Additive printing will be influential to automation in the architecture and construction industries in the upcoming decades. Despite reducing the labor efforts, material wastage, and production time, it ensures a safer work environment [1] . Direct-Ink-Writing (DIW) is an extrusion-based additive manufacturing technique that uses ready-to-print colloidal inks to construct the objects. DIW printers use an external force to extrude the ready-to-print ink through a nozzle onto the substrate in the pre-coded pattern [2] . This procedure occurs in a layer after layer until the whole object is constructed. Several research works have been conducted on different additive printing techniques using different construction materials to study the impacts of printing parameters such as speed, time, curing temperature, and proportion of chemical additives [3] [4] [5] [6] [7] [8] [9] . This study will be an addition to the existing research works to improve the additive printing techniques in the construction field.
As mentioned earlier, DIW uses a nozzle to extrude the ink, the geometry of the nozzle directly affects the geometry of the printed layer. For example, a cylindrical part that is printed with a circular nozzle has a round edge (see Fig.1a ) in each layer, whereas the same part when printed with a square or rectangular nozzle has a flat edge (see Fig.1b ). Since additive printing is a layer-after-layer approach, the geometry of each layer contributes to the overall surface finish of the printed constructs. As a result, it is essential to pre-determine the nozzle geometry to avoid the contour deviations that builds up through the layers.
The term "ready-to-print" denotes the fluidic properties such as viscosity, buildability, and yield stress, which are suitable for instantaneous printing. Previous research works [10] [11] [12] [13] [14] on construction materials suggest that the rheological behavior of the mixture plays a crucial role in printability and buildability.
Additive printing will be influential to automation in the architecture and construction industries in the upcoming decades. Despite reducing the labor efforts, material wastage, and production time, it ensures a safer work environment [1] . Direct-Ink-Writing (DIW) is an extrusion-based additive manufacturing technique that uses ready-to-print colloidal inks to construct the objects. DIW printers use an external force to extrude the ready-to-print ink through a nozzle onto the substrate in the pre-coded pattern [2] . This procedure occurs in a layer after layer until the whole object is constructed. Several research works have been conducted on different additive printing techniques using different construction materials to study the impacts of printing parameters such as speed, time, curing temperature, and proportion of chemical additives [3] [4] [5] [6] [7] [8] [9] . This study will be an addition to the existing research works to improve the additive printing techniques in the construction field.
As mentioned earlier, DIW uses a nozzle to extrude the ink, the geometry of the nozzle directly affects the geometry of the printed layer. For example, a cylindrical part that is printed with a circular nozzle has a round edge (see Fig.1a ) in each layer, whereas the same part when printed with a square or rectangular nozzle has a flat edge (see Fig.1b ). Since additive printing is a layer-after-layer approach, the geometry of each layer contributes to the overall surface finish of the printed constructs. As a result, it is essential to pre-determine the nozzle geometry to avoid the contour deviations that builds up through the layers.
The term "ready-to-print" denotes the fluidic properties such as viscosity, buildability, and yield stress, which are suitable for instantaneous printing. Previous research works [10] [11] [12] [13] [14] on construction materials suggest that the rheological behavior of the mixture plays a crucial role in printability and buildability. Research works also reported the necessity of printing parameters for 3D printing, how changing the printing parameters affects the buildability of the material [15] [16] [17] [18] [19] . Research work was conducted before getting a perfectly 
Additive printing will be influential to automation in the architecture and construction industries in the upcoming decades. Despite reducing the labor efforts, material wastage, and production time, it ensures a safer work environment [1] . Direct-Ink-Writing (DIW) is an extrusion-based additive manufacturing technique that uses ready-to-print colloidal inks to construct the objects. DIW printers use an external force to extrude the ready-to-print ink through a nozzle onto the substrate in the pre-coded pattern [2] . This procedure occurs in a layer after layer until the whole object is constructed. Several research works have been conducted on different additive printing techniques using different construction materials to study the impacts of printing parameters such as speed, time, curing temperature, and proportion of chemical additives [3] [4] [5] [6] [7] [8] [9] . This study will be an addition to the existing research works to improve the additive printing techniques in the construction field.
As mentioned earlier, DIW uses a nozzle to extrude the ink, the geometry of the nozzle directly affects the geometry of the printed layer. For example, a cylindrical part that is printed with a circular nozzle has a round edge (see Fig.1a ) in each layer, whereas the same part when printed with a square or rectangular nozzle has a flat edge (see Fig.1b ). Since additive printing is a layer-after-layer approach, the geometry of each layer contributes to the overall surface finish of the printed constructs. As a result, it is essential to pre-determine the nozzle geometry to avoid the contour deviations that builds up through the layers.
