory metal. Aspect 31. The device of Aspect 29 or 30, wherein one or both of the external tube and the internal tube is constructed from one or more of the alloys selected from: Nickel-Titanium (NiTi or Nitinol), Copper-Aluminum-Nickel (Cu-Al-Ni), Iron- Manganese-Silicon (Fe-Mn-Si), Copper-Zinc-Aluminum (Cu-Zn-Al), and Gold- Cadmium (Au-Cd). Aspect 32. The device of Aspect 29 or 30, wherein the one or both of the external tube and the internal tube is constructed from a fiber-reinforced plastic or a fiber- reinforced polymeric material. Aspect 33. The device of any one of Aspects 29-32, wherein the internal tube defines at least two lumens that coalesce at a tip. Aspect 34. The device of any one of Aspects 29-33, further comprising a radiopaque material embedded within one or more component. Aspect 35. A method for path planning to print a three dimensional (3D) object, the method comprising: obtaining a mesh file, wherein the mesh file describes a 3D object; generating a boundary plane dividing the 3D object into at least two subparts, wherein each subpart is printed by a unique printer nozzle; generating evenly distributed points on each boundary plane for each unique printer nozzle to create a shell for each unique printer nozzle; planning a path based on points within the shell for each unique printer. Aspect 36. The method of Aspect 35, wherein the mesh file describes a raw, unstructured triangulated surface by the unit normal and vertices. Aspect 37. The method of Aspect 35 or 36, wherein the mesh file is selected from an STL file, an OBJ file, a PLY file, a 3MF file, a STEP file, an IGES file, a Parasolid file, a SolidWorks file, a GLTF / GLB file, an FBX file, and an AMF file. Aspect 38. The method of any one of Aspects 35-37, wherein generating a boundary plane utilizes the equation:. Aspect 39. The method of any one of Aspects 35-38, wherein the method further comprises shifting the boundary plane to compensate for material deposited at the interface between two printing nozzles. Aspect 40. The method of Aspect 39, wherein shifting the boundary plane utilizes the equation: . Aspect 41. The method of any one of Aspects 35-40, wherein generating evenly distributed points comprises: a) bounding a printing plane with print volume boundary planes using plane-plane intersection conditions; b) generating minimum and maximum box vertices using line-line intersection conditions; c) generating 2D points within the boundary box; and d) transforming the points from a 2D plane into a 3D volume. Aspect 42. The method of any one of Aspects 35-41, wherein the method further comprises: removing points generated in where the plane boundary condition is violated. Aspect 43. The method of Aspect 43, wherein the method further comprises: computing signed distance values for remaining points to determine which points are inside the 3D object. Aspect 44. The method of any one of Aspects 35-43, wherein planning a path comprises: defining cylindrical coordinates for each point within the 3D object; and sorting the cylindrical coordinates Aspect 45. The method of Aspect 44, wherein planning a path further comprises:identifying a first point to the path; re-sorting the remaining points; and adding a second point to the path. Aspect 46. The method of any one of Aspects 35-43, wherein planning a path comprises: creating a graph by connecting each point to all neighboring points; and identifying the path based on the created graph. Aspect 47. The method of Aspect 46, wherein planning a path further comprises: identifying a disconnected path; and merging the disconnected path into the path. Aspect 48. The method of any one of Aspects 35-43, wherein planning a path comprises: generating a cylindrical slice from the mesh, wherein the cylindrical slice is evenly sampled; unwrapping the cylindrical slice into a 2D binary image; contour filtering the binary image; drawing the contours to an empty image; and generating the path based on the contours. Aspect 49. The method of Aspect 48, wherein generating the path comprises: adding a non-zero pixel to the path; rotating the contour to find the next non-zero pixel is identified; and adding the next non-zero pixel to the path. Aspect 50. The method of any one of Aspects 35-49, wherein the method further comprises: defining a safety radius, wherein points within the safety radius are defined based on Z-axis printing and points outside of the safety radius are defined based on cylindrical coordinates. EXEMPLARY EMBODIMENTS

