3D Printing of Objects with Continuous Spatial Paths by a Multi-Axis Robotic FFF Platform

applied sciences

Article 3D Printing of Objects with Continuous Spatial Paths by a Multi-Axis Robotic FFF Platform

Yuan Yao 1,2,* , Yichi Zhang 1, Mohamed Aburaia 3 and Maximilian Lackner 3

1 Engineering Training Center, Shanghai University, 99 Road Shanda, Shanghai 200444, China; [email protected] 2 Shanghai Key Laboratory of Intelligent Manufacturing and Robotics, Shanghai University, 99 Road Shanda, Shanghai 200444, China 3 Department Industrial Engineering, University of Applied Sciences Technikum Wien, Höchstädtplatz 6, 1200 Vienna, Austria; [email protected] (M.A.); [email protected] (M.L.) * Correspondence: [email protected]; Tel.: +86-189-6407-3365

Abstract: Conventional Fused Filament Fabrication (FFF) equipment can only deposit materials in a single direction, limiting the strength of printed products. Robotic 3D printing provides more degrees of freedom (DOF) to control the material deposition and has become a trend in additive manufacturing. However, there is little discussion on the strength effect of multi-DOF printing. This paper presents an efﬁcient process framework for multi-axis 3D printing based on the robot to improve the strength. A multi-DOF continuous toolpath planning method is designed to promote the printed part’s strength and surface quality. We generate curve layers along the model surfaces and ﬁll Fermat spiral in the layers. The method makes it possible to take full advantage of the multi-axis robot arm to achieve smooth printing on surfaces with high curvature and avoid the staircase effect

and collision in the process. To further improve print quality, a control strategy is provided to synchronize the material extrusion and robot arm movement. Experiments show that the tensile

Citation: Yao, Y.; Zhang, Y.; Aburaia, strength increases by 22–167% compared with the conventional flat slicing method for curved-surface M.; Lackner, M. 3D Printing of parts. The surface quality is improved by eliminating the staircase effect. The continuous toolpath Objects with Continuous Spatial planning also supports continuous fiber-reinforced printing without a cutting device. Finally, we Paths by a Multi-Axis Robotic FFF compared with other multi-DOF printing, the application scenarios, and limitations are given. Platform. Appl. Sci. 2021, 11, 4825. https://doi.org/10.3390/app11114825 Keywords: additive manufacturing; multi-DOF 3D printing; spatial slicing; continuous fibers

Academic Editor: Francesco Colangelo 1. Introduction Received: 17 April 2021 Additive Manufacturing (AM), also known as 3D printing, has gained a lot of at- Accepted: 22 May 2021 Published: 24 May 2021 tention in recent years and has been applied in various ﬁelds such as rapid prototyping, bioengineering, and architecture [1]. Fused Deposition Modeling (FDM), or Fused Filament

Publisher’s Note: MDPI stays neutral Fabrication (FFF), is the most popular process for 3D printing. Standard FDM equipment with regard to jurisdictional claims in usually has three degrees of freedom. The nozzle of the equipment travels along the X/Y/Z published maps and institutional affil- axis and deposits the material in the spatial Cartesian coordinate system. Based on this iations. platform feature, most 3D printing toolpath planning methods can be divided into specific steps: (1) obtain a digital model of the printed part, (2) slice the model equidistant using a set of parallel planes, and (3) perform toolpath planning and generate print toolpaths in each layer section. This method is easy to implement but has potential problems, such as introducing manufacturing constraints and staircase effect on the surface. During manufac- Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. turing, the FDM printer can deposit material only layer by layer, which results in significant This article is an open access article anisotropy. The tensile strength in the build direction (vertical) is about 40% lower than distributed under the terms and that in layer direction (horizontal) [2]. Simultaneously, the sloping surface of printed parts conditions of the Creative Commons will suffer from the staircase effect because of layering, which affects the surface quality Attribution (CC BY) license (https:// and leads to stress concentration. These problems weaken the strength of the FDM product creativecommons.org/licenses/by/ and limit its application scenarios, and prompted the researchers to conduct extensive 4.0/). exploratory work.

Appl. Sci. 2021, 11, 4825. https://doi.org/10.3390/app11114825 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 4825 2 of 15

At present, the mainstream idea is to increase the DOF of the 3D printing system and add more flexibility to the manufacturing process to make up for the FDM deficiency. The conventional method is to add more DOF, which inevitably increases the complexity and cost of existing systems. With the continuous development of robotics, more and more multi-DOF platforms based on robotic arms are applied to 3D printing, making it an interdisciplinary subject in advanced manufacturing [3]. Compared with traditional printing equipment, robot arms are more flexible, have a broader printing range, and a more mature controlling system. However, the toolpath planning method of multi-DOF 3D printing is more complex and less developed [4]. Most of the research on multi-DOF printing aimed to reduce or eliminate the support. There are few work studies on toolpath planning and the fabrication strategy to print parts with complex geometry and corresponding mechanical properties. Because the deposition direction of multi-DOF is different from the traditional 3D printing that deposits in a set of parallel planes, it is necessary to analyze the mechanical properties of the multi-DOF printed parts. In terms of control, there is no set of general control languages for multi-DOF printing. Different platforms usually use different scripting languages to control the hardware, increasing the difficulty of software development. This paper presents a global spatial continuous toolpath planning method and the controlling strategy for the multi-DOF robotic 3D printing platform. The rest of this paper is organized as follows. Section2 reviews the existing multi-DOF 3D Printing systems and corresponding toolpath planning methods. The details of the multi-DOF 3D printing pipeline are presented in Section3. We report the experimental results in Section4 . Section5 gives the conclusion and future works.

2. Related Work 2.1. Multi-DOF 3D Printing Researchers have two main approaches to achieving multi-DOF printing: extending the DOF of a traditional 3D printer or using a multi-axis robotic arm as a platform. The hardware platforms of the above two methods are different. However, their essence is to introduce more DOF to extend the printing process from parallel planes to spatial trajectories. Some research efforts are aimed at adding more freedom to traditional FDM printers. Lee et al. [5] developed a hybrid 3D printing system by adding two axes to the gantry milling machine platform. Their hybrid system can mill the part’s surface after printing to achieve higher finish quality. However, the system can only print the simple shapes on parallel planes in multiple directions, and the effect of the process on mechanical properties is not discussed in detail. Wu et al. [6] proposed a multi-DOF 3D printing system assisted by visual surveillance. Moreover, the system added two more axes of rotation to the platform to increase the printing freedom. The platform can print more complex models without any support, but it is still based on multi-directional flat plane printing. Traditional FDM printing equipment is more suitable for printing on flat surfaces but has difficulty in multi-axis cooperating. Multi-DOF printing needs the precise coordination of multiple axes, which is difficult to control and guarantee accuracy. At the same time, the complicated mechanical structure further reduces the printing space. More research works are devoted to building a robotic arm-based 3D printing platform. Keating et al. [7] conducted a preliminary case study on the 3D printing of the robotic arm. Their platform is based on a six-axis robotic arm fitted with different end effectors for additive manufacturing, milling, and sculpture. Yuan et al. [8] took inspiration from the spider web structure and customized a four-extruder printing nozzle on the robot arm platform. The nozzle can print a self-supporting frame structure in the space. The structure is more decorative than practical. Ding et al. [9] developed a metal 3D printing system that coupled a six-axis robotic arm with a two-axis tilt and rotation positioning system. The 8- DOF system can print metal structures such as propellers without support by collaboration. Dai et al. [10] proposed a method to deposit material on curved layers using a multi-axis Appl. Sci. 2021, 11, 4825 3 of 15

printing system based on a robot arm, significantly reducing the need for support structures and avoid collisions. In order to enhance the strength of the printed parts, De et al. [11] used a robotic printing platform to print continuous carbon fiber on multiple axes. However, the platform had a sophisticated end-effector to achieve multi-material extrusion. Their experiment result shows that the strength of the carbon fiber reinforced parts is about six times higher than that of the non-reinforced parts, but the specific test model and method are not given. Most of the relevant work focuses on support-free printing methods, but there is little research on evaluating the strength of multi-DOF printing.