The term "ready-to-print" denotes the fluidic properties such as viscosity, buildability, and yield stress, which are suitable for instantaneous printing. Previous research works [10] [11] [12] [13] [14] on construction materials suggest that the rheological behavior of the mixture plays a crucial role in printability and buildability. Research works also reported the necessity of printing parameters for 3D printing, how changing the printing parameters affects the buildability of the material [15] [16] [17] [18] [19] . Research work was conducted before getting a perfectly 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to COVID-19) rectangular block using a rectangular extruder by tweaking the printing parameters and extruder structures using iterative approach [20] . Researchers have worked to improve the surface finish of the printed constructs by reducing the layer heights [21] , but reducing the printing speed or layer height increased the production time [22] . It was reported that generally using an elliptical nozzle for printing caused bulky curvatures in the printed structures [23] .
In order to study the contour deviations and changes in mechanical properties while using different nozzle geometries before scaling up to print larger concrete models, commercially available ready-to-print Prai-3D stoneware clay has been used to print the structures using a DIW printer and tested. Section-2 explained the process involved in preparing the clay materials for 3D printing, including the clay properties. This section also describes the curing process, printing parameters, and visual representation of parts printed using different nozzle geometries. Section-3 and Section-4 show the mechanical testing performed on the 3D printed constructs and method used for quantifying the contour deviations and surface roughness. Finally, the results of the tests are discussed and summarized in section 5. 
PRAI-3d stoneware clay [24] for 3D printing was purchased from 3DPotter Inc. The purchased clay was mixed with waterto-clay (w/c) 0.3 weight proportion and set aside at room temperature for 12 hours. The other properties of the clay are shown in Table. 1 below. The clay is pre-prepared and de-aired when purchased from the manufacturer, and hence the hydrated clay is directly loaded into the extruder of the printer. A 3D Potterbot 7 [25] Super printer, which is a DIW machine, was used to 3D print the samples. The Potterbot used in this research was controlled by the Repetier host software. The 3D CAD model of a cylinder was imported, and the tool path for the printer was generated as G-Code from the software. This G-Code is the pattern in which the Potterbot extruder printed the clay onto the substrate.
For this study, cylindrical samples were printed using nozzles with 1) circular and 2) square geometries. A 3D CAD model of a 2x1 inch (height-by-diameter) cylinder was made, and all the printing parameters are kept constant. The following printing parameters were used: 1) Printing speed = 15 mm/s 2) Circular nozzle diameter = 6 mm 3)
Square nozzle size = 6x6 mm 4) Infill = 0.8 on 1 5) Extrusion speed = 20 mm/s All the printed cylindrical samples were dried at room temperature for 72 hours and then sintered in a hot plate at 100 ℃ for 24 hours. 
The samples 3D printed with circular and square nozzles, although using the same 0.8 infill, the density of the construct differs. With the same 0.8 infill, the volume of clay in cylindrical samples, 3D printed with different nozzle varies. This difference in volume affects the mechanical properties of the printed constructs.
The compression test is one of the most conventional tests used to characterize the mechanical properties of a mixture/ink. The aim of this test is to determine the compressive strength of PRAI 3D stoneware clay so that it can be used to conduct a comparative study with the compression strength of 3D printed clay constructs. To determine the compressive strength of clay, two cylindrical molds (2x1 inch) were 3D printed using Uprint, a Fused Deposition Modeling (FDM) polymer printer, and the molds are filled with the clay and compacted. The molds were stripped off after curing for 72 hours with a tolerance of ±2 hours at room temperature, and the specimens were sintered in a hot plate at 100 ℃ for 24 hours before testing. The samples were loaded in the Shimadzu UH-F300kNX hydraulic universal testing machine (UTM) until failure without any shock loading. The ultimate load until failure was noted for clay samples and was used to calculate the compression strength of the mixtures using the following equation. Two samples were tested, and a type 3 "columnar vertical cracking with no cones" type of failure was noted on both the samples [26] . The diameter of the samples both printed and casted was measured at three different locations and the average diameter was used to calculate the compression strength using the formula given above.
A set of two samples each for both square and cylindrical nozzles were 3D printed. The printed cylinders were cured and sintered in the same way as the regular clay mold and are loaded into the UTM machine. The top and the bottom surfaces of the 3D printed samples were smoothened before loading, and the maximum load until failure was noted. Using the same equation, the compression strength of all the four samples were noted. 