[0121] Although the following embodiments provide details on certain embodiments of the inventions, it should be understood that these are only exemplary in nature and are not intended to limit the scope of the invention.Example 1: Multi-Nozzle Printing

[0122] Multiple nozzles may be used to simultaneously print or deposit materials at multiple locations simultaneously. A tricuspid valve was printed using a three-nozzle device, where the three nozzles extend from the outer tube with equal spacing (i.e., radially symmetric)—such as the embodiment illustrated in Figure 4. Figure 13A shows an axial view of the tricuspid valve during its print. Additionally, with such devices, “outside-in” printing is possible, where outer structures can be printed prior to deposition of internal structures. The outside-in process differs from traditional 3D printing that uses a layer-by-layer deposition, which may not allow certain structures, such as the tricuspid valve illustrated in Figure 13A, where the valvular leaflets would be printed as loose or freestanding structures until the layers are joined.

[0123] Figures 13B and 13C illustrate printing of a heart valve via this outside-in method. Figure 13B illustrates how the outer sleeve or body were printed first. Figure 13C shows a subsequent time point, when the leaflets were printed. Example 2: Collaborative Printing

[0124] Multiple printheads can be used simultaneously to print a single object. In this example, a full-size human heart (Figure 27A) and a rabbit (Figure 27B) were printed using six printheads simultaneously. Figure 27A illustrates a 3D graph showing the sector printed by each printhead. Figure 27B illustrates the path planning of the printheads to print the rabbit. Example 3: Printing Pipeline

[0125] As described previously, a viscoplastic support matrix used in a pipeline system has predictable properties of shearing or distortion which may be accounted for in printing. Figure 28A illustrates an exemplary setup of a pipeline printing system as described herein. The object being printed is a “3D Benchy,” which is a common 3D-printed object. In this setup, five 3D Benchys are being printed at different positions and stages of completion. Figure 28B provides a closer view of the five 3D Benchys during printing,while Figure 28C illustrates a top-down view of the 3D Benchys showing the three- dimensionality of the 3D Benchys.

[0126] As noted previously, the shearing properties of a viscoplastic matrix are known and modellable. Figure 28D illustrates a pipeline system including a bend. In this example, a 3D Benchy was printed as time t=0 min. Figure 28D shows the 3D Benchy as it passes through an elbow bend at t=0.3 min, t=0.5 min, and t=0.7 min. As seen when the 3D Benchy has passed the elbow, the 3D Benchy was no longer distorted. This shows that the distortion is predictable in a moving support matrix, thus allowing for a system to occupy less, linear space by using bends or elbows while still having a complete and undistorted final product. Example 4: Dendritic Printing

[0127] Dendritic printing has the ability to print complex structures by using the individual nozzles at the ends of each tube. Figures 14A-14B illustrate exemplary structures generated from a 2-generation 3-tube printhead and a 3-generation 2-tube printhead—i.e., the embodiments illustrated in Figures 5A-5B respectively. The structure illustrated in Figure 14A was created by depositing the ink in the support matrix while the nozzles are all retracted, then as the layers are extended individually, then retracting the layers to return to a single nozzle. The structure illustrated in Figure 14B shows branched network structure made from the embodiment of Figure 5B and was printed in less than 1 second, showing the capacity of embodiments to rapidly generate connected and branched networks.

[0128] Additionally, Figures 29A-29D illustrate various structures produced by a single 3-generation 3-tube system. By manipulating one or more of the parameters (e.g., radial, rotational, and axial) of one or more of the generations, a single dendritic printer can created multiple patterns. These structures were each printed in less than 1 second, showing how such devices can be used for high-speed and / or high-throughput printing and production. Example 5: Embedded Bioprinting