2.2. Toolpath Planning More studies have been done on the toolpath planning strategies for different goals in recent years. According to the implementation method, toolpath planning methods of multi-degree-of-freedom FFF can be divided into three categories: (1) Toolpath planning of frame structure: the frame structure includes some supporting beams. Mueller et al. [12] developed the WirePrint printing system to shorten the printing time. Compared with the solid printing model, the frame structure’s processing speed is more than ten times higher than the traditional FFF printing speed. To make full use of multi-axis printing characteristics, Wu et al. [13] proposed a method for printing frame models on a five-axis printer. They used a graph structure to describe the collision problem, found a locally minimal constraint set outside the grid through global optimization, and then ordered the edge wireframes to avoid interference. Huang et al. [14] proposed a new algorithm for generating print sequences. Firstly, a sparse optimization model was constructed according to constraints, and the input shapes were decomposed into stable layers. Then, feasible print sequences were searched for each layer through local optimization methods and strategies to avoid collisions between the printed area and the manufacturing mechanism. Dorfler et al. [15] developed Mesh-Mould for large-scale building structures with higher load-bearing requirements, which collaboratively works on the building site in a distributed way and can be extended to different project scales through parallelization. Frame printing has a wide range of potential applications such as art, sculpture, architecture, and geometric manufacturing. Considering the need to use the inverse kinematics of robotic arm structure to solve the different motor rotation, to make the tool side positioning to the target position, may have a singular point in some position. Compared with conventional 3D printing, the frame model does not need intensive positioning and fill-in space, simplifying the control difficulty of multi-axis equipment. (2) Curved surface toolpath planning: The toolpath on the curved surface directly uses the ability of multi-axis printing equipment to extend the existing plane toolpath planning to the spatial surface to reduce the ladder effect and improve the surface quality. In the work of Chakraborty et al. [16] in 2007, surface layering was the first attempt to generate surface structures of equal thickness. Yerazunis et al. [17] designed a five-axis FFF platform to print a disc-like structure with protrusion. Due to the printing toolpath’s alignment with the compressive stress tensor, the compressive strength was increased to 4.5 times that of conventional printing. Singamneni et al. [18] further investigated the effect of curved layers on structural strength. However, the toolpath planning methods designed in these works are only applicable to specific simple models. To further use the advantages of multi-axis 3D printing, an extensible toolpath generation algorithm needs to be designed according to the requirements. Some typical methods include combining plane and curved layers near the outer shell [19], introducing the anti-aliasing method in graphics to slightly adjust the change of material extrusion volume to compensate for the surface ladder effect [20], and the curve interpolation method for the bending pipe structure [21]. Etienne and Panozzo et al. [22] deformed the input model into a flat top model in the voxel domain, generated the plane slices and toolpaths in the conventional method, and then mapped the toolpath to the input parameter domain. Thus, after limiting the deformation range, a generally curved toolpath can be obtained, supporting curved Appl. Sci. 2021, 11, 4825 4 of 15 Appl. Sci. 2021, 11, 4825 4 of 15

deformation range, a generally curved toolpath can be obtained, supporting curved sur- surfacesfaces printed printed on on a three-axis a three-axis printer. printer. This This kind kind of ofcurved curved toolpath toolpath planning planning method method can canavoid avoid the the ladder ladder effect, effect, but but the the effect effect on on anisotropy anisotropy and strength andand itsits application application to to multi-axismulti-axis equipment equipment are are not not discussed. discussed. (3)(3) Spatial Spatial field field drivingdriving toolpath planning: planning: spatial spatial planning planning can can accurately accurately control control the thelocation location and and direction direction of ofmaterial material deposition deposition according according to tothe the stress stress field field and and processing process- ingconstraints constraints and and make make full full use use of the of thecapabili capabilityty of multi-axis of multi-axis equipment equipment to provide to provide cus- customizedtomized design design and and manufacturing. manufacturing. Dai Daiand and Liu Liuet al. et [10], al. [ 10aiming], aiming at unsupported at unsupported print- printing,ing, proposed proposed a voxel-based a voxel-based surface surface generation generation method method to generate to generate the current the current print print layer layeraccording according to the to thesupportable supportable conditions conditions and and non-collision non-collision requirements. requirements. However, However, the thepositioning positioning in voxel in voxel space space can easily can easily cause cause errors. errors. Although Although this method this method cuts the cutslocations the locationsbeyond the beyond range the through range throughBoolean Booleanoperation, operation, the surface the quality surface still quality cannot still reach cannot the reachlevel theof ordinary level of ordinaryFFF parts. FFF Steuben parts. et Steuben al. [23] etproposed al. [23] proposedan implicit an toolpath implicit calculation toolpath calculationalgorithm algorithmbased on arbitrary based on heuristics arbitrary or heuristics level sets or in level the physical sets in the domain, physical introducing domain, introducingexternal constraints external constraintssuch as stresses such aswhen stresses generating when generating planar toolpaths. planar toolpaths.Fang and Zhang Fang andet al. Zhang [24] saved et al. [the24] finite saved element the finite analysis element results analysis in a results tetrahedral in a tetrahedral grid. They grid.generated They a generated a spatial print toolpath aligned with the principal stress direction through stress spatial print toolpath aligned with the principal stress direction through stress field con- field constraints and machining direction constraints. Experiments show that polymer straints and machining direction constraints. Experiments show that polymer printed printed parts’ strength under specific stress conditions can be increased to 6.35 times that parts’ strength under specific stress conditions can be increased to 6.35 times that of the of the traditional process, but the processing speed is slow and the product has a rough traditional process, but the processing speed is slow and the product has a rough surface. surface.

3.3. Methodology Methodology 3.1.3.1. Overview Overview OurOur approach approach ﬁrst first generates generates a a multi-DOF multi-DOF continuous continuous toolpath toolpath on on curve curve layers layers to to optimizeoptimize the the material material deposit deposit direction direction and and improve improve print print quality, quality, then then coordinate coordinate the the robotrobot platform’s platform’s pose pose and and the the extrusion extrusion to to carry carry out out the the fabrication fabrication of of the the print print part. part. In In orderorder to to satisfy satisfy manufacturability manufacturability requirements, requirements, it it is is necessary necessary to to avoid avoid collisions collisions in in space, space, keepkeep the the accessibility accessibility of of the the processing processing surface, surface, guarantee guarantee the the supportability supportability of of the the printed printed model,model, and and synchronize synchronize the the material material extrusion extrusion deposited deposited toolpath. toolpath. The The overview overview of of our our multi-DOFmulti-DOF 3D 3D printing printing process process is is illustrated illustrated in in Figure Figure1. 1.

FigureFigure 1. 1.Process Process of of multi-axis multi-axis continuous continuous pathpath FFFFFF printing.printing. The input mesh model is fabricated afterafter path path planning planning and and platform platform printing. printing.

OnceOnce the the inputinput modelmodel andand the printing dire directionction are are given, given, we we generate generate supports supports for forthe the model model and and print print it with it with the regular the regular path on path the on 2D the plane. 2D plane.The input The model input is model voxelized is voxelizedand then and deformed then deformed into a flattened into a ﬂattened shape acco shaperding according to the toprinting the printing accessibility. accessibility. Then,

Appl.Appl. Sci. Sci.2021 2021, 11, 11, 4825, 4825 55 of of 15 15

Then,applying applying path pathplanning planning on the on flattened the ﬂattened model model and the and continuous the continuous curve curve toolpath toolpath is gen- is generated.erated. The The hardware hardware platform platform consists consists of of a arobotic robotic arm arm with with a control boxbox andand anan FFF FFF extruderextruder with with an an embedded embedded controller. controller. The The former former is is usually usually a a vendor-dependent vendor-dependent black black boxbox system, system, while while the the latter latter is is a a standard standard extrusion extrusion mechanism. mechanism.