[0129] In this example, gelatin was printed inside a mold of induced pluripotent stem cells (iPSCs) suspended in a matrix. This example shows the ability of embodiments to print inside of a mold (including injection molded objects) as well as being successful in biological applications. As shown in Figure 30A, the matrix includes compacted iPSC embryoid body slurry with a fibrinogen / thrombin scaffold, or can be a photocurable hydrogel laden with cells shown in cross-sectional view in Figure 30B. A dendritic printhead printed a network formed of gelatin microparticles within the scaffold. The matrix is then allowed to cure either through time for fibrinogen / thrombin or UV light for the photocurable hydrogel to create a scaffold The gelatin microparticles were then melted in an incubator, creating lumens for perfusion. Nutrients were perfused through the mold, and Figure 30B illustrates the viability of cells in proximity to the lumen at all levels of the print, through Live / Dead Staining (CaAM / EthD-1) stains, where green represents live cells and red pixels represent red cells. Example 6: Multi-Material Printing

[0130] Using a multi-material printing apparatus, such as illustrated in Figure 3 will be used to print a soft robot. Soft robots are generally manufactured using compliant materials, allowing for adaptability to the environment, safer human-robot interaction, and manipulation of fragile or irregular-shaped objects. In many instances, soft robots possess sensors embedded within their structure to allow for monitoring and control of a robot’s shape and / or location.

[0131] By printing within an injection mold and / or within a support matrix, a soft robot will be printed using multiple ink types, including one or more of viscoelastic elastomeric, conductive, and fugitive inks—specifically, silicones, conductive carbon grease, and Carbopol. Example 7: In Vivo Bio Printing

[0132] An artificial valve will be designed and printed into vasculature using a transcatheter system. A first implementation will utilize an artificial blood vessel constructed of silicone as a vascular mimic in which the artificial valve will be printed. The printed valve will include one or both of bicuspid and tricuspid valves, which can beassessed for efficacy within the mimic. The printing will use the Freeform Reversible Embedding of Suspended Hydrogels (FRESH) process. Thrombin will be embedded into the FRESH hydrogel to facilitate fibrin polymerization upon extrusion of fibroblast cellularized fibrinogen.

[0133] Efficacy of the valve will be assessed by suturing the valve into a Dacron tube and mimicking a physiologic environment using a bioreactor, where systole and diastole are represented by pulsatile flow through the valve using a piston pump and a viscoelastic impedance adapter.

[0134] In vivo analysis of a printed valve will use a porcine model, due to the similarities in anatomical size and cardiovascular characteristics between pigs and humans. Entry into a vein will be accomplished using the Seldinger technique to puncture and dilate a vein, with the iliac vein being a desirable position.

[0135] All the procedures will be performed under sterile conditions with general anesthesia, and antegrade and retrograde control phlebography will be performed before ligation of the femoral vein and closure of the skin. Moreover, antegrade and retrograde phlebography evaluations will be performed in the weeks after the surgical procedure to analyze valvular patency and functioning, as well as echocardiography measurement to analyze EOA and REG. After animal sacrifice, the bioprinted prostheses will be explanted and processed for examination of histology, in addition to evaluation of thrombus formation. DOCTRINE OF EQUIVALENTS

[0136] Having described several embodiments, it will be recognized by those skilled in the art that various modifications, alternative constructions, and equivalents may be used without departing from the spirit of the invention. Additionally, a number of well- known processes and elements have not been described in order to avoid unnecessarily obscuring the present invention. Accordingly, the above description should not be taken as limiting the scope of the invention.

[0137] Those skilled in the art will appreciate that the foregoing examples and descriptions of various preferred embodiments of the present invention are merely illustrative of the invention as a whole, and that variations in the components or steps ofthe present invention may be made within the spirit and scope of the invention. Accordingly, the present invention is not limited to the specific embodiments described herein, but, rather, is defined by the scope of the appended claims.

Claims

WHAT IS CLAIMED IS:

1. A device for embedded three dimensional printing, comprising: an outer tube; and an internal tube constructed of a flexible material disposed within the outer tube and forming a curve; wherein extension of the internal tube determines a radial position of a distal tip of the device, rotation of the inner tube and the outer tube determines a rotational position of the device, and a linear position of the inner tube and the outer tube determines an axial position of the device.

2. The device of claim 1, wherein the internal tube is constructed from a shape- memory metal.

3. The device of claim 1 or 2, wherein the internal tube is constructed from one or more of the alloys selected from: Nickel-Titanium (NiTi or Nitinol), Copper- Aluminum-Nickel (Cu-Al-Ni), Iron-Manganese-Silicon (Fe-Mn-Si), Copper-Zinc- Aluminum (Cu-Zn-Al), and Gold-Cadmium (Au-Cd).

4. The device of any one of claims 1-3, further comprising a second internal tube constructed of a flexible material disposed within the outer tube and forming a curve.

5. The device of claim 4, further comprising a third internal tube constructed of a flexible material disposed within the outer tube and forming a curve.

6. The device of claim 4 or 5, wherein each of the internal tubes comprise at least two additional internal tubes each constructed of a flexible material and each disposed within each of the internal tubes.

7. The device of claim 6, wherein each of the at least two additional internal tubes disposed with each of the internal tubes comprise at least two additional internal tubes each constructed of a flexible material and each disposed within each of the at least two additional internal tubes.

8. The device of claim 4, wherein the internal tube and the second internal tube each comprise two additional internal tubes, each of which comprise two additional internal tubes.

9. The device of claim 5, wherein the internal tube, the second internal tube, and the third internal tube each comprise three additional internal tubes.

10. The device of any one of claims 1-3, wherein the internal tube defines at least two lumens that coalesce at a tip.

11. The device of any one of claims 1-10, further comprising a radiopaque material embedded within one or more component.

12. The device of any one of claims 1-3, further comprising a second internal tube constructed of a flexible material disposed within the internal tube and forming a curve.

13. The device of claim 12, further comprising co-rotating bearings between the internal tube and the second internal tube to minimize torsional buildup between the internal tube and the second internal tube.

14. A system for embedded three dimensional printing, comprising: the device of any one of claims 1-13; and a print bed defined by a plurality of surfaces and containing a viscoplastic support matrix; wherein the device can be inserted into the viscoplastic support matrix todeposit one or more materials.

15. The system of claim 14, further comprising a second device of any one of claims 1-10, wherein the second device is positioned to be inserted into the viscoplastic support matrix at a different position and / or angle from the first device.

16. The system of claim 14 or 15, further comprising one or more of a motor, gear, and drive screw configured to move and / or position the device.

17. The system of any one of claims 14-16, wherein the print bed comprises an insertion port to allow printing and minimizing leakage of the viscoplastic support matrix.

18. The system of claim 17, wherein the insertion port comprises an O-ring and a duckbill valve.

19. The system of claim 17, wherein the insertion port comprises a sleeve bearing clamped to a rubber sheet and a strip brush.

20. The system of any one of claims 14-19, wherein the print bed is defined by an injection mold, wherein the injection mold is comprised of at least two parts and defines a port for injection of the molded material and a key hole for insertion of the device.

21. The system of any one of claims 14-19, wherein the print bed is defined as a pipeline, such that the viscoplastic support matrix can move linearly through the print bed, and wherein the print bed defines multiple keyholes for insertion of the device.

22. A method of printing a vascular valve, comprising: accessing a vein or anatomical mimic; inserting a device of any one of claims 1-13 into the vein; and printing a valve within the vein using the device.

23. The method of claim 22, wherein printing comprises depositing fibroblast cellularized fibrinogen within the vein.

24. A method for printing a 3D structure, comprising: inserting a printing device into a print bed via a keyhole; and printing a structure within the print head using the device.

25. The method of claim 24, wherein a distal end of the device in manipulated in cylindrical coordinates.

26. The method of claim 24 or 25, wherein the cylindrical coordinates include radial, rotational, and axial coordinates.

27. The method of any one of claims 24-26, wherein the device is selected from a cylindrical tube robot or a push-pull type robot.