3.1.1.3.1.1. Hardware Hardware Platform Platform TheThe hardware hardware system system consists consists of of a robotica robotic arm arm system, system, a customizeda customized extruder, extruder, a single a sin- extrusiongle extrusion control control board board and a printand a hotbed. print hotbed. The customized The customized extruder (Figureextruder2) mounted(Figure 2) onmounted the robot on armthe robot can printarm can ordinary print ordinary thermoplastic thermoplastic materials materials or continuous or continuous reinforced rein- ﬁbers.forced Since fibers. the Since robotic the arm robotic and thearm extruder and the areextruder independently are independently controlled, controlled, this hardware this setuphardware can support setup can different support types different of multi-DOF types of multi-DOF industrial robots.industrial The robots. former The is usually former ais vendor-dependentusually a vendor-dependent black box black system, box while system, the wh latterile the is a latter simple is extruder.a simple extruder. Therefore, There- the synchronizationfore, the synchronization control of control both determines of both determines print quality. print The quality. hotbed The is unnecessaryhotbed is unneces- since thesary robotic since armthe robotic can be arm recalibrated can be recalibrated on an arbitrary on an plane. arbitrary plane.

(a) (b) (c)

FigureFigure 2. 2.Customized Customized extruder.extruder. ((aa)) PrintingPrinting thermoplasticthermoplastic material,material, the the pinch pinch roller roller engages engages with with thethe motor. motor. ( b(b)) printing printing the the continuous continuous fiber, fiber, the the pinch pinch roller roller is is relaxed relaxed to to prevent prevent crushing crushing the the fiber. fiber. (c) Extrusion device that can be mounted on a robotic arm. (c) Extrusion device that can be mounted on a robotic arm. 3.1.2.3.1.2. Multi-Axis Multi-Axis Printing Printing Toolpath Toolpath Planning Planning EliminatingEliminating thethe staircasestaircase effect on on the the part’s part’s surface surface is is an an effective effective way way to toreduce reduce the thestress stress concentration concentration and and improve improve mechanical mechanical performance. performance. Our Our method method is to is deposit to deposit ther- thermoplasticmoplastic materials materials on ona set a setof curved of curved surfaces surfaces parallel parallel to tothe the object’s object’s surface surface depending depending on onthe the multi-axis multi-axis platform. platform. First, First, the original the original model model will be will deformed be deformed to be flatter. to be flatter.The triangu- The triangularlar surface surface whose angle whose is anglelower isthan lower the spec thanified the threshold specified thresholdis flattened is into flattened a horizontal into aplane. horizontal All deformation plane. All data deformation during this data proce duringss are thisstored process to restore are storedthe deformation to restore later. the deformationThen, the deformed later. Then, model the will deformed be sliced model into 2D will layers be sliced by a set into of 2D parallel layers planes, by a set and of a parallelcontinuous planes, toolpath and a continuousis generated toolpath from the is co generatednnected regions from the on connected each layer. regions There on are each two layer.main Thereadvantages are two to main generating advantages continuous to generating toolpaths: continuous avoid redundant toolpaths: movement avoid redundant and im- movementprove efficiency. and improve Second, efficiency. continuous Second, fiber-rei continuousnforced printing fiber-reinforced can be supported printing without can be supportedadding more without cutting adding devices. more We cutting can restore devices. the Weplanar can restoretoolpath the to planarspatial toolpathtoolpath toby spatialcached toolpath deformation by cached data. deformationConsidering that data. th Consideringe bottom face that may the not bottom be flat face after may defor- not bemation, flat after the deformation,support structure the supportneeds to structurebe generated needs and to printed be generated with different and printed materials. with different materials. 3.1.3. Process Controlling 3.1.3. Process Controlling Unlike traditional three-axis printing, the multi-axis printing mechanism based on Unlike traditional three-axis printing, the multi-axis printing mechanism based on the the robot arm is separate from the control of the hotbed and extruder. This scheme pro- robot arm is separate from the control of the hotbed and extruder. This scheme provides vides much convenience for extending the platform and the print size and increases the much convenience for extending the platform and the print size and increases the system’s system’s complexity. Process control requires an initial plane alignment so that printing complexity. Process control requires an initial plane alignment so that printing can start can start on any plane. Precise synchronization is also required between toolpath motion on any plane. Precise synchronization is also required between toolpath motion control, materialcontrol, extrusivematerial extrusive direction, direction, and material and extrusionmaterial extrusion speed control speed to control ensure to print ensure quality. print Processquality. control Process provides control synchronization provides synchronization strategies and strategies control algorithmsand control between algorithms robotic be- armtween motion robotic and arm material motion extrusion. and material extrusion.

Appl. Sci. 2021, 11, 4825 6 of 15 Appl. Sci. 2021, 11, 4825 6 of 15

3.2. Multi-Axis Toolpath Planning 3.2.3.2.1. Multi-Axis Curve Slicing Toolpath Planning 3.2.1. Curve Slicing When printing on a curved surface, the multi-axis robotic arm can adjust the direction Whenof the nozzle printing so on that a curved it remains surface, perpendicular the multi-axis to the robotic print arm surface can adjustto avoid the collisions. direction ofTo the generate nozzle the so curve that it plane, remains we perpendicular use TetWild [25] to theto convert print surface the STL to model avoid into collisions. a tetrahe- To generatedral mesh the and curve then plane, use the we method use TetWild provided [25] toby convert the CurviSlicer the STL model[22] to intodeform a tetrahedral the mesh. mesh and then use the method provided by the CurviSlicer [22] to deform the mesh. Considering the accessibility of the platform, we defined an appropriate flatten angle thresh- Considering the accessibility of the platform, we defined an appropriate flatten angle old to control the curve layer’s generation and avoid the collision. As shown in Figure 3, all threshold to control the curve layer’s generation and avoid the collision. As shown in the mesh surfaces within 45 degrees will be flattened, while the surface whose slope is Figure3, all the mesh surfaces within 45 degrees will be flattened, while the surface whose greater than 45 degrees is inclined as vertical as possible. This type of deformation is partic- slope is greater than 45 degrees is inclined as vertical as possible. This type of deformation ularly suitable for curved structures when equally thick. Each vertex’s deformation data on is particularly suitable for curved structures when equally thick. Each vertex’s deformation the tetrahedral mesh will be saved during the process. Next, parallel plane slicing and tool- data on the tetrahedral mesh will be saved during the process. Next, parallel plane slicing path planning is performed on the deformed model. Once the toolpath is generated, it can and toolpath planning is performed on the deformed model. Once the toolpath is generated, be restored to its original model form based on the previously deformation data. it can be restored to its original model form based on the previously deformation data.

FigureFigure 3. CurveCurve slice: slice: surfaces surfaces within within safe safe range range will will be flattened, be ﬂattened, then then apply apply slicing slicing and path and pathgen- generatingerating on the on thedeformed deformed model. model. Finally, Finally, rest restoreore the thetoolpath toolpath to its to itsoriginal original shape. shape.

3.2.2.3.2.2. Global ContinuousContinuous ToolpathToolpath PlanningPlanning WeWe can use use a a standard standard way way to tofinish finish toolpath toolpath planning planning on the on 2D the sliced 2D sliced planes. planes. How- However,ever, considering considering that thatthe robotic the robotic arm armmoves moves spatially spatially when when the theplanes planes restore restore it to it toits itsoriginal original shape, shape, redundant redundant movements movements must must be be avoided avoided as as much much as as possible to preventprevent collisionscollisions oror singularities.singularities. That will alsoalso reducereduce post-processingpost-processing workloadworkload whenwhen usingusing continuouscontinuous fiber-reinforcedfiber-reinforced compositescomposites asas printingprinting material.material. To achieveachieve thesethese goals,goals, wewe dividedivide thethe toolpathtoolpath planningplanning intointo twotwo steps:steps: (1)(1) spatialspatial printingprinting sequencesequence generationgeneration andand (2)(2) continuouscontinuous toolpathtoolpath planning.planning. After slicing, a series of plane layers L= (l , l , ···, ln) is generated. Each layer l After slicing, a series of plane layers L= (l1, 1l2, ···2 , ln) is generated. Each layer lk con-k consists of one or more simply connected regions rk,i. Then, we get a collection D = {rk,i} sists of one or more simply connected regions rk,i. Then, we get a collection D = {rk,i} that that includes all 2D simply connected regions layer by layer. Where i is the index of includes all 2D simply connected regions layer by layer. Where i is the index of the simply the simply connected region in each layer, k represents the layer index. To improve connected region in each layer, k represents the layer index. To improve printing effi- printing efficiency and simplify control, we need to ensure that the continuous fibers are ciency and simplify control, we need to ensure that the continuous fibers are not cut dur- not cut during printing. Therefore, unnecessary movement during printing needs to be ing printing. Therefore, unnecessary movement during printing needs to be avoided. Our avoided. Our strategy is to connect the adjacent simply connected region in the upper and strategy is to connect the adjacent simply connected region in the upper and lower layers and lower layers and then connect other simply connected regions according to the geometric then connect other simply connected regions according to the geometric interference relation- interference relationship between the extruder nozzle and the workpiece. The procedure is ship between the extruder nozzle and the workpiece. The procedure is given in Algorithm 1. given in Algorithm 1. The output of Algorithm 1 is R = {rk,i}, which contains a sorted sequence of connected

regions. The index of rk,i is the same as that in D. The algorithm contains two critical decision processes: NoInterfere and FindUpperRegion. The former is employed to check if the nozzle will collide with the printed part when printing rk,i. This process can be realized by calculating the closest distance between the contours in the same layer and comparing that with the nozzle’s preset parameters in the undeformed space. FindUpperRegion detects if it can be supported by a processed region rk−1,j in layer k − 1.

Appl. Sci. 2021, 11, 4825 7 of 15

Algorithm 1 Spatial printing sequence generation 1: Spatial Printing Sequence (D) 2: R ← ∅ 3: rk,i ← D.Get End () 4: while D is not empty do 5: R.Append (rk,i) 6: D.Remove Item (rk,i) 7: if Not Interfere (rk,i) then 8: rk,i ← D.Find Upper Region (rk+1,i) 9: if rj,k = ∅ then 10: rj,k ← D.Get End () 11: end if 12: else 13: rk,i ← D.Get End () 14: end if 15: end while 16: return r

A simply connected region is a toolpath-connected domain where one can continu- ously shrink any simple closed curve into a point while remaining in the region. This type of region can be divided by a set of convex polygons. Each convex polygon is capable of being filled with a single continuous toolpath. As mentioned above, many space-filling curves such as the Zigzag curve [26], Hilbert curve [27], and Fermat spiral [28] can be used to generate the continuous toolpath. The collection R generated by algorithm 1 consists of an ordered sequence of simply connected regions. Therefore, our continuous toolpath planning strategy can also be decomposed into two steps: (1) fill each rk,i in R with a continuous toolpath and (2) connect each continuous toolpath by order of R. Compared with the Zigzag and the Hilbert curve, the Fermat spiral-based 2D filling pattern presented by Zhao et al. [29] has the characteristics of definite starting and ending position and smooth transition. This pattern is more suitable for continuous fiber-reinforced printing without fiber cutting. We traverse the connected region queue R to close each connected region’s boundaries. Then, a continuous spiral is generated to fill each region with the minimum spanning tree method. To avoid the intersection of the spirals, principal component analysis and Curvature Scale Space feature are used to extract the smooth Appl. Sci. 2021, 11, 4825 8 of 15 region to connect the continuous spirals between convex polygons [28]. The corresponding spatial continuous toolpaths generated for different structures are illustrated in Figure4.

(a) (b) (c) (d) (e)

Figure 4. 4. DemonstrationDemonstration parts parts for for contin continuousuous toolpath toolpath planning. planning. ( (aa)) Two-branch. Two-branch. ( (bb)) Split Split up up and and down. down. ( (cc)) Multiple Multiple parts. parts. (d) Structure with holes. ( e) Curve structure.

TheThe models models in in Figure Figure 44 areare slicedsliced sparselysparsely toto showshow thethe connectionconnection betweenbetween differentdifferent partsparts of a model. The corresponding parametersparameters of of nozzle nozzle size size can can be be regulated regulated for for different differ- entprinting printing platforms platforms to to compute compute a machine-orienteda machine-oriented printing printing sequence. sequence. Then,Then, the global continuouscontinuous toolpath toolpath can can be be generated generated by by connecting connecting the the toolpath toolpath segments segments in the the order order of thethe sequence sequence provided provided by by Algorithm Algorithm 1. 1.

3.2.3. Printing with Support In multi-DOF printing, overhanging structures printed with curved slices need strong support. We find all the downward facets on the surface of the input model. Then, the facets are grouped and the corresponding boundary contours are extracted. The upper surface of the support and the hotbed form the initial printing surface of the printed part. To produce a high-quality contact surface, the material of support is different from that of the printed object. Soluble materials such as PVA and HIPS or other specialized support materials are ideal choices. When the hotbed is working, the printed object and support can be attached while being easy to separate after cooling. Once the support is printed, the upper surface of the support and the hotbed form the initial printing surface of the printed part.

3.3. Process Controlling Algorithm 3.3.1. Material Extrusion Synchronization Accurate coordination between the robot and the end-effector extruder is necessary to ensure the printing quality. Excessive extrusion can cause the printed parts to collide with the nozzle. Insufficient extrusion will reduce the strength of the printed parts, the material cannot be effectively deposited on the previous layer, or even lead to the failure of printing. Both two cases will affect the surface quality of the parts. The print toolpath contains extrusion information. According to the extrusion information, we divide the whole printing toolpath into two sub-paths: printing toolpath and empty travel. The empty travel does not contain the extrusion information, while the printing toolpath contains both the extrusion information and the nozzle movement path. By regulating the print toolpath’s speed and acceleration, the robotic arm will print at a constant speed during the printing toolpath to ensure a stable and accurate movement. Simultaneously, the extruder feeds printed material at a constant speed, providing a smooth extrusion. After completing a printing toolpath, the upper computer will determine whether the next subpath is the type of empty travel. The extruder will not receive the upper computer’s extrusion command during the empty travel and will remain in a paused state until it starts to print the next printing toolpath.

Appl. Sci. 2021, 11, 4825 8 of 15

3.2.3. Printing with Support In multi-DOF printing, overhanging structures printed with curved slices need strong support. We ﬁnd all the downward facets on the surface of the input model. Then, the facets are grouped and the corresponding boundary contours are extracted. The upper surface of the support and the hotbed form the initial printing surface of the printed part. To produce a high-quality contact surface, the material of support is different from that of the printed object. Soluble materials such as PVA and HIPS or other specialized support materials are ideal choices. When the hotbed is working, the printed object and support can be attached while being easy to separate after cooling. Once the support is printed, the upper surface of the support and the hotbed form the initial printing surface of the printed part.

3.3. Process Controlling Algorithm 3.3.1. Material Extrusion Synchronization Accurate coordination between the robot and the end-effector extruder is necessary to ensure the printing quality. Excessive extrusion can cause the printed parts to collide with the nozzle. Insufﬁcient extrusion will reduce the strength of the printed parts, the material cannot be effectively deposited on the previous layer, or even lead to the failure of printing. Both two cases will affect the surface quality of the parts. The print toolpath contains extrusion information. According to the extrusion information, we divide the whole printing toolpath into two sub-paths: printing toolpath and empty travel. The empty travel does not contain the extrusion information, while the printing toolpath contains both the extrusion information and the nozzle movement path. By regulating the print toolpath’s speed and acceleration, the robotic arm will print at a constant speed during the printing toolpath to ensure a stable and accurate movement. Simultaneously, the extruder feeds printed material at a constant speed, providing a smooth extrusion. After completing a printing toolpath, the upper computer will determine whether the next subpath is the type of empty travel. The extruder will not receive the upper computer’s extrusion command during the empty travel and will remain in a paused state until it starts to print the next printing toolpath.