28. The method of any one of claims 24-27, wherein the device is a device selected from one or more of claims 1-13.

29. A device for embedded three dimensional printing, comprising: an external tube comprising a plurality of cuts made into the tube; and an internal tube comprising a plurality of cuts made into the tube; wherein pushing, pulling, and / or twisting one of the external or internal tube deforms the combination of the inner and outer tube into a particular conformation.

30. The device of claim 29, wherein one or both of the external tube and the internal tube is constructed from a shape-memory metal.

31. The device of claim 29 or 30, wherein one or both of the external tube and the internal tube is constructed from one or more of the alloys selected from: Nickel- Titanium (NiTi or Nitinol), Copper-Aluminum-Nickel (Cu-Al-Ni), Iron-Manganese- Silicon (Fe-Mn-Si), Copper-Zinc-Aluminum (Cu-Zn-Al), Gold-Cadmium (Au-Cd), and a plastic or polymeric material.

32. The device of claim 29 or 30, wherein the one or both of the external tube and the internal tube is constructed from a fiber-reinforced plastic or a fiber-reinforced polymeric material.

33. The device of any one of claims 29-32, wherein the internal tube defines at least two lumens that coalesce at a tip.

34. The device of any one of claims 29-33, further comprising a radiopaque material embedded within one or more component.

35. A method for path planning to print a three dimensional (3D) object, the method comprising: obtaining a mesh file, wherein the mesh file describes a 3D object; generating a boundary plane dividing the 3D object into at least two subparts, wherein each subpart is printed by a unique printer nozzle; generating evenly distributed points on each boundary plane for each unique printer nozzle to create a shell for each unique printer nozzle; planning a path based on points within the shell for each unique printer.

36. The method of claim 35, wherein the mesh file describes a raw, unstructured triangulated surface by the unit normal and vertices.

37. The method of claim 35 or 36, wherein the mesh file is selected from an STL file, an OBJ file, a PLY file, a 3MF file, a STEP file, an IGES file, a Parasolid file, a SolidWorks file, a GLTF / GLB file, an FBX file, and an AMF file.

38. The method of any one of claims 35-37, wherein generating a boundary plane utilizes the equation: .

39. The method of any one of claims 35-38, wherein the method further comprises shifting the boundary plane to compensate for material deposited at the interface between two printing nozzles.

40. The method of claim 39, wherein shifting the boundary plane utilizes the equation: .

41. The method of any one of claims 35-40, wherein generating evenly distributed points comprises: a) bounding a printing plane with print volume boundary planes using plane-plane intersection conditions; b) generating minimum and maximum box vertices using line-line intersection conditions; c) generating 2D points within the boundary box; and d) transforming the points from a 2D plane into a 3D volume.

42. The method of any one of claims 35-41, wherein the method further comprises:removing points generated in where the plane boundary condition is violated.

43. The method of claim 43, wherein the method further comprises: computing signed distance values for remaining points to determine which points are inside the 3D object.

44. The method of any one of claims 35-43, wherein planning a path comprises: defining cylindrical coordinates for each point within the 3D object; and sorting the cylindrical coordinates 45. The method of claim 44, wherein planning a path further comprises: identifying a first point to the path; re-sorting the remaining points; and adding a second point to the path.

46. The method of any one of claims 35-43, wherein planning a path comprises: creating a graph by connecting each point to all neighboring points; and identifying the path based on the created graph.

47. The method of claim 46, wherein planning a path further comprises: identifying a disconnected path; and merging the disconnected path into the path.

48. The method of any one of claims 35-43, wherein planning a path comprises: generating a cylindrical slice from the mesh, wherein the cylindrical slice is evenly sampled; unwrapping the cylindrical slice into a 2D binary image; contour filtering the binary image; drawing the contours to an empty image; and generating the path based on the contours.

49. The method of claim 48, wherein generating the path comprises: adding a non-zero pixel to the path; rotating the contour to find the next non-zero pixel is identified; and adding the next non-zero pixel to the path.

50. The method of any one of claims 35-49, wherein the method further comprises: defining a safety radius, wherein points within the safety radius are defined based on Z- axis printing and points outside of the safety radius are defined based on cylindrical coordinates.

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