3.3.2. End Effector Pose Controlling After the toolpath planning, we generated a set of paths. The points in each path contain only the position information in the global coordinate system but not the end effectors’ pose information. The end effectors’ pose needs to be planned through path points to avoid collision during printing. Each tool path consists of a list of sequential points pi(xi, yi, zi)i=0,1,...,m. To prevent the collision, the angle between the end effector’s nozzle and the print path should be within a safe range. Considering the accessibility of the platform, we constraint the nozzle’s orientation within a reasonable range in the global coordinate system at the same time. The Figure5 shows an example for nozzle pose controlling algorithm. The speciﬁc steps of the algorithm are as follows:

(1) For each point pi in the path, connect the next point pi+1 to form a line segment lpi pi+1 .

(2) Create a vertical plane Sv perpendicular to the hotbed and through the lpi pi+1 , using the Sv as a constraint. (3) The nozzle’s orient Ni at pi should be parallel to Sv and point to the negative direction of the z-axis.

(4) Ni also needs to be perpendicular to the lpi pi+1 . (5) Boundary condition: If the angle between Ni and the z-axis exceeds the safe range, Ni will be limited within the range. (6) Use cubic splines to smooth the Ni to ensure stable printing. (7) Append the Ni to corresponding pi and the integrated print toolpath is P = {pi(xi, yi, zi, Rxi, Ryi, Rzi)}i=0,1,...,m . Appl. Sci. 2021, 11, 4825 9 of 15

Each tool path consists of a list of sequential points ,,,,…,. To prevent the collision, the angle between the end effector’s nozzle and the print path should be within a safe range. Considering the accessibility of the platform, we constraint the nozzle’s orientation within a reasonable range in the global coordinate system at the same time. The Figure 5 shows an example for nozzle pose controlling algorithm. The specific steps of the algorithm are as follows:

(1) For each point in the path, connect the next point to form a line segment .

(2) Create a vertical plane perpendicular to the hotbed and through the , using the as a constraint. (3) The nozzle’s orient at should be parallel to and point to the negative direction of the z-axis.

(4) also needs to be perpendicular to the . (5) Boundary condition: If the angle between and the z-axis exceeds the safe range, will be limited within the range. Appl. Sci. 2021, 11, 4825 9 of 15 (6) Use cubic splines to smooth the to ensure stable printing. (7) Append the to corresponding and the integrated print toolpath is ,,,,,,,…, . AA unique unique pose pose vector vector corresponds corresponds to to every ever pointy point on on the the print print path. path. We We could could translate trans- thislate into this ainto motion a motion script script for the for robotic the robotic arm witharm Cartesianwith Cartesian path planning.path planning.

FigureFigure 5. 5.Nozzle Nozzle orientation orientation example example for for the the spatial spatial path. path.

4.4. Experiments Experiments and and Discussion Discussion AsAs shownshown in Figure 66,, our multi-DOF multi-DOF printing printing platform platform is isbased based on ona UR3 a UR3 robot. robot. UR3 UR3is a desktop is a desktop collaborative collaborative robot, robot, including including a robot a robot manipulator manipulator and a and control a control box. It box. has Itsix has rotating six rotating joints, joints,and the and repeat the positionin repeat positioningg accuracy accuracy is ±0.1 mm. is ± Peripheral0.1 mm. Peripheral equipment equipmentincludes an includes Arduino an Mega Arduino 2560 Mega board 2560 runni boardng runningMarlin firmware, Marlin ﬁrmware, a hotbed, a hotbed, and an and end aneffector end effector for printing. for printing. The end The effector end effectorsimilar to similar the standard to the standard3D printer 3D nozzle, printer mounting nozzle, mountingon the robot’s on the flange. robot’s The ﬂange. upper Thecomputer upper is computer a personal is computer a personal running computer Ubuntu running and UbuntuRobot Operating and Robot System Operating (ROS) System and translates (ROS) and th translatese print path the into print robot path script into robot and scriptgcode. andBy sending gcode. Bygcode sending through gcode the throughserial port the to serial the Arduino port to theboard, Arduino the upper board, computer the upper can computercontrol peripheral can control devices’ peripheral running devices’ state, running such as state, extrusion such length as extrusion and print length temperature. and print Appl. Sci. 2021, 11, 4825 temperature.Although different Although types different of robot types arms of use robot different arms use script different languages, script many languages, robot manymanu-10 of 15

robotfacturers manufacturers provide ROS provide interfaces, ROS interfaces,making our making algorithm our portable. algorithm portable.

FigureFigure 6. 6.Multi-DOF Multi-DOF FFF FFF printing printing platform platform for for multi-axis multi-axis continuous continuous path path printing. printing.

WeWe printed printed several several demonstration demonstration parts parts and and test test parts parts through through our our platform. platform. The The demonstrationdemonstration parts parts showed showed the the platform’s platform’s printing printing capability capability for for continuous continuous fibers, fibers, global global pathpath planning,planning, and spatial spatial curve curve path. path. Then, Then, we wecarried carried out the out tensile the tensile and flexural and flexural experi- experimentment on the on test the parts test to parts compare to compare the printing the path’s printing influence path’s on influence mechanical on mechanicalproperties. properties. 4.1. Model Printing We used continuous polyester fibers prepreg with PLA to print the parts shown in Figure 7 to verify the global continuous path planning method. The parts were printed at the temperature of 210 °C, 5 mm/s speed, and 0.3 mm layer thickness. These parameters refer to the experiment of Li et al. [30]. The length, width and height of the model are 35 mm, 17 mm, and 9 mm. Compared to the conventional path planning method in Figure 7a, our proposed method has less empty travel between layers and more convenient post-processing parts (Figure 7b).

(a) (b) Figure 7. Example for spatial printing sequence generation for continuous fibers. (a) Conventional printing sequence. (b) Scheduled printing sequence.

A curved part is printed on the support using the spatial Fermat spiral path (Figure 8). The length, width, and thickness of the part are 50 mm,10 mm, and 3 mm, respectively. Compared to the planar slicing method, this method significantly improves the printed parts’ surface quality, eliminates the staircase effect, and simplifies the continuous fiber parts’ printing path on the curved surface.

Figure 8. The printing process of the global continuous path.

Appl. Sci. 2021, 11, 4825 10 of 15 Appl. Sci. 2021, 11, 4825 10 of 15

Figure 6. Multi-DOF FFF printing platform for multi-axis continuous path printing. Figure 6. Multi-DOF FFF printing platform for multi-axis continuous path printing.

Appl. Sci. 2021, 11, 4825 WeWe printed printed several several demonstration demonstration parts parts an andd test test parts parts through through our our platform. platform.10 ofThe The 15 demonstrationdemonstration parts parts showed showed the the platform’s platform’s prin printingting capability capability for for continuous continuous fibers, fibers, global global pathpath planning, planning, and and spatial spatial curve curve path. path. Then, Then, we we carried carried out out the the tensile tensile and and flexural flexural experi- experi- ment on the test parts to compare the printing path’s influence on mechanical properties. ment4.1. Model on the Printing test parts to compare the printing path’s influence on mechanical properties. We used continuous polyester ﬁbers prepreg with PLA to print the parts shown in 4.1.4.1. Model Model Printing Printing Figure7 to verify the global continuous path planning method. The parts were printed at We used continuous polyester fibers prepreg with PLA to print the parts shown in Figure the temperatureWe used continuous of 210 ◦ C,polyester 5 mm/s fibers speed, prepreg and 0.3with mm PLA layer to print thickness. the parts These shown parameters in Figure 7 to verify the global continuous path planning method. The parts were printed at the temper- 7refer to verify to the the experiment global continuous of Li et path al. [planning30]. The method. length, The width parts and were height printed of the at the model temper- are ature of 210 °C, 5 mm/s speed, and 0.3 mm layer thickness. These parameters refer to the ex- ature35 mm, of 210 17 °C, mm, 5 mm/s and 9 speed, mm. and Compared 0.3 mm tolayer the thickness. conventional Thesepath parameters planning refer method to the ex- in periment of Li et al. [30]. The length, width and height of the model are 35 mm, 17 mm, and 9 perimentFigure7a, of our Li proposedet al. [30]. methodThe length, has width less empty and height travel of between the model layers are and35 mm, more 17 convenient mm, and 9 mm. Compared to the conventional path planning method in Figure 7a, our proposed method mm.post-processing Compared to parts the conventional (Figure7b). path planning method in Figure 7a, our proposed method hashas less less empty empty travel travel between between layers layers and and more more convenient convenient post-process post-processinging parts parts (Figure (Figure 7b). 7b).

(a) (b) (a) (b) Figure 7. Example for spatial printing sequence generation for continuous fibers. (a) Conventional Figure 7. ExampleExample for for spatial spatial printing printing sequence sequence generation generation for for continuous continuous fibers. ﬁbers. ( (aa)) Conventional Conventional printing sequence. (b) Scheduled printing sequence. printing sequence. ( b)) Scheduled Scheduled printing sequence.

AA curved curved part part isis is printedprinted printed onon on the the the support support support using using using the the the spatial spatial spatial Fermat Fermat Fermat spiral spiral spiral path path path(Figure (Figure (Figure8) . 8).The8). The The length, length, length, width, width, width, and and and thickness thickness thickness of of theof the the part pa part arert are are 50 50 50 mm, mm,10 mm,10 10 mm,mm, mm, and and 3 3mm, mm, mm, respectively. respectively. respectively. ComparedCompared to to the the planar planar slicing slicing method, method, this this method method significantlysignificantly significantly improves improves the the printed printed parts’parts’ surface surface quality, quality, eliminates eliminates the the staircasestaircas staircase e effect, effect, and and simplifiessimplifies simplifies the the continuous continuous fiberfiber fiber parts’parts’ printing printing path path on on the the curved curved surface. surface.

Figure 8. The printing process of the global continuous path. Figure 8. The printing process of the global continuous path.

As shown in Figure9, the test part contains an arch bridge structure in the middle. The

total length of the test parts is 75 mm, the width is 10 mm, and the thickness is 3 mm. This shape was chosen because standard test pieces usually have regular shapes that cannot accentuate multi-DOF printing advantages. Appl. Sci. 2021, 11, 4825 11 of 15 Appl. Sci. 2021, 11, 4825 11 of 15

As shown in Figure 9, the test part contains an arch bridge structure in the middle. As shown in Figure 9, the test part contains an arch bridge structure in the middle. The total length of the test parts is 75 mm, the width is 10 mm, and the thickness is 3 mm. Appl. Sci. 2021, 11, 4825 The total length of the test parts is 75 mm, the width is 10 mm, and the thickness is11 3 ofmm. 15 This shape was chosen because standard test pieces usually have regular shapes that can- This shape was chosen because standard test pieces usually have regular shapes that cannot accentuate multi-DOF printing advantages. not accentuate multi-DOF printing advantages.

Figure 9. Continuous fiber part printed using spatial Fermat spiral path on curve layer. FigureFigure 9.9. ContinuousContinuous fiberfiber partpart printedprinted usingusing spatialspatial FermatFermat spiralspiral pathpath on on curve curve layer. layer. The test parts for mechanical test were respectively sliced and printed using a multi- The test parts for mechanical test were respectively sliced and printed using a multi- DOFThe continuous test parts path for mechanicalwith Fermat test spiral were and respectively conventional sliced slicing and along printed the using X/Y/Z a multi-direc- DOF continuous path with Fermat spiral and conventional slicing along the X/Y/Z direc- DOFtion with continuous Zigzag pathinfill, with as shown Fermat in spiral Figure and 10. conventional We used our slicing multi-DOF along theprint X/Y/Z platform direc- to tiontion withwith ZigzagZigzag infill,infill, asas shownshown inin FigureFigure 10 10.. WeWe used used our our multi-DOF multi-DOF printprint platform platform toto print the continuous path test parts, while a general FFF printer printed the XYZ direction printprint thethe continuouscontinuous pathpath testtest parts,parts, whilewhile aa generalgeneral FFFFFF printerprinter printedprinted thethe XYZXYZ directiondirection sliced test parts. All test parts are printed by a 0.6 mm nozzle with polylactic acid (PLA) slicedsliced testtest parts.parts. AllAll testtest partsparts areare printedprinted byby aa 0.60.6 mmmm nozzlenozzle withwith polylacticpolylactic acidacid (PLA)(PLA) at 210 °C, 30 mm/s, 0.2 mm layer thickness, and 100% infill density. Figure 11 shows the atat 210210 ◦°C,C, 3030 mm/s,mm/s, 0.2 mm layer thickness, and 100%100% infillinfill density.density. FigureFigure 1111 shows shows thethe printed test parts. printedprinted testtest parts.parts.

Appl. Sci. 2021, 11, 4825 13 of 16

FigureFigure 10.10. SliceSlice typestypes ofof thethe testtest parts.parts. ((aa)) CurveCurve slicing.slicing. ((bb)) Z-direction.Z-direction. ((cc)) X-direction.X-direction. ((d)) Y-direction.Y-direction. Figure 10. Slice types of the test parts. (a) Curve slicing. (b) Z-direction. (c) X-direction. (d) Y-direction.

Figure 11. Printed test parts with PLA. FigureFigure 11.11. PrintedPrinted testtest partsparts withwith PLA.PLA. 4.2. Mechanical Test 4.2.4.2. MechanicalMechanical TestTest Tensile tests and flexural tests were designed to verify the printed part’s mechanical TensileTensile teststests andand ﬂexuralflexural teststests werewere designeddesigned toto verifyverify thethe printedprinted part’spart’s mechanicalmechanical propertiesFigure 11. Printed between test the parts different with PLA slice. types. We printed groups’ test parts for each of the propertiesproperties betweenbetween thethe differentdifferent sliceslice types.types. WeWeprinted printed groups’groups’ testtest partsparts forforeach eachof ofthe the slice types in the experiment and then obtained their average values. sliceslice typestypes inin thethe experimentexperiment andand thenthen obtainedobtained theirtheir averageaverage values.values. 4.2. MechanicalTable 1 and TestFigure 12 show the result of the tensile test. The distance between the two TableTable1 1and and Figure Figure 12 12 show show the the result result of of the the tensile tensile test. test. The The distance distance between between the the two two clampsTensile is 60mm, tests and and the flexural test speed tests is were 2 mm designed/min on tothe verify equipment the printed shows part in Figure’s mechanical 13. clampsclamps isis 6060mm, mm, and and the the test test speed speed is is 2 2 mm mm/min/min on on the the equipment equipment shows shows in inFigure Figure 13. 13 . properties between the different slice types. We printed groups’ test parts for each of the slice types in the experiment and then obtained their average values. Table 1 and Figure 12 show the result of the tensile test. The distance between the two clamps is 60mm, and the test speed is 2 mm/min on the equipment shows in Figure 13.

Table 1. Experiment data of tensile test.

Slice Type Max Load (N) Max Deformation (mm) Curve slicing 750.47 4.934 Z-direction 420.66 3.905 X-direction 614.61 4.594 Y-direction 280.89 2.552

(a) (b) Figure 12. Tensile test results of different slice types. (a) Maximum tensile load. (b) Force-deformation curve.

Appl. Sci. 2021, 11, 4825 12 of 15 Appl. Sci. 2021, 11Appl., 4825 Sci. 2021, 11, 4825 12 of 15 12 of 15

TableTable 1. 1.Experiment ExperimentTable data data 1. Experiment of of tensile tensile test. test. data of tensile test.

SliceSlice Type Type Slice Type Max Max Load (N)(N) Max Load (N) Max Max Deformation Deformation Max (mm) Deformation(mm) (mm) CurveCurve slicing slicing Curve slicing 750.47 750.47 750.47 4.934 4.934 4.934 Z-directionZ-direction Z-direction 420.66 420.66 420.66 3.905 3.905 3.905 X-directionX-direction X-direction 614.61 614.61 614.61 4.594 4.594 4.594 Y-direction 280.89 2.552 Y-direction Y-direction 280.89 280.89 2.552 2.552

(a) (a) (b) (b)

FigureFigure 12. 12.Tensile TensileFigure test test results 12.results Tensile of of different different test results slice slice types. of types. different (a) Maximum slice types. tensile load. (b) Force-deformation curve.(a) Maximum tensile(a) Maximum load. (b )tensile Force-deformation load. (b) Force-deformation curve. curve.

FigureFigure 13.13. TensileTensileFigure test.test. 13. ( aa)) TensileEquipment Equipment test. for( fora) Equipmenttensile tensile test test andfor and tensileflexural ﬂexural test test. test. and (b ()flexuralb Fractured) Fractured test. parts (b parts) Fractured in the in the parts in the tensiletensile test. test. tensile test. We used the three-point ﬂexural test to examine the test part’s maximum bending We used the three-pointWe used the flexural three-point test to flexural examine test the to testexamine part’s the maximum test part’s bending maximum bending Appl. Sci. 2021, 11, 4825load. The test speed is 2 mm/min, the span is 60 mm, and the result is shown in Table2 13 of 15 load. The testload. speed The is 2test mm/min, speed isthe 2 mm/min,span is 60 the mm, span and is the 60 resultmm, and is shown the result in Table is shown 2 in Table 2 and Figure 14. and Figure 14.and Figure 14.

Table 2. ExperimentTable data 2. Experiment of three-point data flexural of three-point test. flexural test.

Slice Type Slice Type Max Load (N) Max Load (N) Max Deflection Max (mm) Deflection (mm) Curve slicing Curve slicing 135.70 135.70 5.825 5.825 Z-direction Z-direction 119.70 119.70 6.103 6.103 X-direction X-direction 140.66 140.66 7.172 7.172 Y-direction Y-direction 102.27 102.27 5.215 5.215

(a) (b)

Figure 14. FlexuralFigure test 14. resultsFlexural of test different results sliceof different types. slice (a) Maximumtypes. ﬂexural load. (b) Force- deformation curve.(a) Maximum flexural load. (b) Force-deformation curve.

4.3. Result and Discussion The result shows that our method avoids the strength decrease caused by anisotropy.

In the tensile test, the result shows that the test part with the curve slicing path can withstand the maximum load compared to other ordinary slice types. The tensile strength of the curved sliced part is approximately 22% higher than X-direction and 167% higher than Y-direction. Parts printed in the Y and Z direction showed significant brittleness, while parts printed along curve layers showed plasticity and fractured due to bending. In the flexural test, the strength of curve slicing is second to the X direction. The result is probably due to insufficient extrusion on the surface where the parts and support contact, resulting in more pronounced stress concentration. There is little difference in the flexural strength values between different slice types, but the plasticity of parts is still obviously affected by the slice type. Compared to the work of Fang et al. [24], which aims to reinforce the strength of FFF, our method provides a similar result (maximum more 100% strength increase than traditional FFF) but with a higher surface resolution and a more feasible process. The surface quality of our method is satisfactory: all the layers are well aligned to the surface and has no staircase effect. Compared to the robotic printing of Dai et al. [10], our method has a smaller gap between toolpaths and eliminates the staircase on convex surfaces. Our method can be used for print parts with overhanging structures and require mechanical strength because it optimized the material deposit direction, making the toolpath along the part surface. Aerospace components, for example, usually have smooth surfaces and require high strength and lightweight, so our method can be utilized to fabricate such parts using continuous fibers. Moreover, our approach is portable and not limited to specific robot hardware or slicing software, providing a universal interface for construction. It is worth mentioning that our method does not avoid the need for support, as slice planning is based on the part surface rather than an unsupported strategy.

5. Conclusions Multi-DOF printing gets rid of the limitation of traditional FFF that deposits materials along a single direction. Unlike conventional FFF printing, we propose a multi-axis continuous toolpath planning method and a process control strategy for the robotic arm- based 3D printing platform, making it possible to take full advantage of the multi-axis printing platform’s advantages and improve the mechanical strength and surface quality of the printed part. Our method is based on open-source architecture and can be extended to a universal solution for multi-DOF printing. The most challenging task is to define an appropriate set of curve layers to slice the model. We flattened the model based on accessibility, then generated the toolpath with a continuous path and restored it to its original shape. The multi-axis FFF platform printed

Appl. Sci. 2021, 11, 4825 13 of 15

Table 2. Experiment data of three-point ﬂexural test.

Slice Type Max Load (N) Max Deﬂection (mm) Curve slicing 135.70 5.825 Z-direction 119.70 6.103 X-direction 140.66 7.172 Y-direction 102.27 5.215

4.3. Result and Discussion The result shows that our method avoids the strength decrease caused by anisotropy. In the tensile test, the result shows that the test part with the curve slicing path can withstand the maximum load compared to other ordinary slice types. The tensile strength of the curved sliced part is approximately 22% higher than X-direction and 167% higher than Y-direction. Parts printed in the Y and Z direction showed significant brittleness, while parts printed along curve layers showed plasticity and fractured due to bending. In the flexural test, the strength of curve slicing is second to the X direction. The result is probably due to insufficient extrusion on the surface where the parts and support contact, resulting in more pronounced stress concentration. There is little difference in the flexural strength values between different slice types, but the plasticity of parts is still obviously affected by the slice type. Compared to the work of Fang et al. [24], which aims to reinforce the strength of FFF, our method provides a similar result (maximum more 100% strength increase than traditional FFF) but with a higher surface resolution and a more feasible process. The surface quality of our method is satisfactory: all the layers are well aligned to the surface and has no staircase effect. Compared to the robotic printing of Dai et al. [10], our method has a smaller gap between toolpaths and eliminates the staircase on convex surfaces. Our method can be used for print parts with overhanging structures and require mechanical strength because it optimized the material deposit direction, making the toolpath along the part surface. Aerospace components, for example, usually have smooth surfaces and require high strength and lightweight, so our method can be utilized to fabricate such parts using continuous fibers. Moreover, our approach is portable and not limited to specific robot hardware or slicing software, providing a universal interface for construction. It is worth mentioning that our method does not avoid the need for support, as slice planning is based on the part surface rather than an unsupported strategy.

5. Conclusions Multi-DOF printing gets rid of the limitation of traditional FFF that deposits materials along a single direction. Unlike conventional FFF printing, we propose a multi-axis continuous toolpath planning method and a process control strategy for the robotic arm- based 3D printing platform, making it possible to take full advantage of the multi-axis printing platform’s advantages and improve the mechanical strength and surface quality of the printed part. Our method is based on open-source architecture and can be extended to a universal solution for multi-DOF printing. The most challenging task is to define an appropriate set of curve layers to slice the model. We flattened the model based on accessibility, then generated the toolpath with a continuous path and restored it to its original shape. The multi-axis FFF platform printed the demonstration parts and the test parts through our specially designed control architecture to verify our method. The experimental result is satisfying, showing that the continuous spatial toolpath can improve the tensile strength by 22–167% higher than that of the conventional slice type when the same printing material is used. Our method also allows the platform to print continuous reinforced fibers on the curve surfaces, further enhancing the part’s strength. In the meantime, layers generated by our method are parallel to the model’s surface, which effectively eliminates the staircase effect and improves the surface quality. Appl. Sci. 2021, 11, 4825 14 of 15

The major limitation of our approach is the generation of support when the model is complex. At present, we can not print the part with a hollow or cavity that needs internal support, as the support has to be printed entirely before the part. Another problem is that print quality is sensitive to the distance of support and the part’s initial layer. As shown in the experiment result, the improper distance may affect the deposition quality and strength. We may make further improvements to achieve more ﬂexible printing in the future.

Author Contributions: Y.Y. presented the conception and drafted the framework of the article. Y.Z. designed the platform, tested experiments, and the drafted article. M.A. and M.L. made the modification and critical revision of the paper. All authors have read and agreed to the published version of the manuscript. Funding: The Natural 3D: Bio-based fiber/particle reinforced thermoplastics efficiently used by additive manufacturing in the load path direction, grant number 860384, funded this research. Conflicts of Interest: The authors declare no conflict of interest.

References 1. Ngo, T.D.; Kashani, A.; Imbalzano, G.; Nguyen, K.T.Q.; Hui, D. Additive manufacturing (3D printing): A review of materials, methods, applications and challenges. Compos. Part B Eng. 2018, 143, 172–196. [CrossRef] 2. Kim, G.D.; Oh, Y.T. A benchmark study on rapid prototyping processes and machines: Quantitative comparisons of mechanical properties, accuracy, roughness, speed, and material cost. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 2008, 222, 201–215. [CrossRef] 3. Urhal, P.; Weightman, A.; Diver, C.; Bartolo, P. Robot assisted additive manufacturing: A review. Robot. Comput. Integr. Manuf. 2019, 59, 335–345. [CrossRef] 4. Chenming, W.; Chengkai, D.; Changling, W.; Yongjin, L. Recent Progress on Multi-DOFs 3D Printing: A Survey. Chin. J. Comput. 2019, 9, 1918–1938. 5. Lee, W.C.; Wei, C.C.; Chung, S.C. Development of a hybrid rapid prototyping system using low-cost fused deposition modeling and five-axis machining. J. Mater. Process. Technol. 2014, 214, 2366–2374. [CrossRef] 6. Wu, L.; Yu, M.; Gao, Y.; Yan, D.M. Multi-DOF 3D Printing with Visual Surveillance. In Proceedings of the SIGGRAPH Asia 2017, Bangkok, Thailand, 27–30 November 2017; pp. 3–4. [CrossRef] 7. Keating, S.; Oxman, N. Compound fabrication: A multi-functional robotic platform for digital design and fabrication. Robot. Comput. Integr. Manuf. 2013, 29, 439–448. [CrossRef] 8. Yuan, P.F.; Meng, H.; Yu, L.; Zhang, L. Robotic Fabrication in Architecture, Art and Design 2016. Robot. Multi-Dimens. Print. Based Struct. Perform. 2016.[CrossRef] 9. Ding, Y.; Dwivedi, R.; Kovacevic, R. Process planning for 8-axis robotized laser-based direct metal deposition system: A case on building revolved part. Robot. Comput. Integr. Manuf. 2017, 44, 67–76. [CrossRef] 10. Dai, C.; Wang, C.C.L.; Wu, C.; Lefebvre, S.; Fang, G.; Liu, Y.J. Support-free volume printing by multi-axis motion. ACM Trans. Graph. 2018, 37.[CrossRef] 11. de Backer, W.; van Tooren, M.J.L.; Bergs, A.P. Multi-axis multi-material fused filament fabrication with continuous fiber reinforcement. In Proceedings of the 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Kissimmee, FL, USA, 8–12 January 2018. [CrossRef] 12. Mueller, S.; Im, S.; Gurevich, S.; Teibrich, A.; Guimbretière, F.; Baudisch, P. WirePrint: Fast 3D Printed Previews. In Proceedings of the 27th Annual ACM Symposium on User Interface Software and Technology, Honolulu, HI, USA, 5–8 October 2014; pp. 273–280. 13. Wu, R.; Peng, H.; Guimbretière, F.; Marschner, S. Printing arbitrary meshes with a 5DOF wireframe printer. ACM Trans. Graph. 2016, 35, 1–9. [CrossRef] 14. Huang, Y.; Zhang, J.; Hu, X.; Song, G.; Liu, Z.; Yu, L.; Liu, L. FrameFab: Robotic Fabrication of Frame Shapes. ACM Trans. Graph. 2016, 35, 1–11. [CrossRef] 15. Dörfler, K.; Hack, N.; Sandy, T.; Giftthaler, M.; Lussi, M.; Walzer, A.N.; Buchli, J.; Gramazio, F.; Kohler, M. Mobile robotic fabrication beyond factory conditions: Case study Mesh Mould wall of the DFAB HOUSE. Constr. Robot. 2019, 3, 53–67. [CrossRef] 16. Chakraborty, D.; Aneesh Reddy, B.; Roy Choudhury, A. Extruder path generation for Curved Layer Fused Deposition Modeling. CAD Comput. Aided Des. 2008, 40, 235–243. [CrossRef] 17. Yerazunis, W.S.; Barnwell, J.C., III; Nikovski, D.N. Strengthening ABS, nylon, and polyester 3D printed parts by stress tensor aligned deposition paths and five-axis printing. In Proceedings of the Solid Freeform Fabrication Symposium, Austin, TX, USA, 8–10 August 2016. 18. Singamneni, S.; Roychoudhury, A.; Diegel, O.; Huang, B. Modeling and evaluation of curved layer fused deposition. J. Mater. Process. Technol. 2012, 212, 27–35. [CrossRef] 19. Ahlers, D.; Wasserfall, F.; Hendrich, N.; Zhang, J. 3D printing of nonplanar layers for smooth surface generation. IEEE Int. Conf. Autom. Sci. Eng. 2019, 2019, 1737–1743. [CrossRef] Appl. Sci. 2021, 11, 4825 15 of 15

20. Song, H.C.; Ray, N.; Sokolov, D.; Lefebvre, S. Anti-aliasing for fused filament deposition. CAD Comput. Aided Des. 2017, 89, 25–34. [CrossRef] 21. Ezair, B.; Fuhrmann, S.; Elber, G. Volumetric covering print-paths for additive manufacturing of 3D models. CAD Comput. Aided Des. 2018, 100, 1–13. [CrossRef] 22. Etienne, J.; Ray, N.; Panozzo, D.; Hornus, S.; Wang, C.C.L.; Martínez, J.; McMains, S.; Alexa, M.; Wyvill, B.; Lefebvre, S. Curvislicer: Slightly curved slicing for 3-axis printers. ACM Trans. Graph. 2019, 38.[CrossRef] 23. Steuben, J.C.; Iliopoulos, A.P.; Michopoulos, J.G. Implicit slicing for functionally tailored additive manufacturing. CAD Comput. Aided Des. 2016, 77, 107–119. [CrossRef] 24. Fang, G.; Zhang, T.; Zhong, S.; Chen, X.; Zhong, Z.; Wang, C.C.L. Reinforced FDM: Multi-axis filament alignment with controlled anisotropic strength. ACM Trans. Graph. 2020, 39.[CrossRef] 25. Hu, Y.; Zhou, Q.; Gao, X.; Jacobson, A.; Zorin, D.; Panozzo, D. Tetrahedral meshing in the wild. ACM Trans. Graph. 2018, 37. [CrossRef] 26. McMains, S.; Smith, J.; Wang, J.; Séquin, C. Layered Manufacturing of Thin-Walled Parts. In Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, Baltimore, MD, USA, 10–13 September 2000; pp. 379–387. 27. Griffiths, J.G. Toolpath based on Hilbert’s curve. Comput. Des. 1994, 26, 839–844. [CrossRef] 28. Sun, S.; Yao, Y.; Jiang, Y. A 3D Continuous Path Generation Method and Evaluation for Fused Deposition Manufacturing in Tissue Engineering. J. Biomater. Tissue Eng. 2019, 9, 273–282. [CrossRef] 29. Zhao, H.; Gu, F.; Huang, Q.-X.; Garcia, J.; Chen, Y.; Tu, C.; Benes, B.; Zhang, H.; Cohen-Or, D.; Chen, B. Connected Fermat Spirals for Layered Fabrication. ACM Trans. Graph. 2016, 35.[CrossRef] 30. Yao, Y.; Li, M.; Lackner, M.; Herfried, L. A continuous fiber-reinforced additive manufacturing processing based on PET fiber and PLA. Materials 2020, 13, 3044. [CrossRef]