As discussed in Fig.1 of Section-1, using different nozzle geometry for printing affects the contour of the 3D printed part. The purpose of the study in this section is to scan the cylinders printed with circular and square nozzles and compare them with the regular CAD file of the cylindrical part to determine the contour deviations. Fig. 4 . Schematic representation structured light scanning (SLS) system. The structured light system (SLS) is an extension of stereo vision. The difference is that the latter uses two cameras whereas the former uses a projector and a camera for acquiring the 3D information of the object. However, correspondence detection using stereo vision becomes difficult in the case of objects with uniform or repetitive texture. In order to solve this problem, SLS uses a projector in place of one of the two cameras. Fig.4 represents the principle of the structured light system. Here A represents a projector pixel, D represents a camera pixel, and the B is the object point being scanned. The projector projects codified fringe patterns on the object. The projected fringe patterns will get distorted because of the surface variations in the object, and this image (object with distorted fringe patterns) is captured by the camera. Using the codifications in the fringe patterns, the correspondence between the camera and projector points is determined.
The 3D geometry of the object subjected to a scan can be found by estimating the phase of the projected fringe patterns. There have been many phases shifting algorithms in the past among them; the three-step phase shifting algorithm uses minimum number of fringe patterns for phase calculation. A three-step phase shifting algorithm with an equal phase shift can be mathematically defined as, where I' (x,y) represents the average intensity, I'' (x,y) represents the intensity modulation and ∅ (x,y) is the phase to be solved. On solving the three equations (Eq. 1-3) we get the phase as From Eq. 4 we can see that an arctangent function is used in the phase equation, so the computed phase (Eq. 4) will range from -π to + π with a 2π modulus. Therefore, an unwrapping process (spatial or temporal) has to be done to get a continuous phase map. The unwrapping process estimates the 2π discontinuities and removes the jumps by adding or subtracting k(x, y) multiples of 2π. So the unwrapped phase will be, In this research, we have used the enhanced two-frequency phase shifting method [27] for the phase unwrapping. We have used the method as described in [28] to perform scanning and 3D reconstruction. The calibration method [29] has been used to finally reconstruct the 3D geometry.
The experimental setup consists of a digital light processing projector (LightCrafter 4500) for pattern projection, a complimentary-metal-oxide-semiconductor (CMOS) camera (model: FLIR Grasshopper3 GS3-U3-41C6C-C) for image acquisition and an external trigger for synchronizing the camera and projector. The projector resolution was set to 912 × 1140 pixels whereas the camera resolution was set to 1280 × 960 pixels. The image acquisition rate was set to 166 Hz. The accuracy of the scanning system (minimum resolution) is 100 micrometers. We have used three-step phase-shifted patterns for phase retrieval and another set of three-step phase-shifted binary dithered patterns for phase unwrapping. Fig.5 shows the reconstructed 3D geometry of the clay model. 
The SLS system was used to scan the samples all around in three rotations (3 poses at 120º through each rotation) so that the entire surface of the printed sample is reconstructed. The point cloud data obtained from the samples are compared with the STL file of the regular cylinder, which using the same cut section as the printed samples. CloudCompare software [30] was used for comparing the point-cloud and to determine the overall deviation of the printed sample from the regular cylinder. A standard procedure was maintained to perform this analysis which is shown in the flow chart below (Fig.6 ). 
The mean distance and the standard deviation (SD) obtained from each pose of the samples from CloudCompare analysis were used to compute the overall mean distance which denotes the deviation in the printed samples from the regular cylinder.
The scanned point cloud data of printed samples will be overlapped with the STL file of the CAD model. After a center axis alignment, the cut profile (1 to 120-degree rotation) will be used for data analysis. This overall mean distance is the difference in mm from the printed samples to the regular cylinder. Apart from this cloud-to-cloud mean distance deviation, the surface roughness of the samples was computed using the point cloud data. Fig.7 shows the result of the CloudCompare point-cloud data analysis, which has both point-cloud cloud-to-cloud mean distance. 
The compression test results in Fig.8 shows that the cylindrical sample printed with square nozzle has higher compression strength than the sample printed with a circular nozzle. Since square nozzle extrudes a higher volume of clay per layer than the circular nozzle, the density of the clay for the sample printed with square nozzle is higher than the circular nozzle and hence the compression strength of the sample is higher. Interestingly, the compression strength of the 3D printed samples is higher than the regular cylindrical mold despite the infill set to 0.8 on 1. The compacted clay inside the mold has no way to expand and while curing, the sample lost its moisture and hence the size of the cured part reduced. Whereas the printed samples are not confined into any molds are free for expansion right after printing. This makes a slight difference in the sizes of the printed parts and the molded cylinder which affected the compression strength. The point cloud analysis result shows that the cylindrical samples printed with a circular nozzle have lesser cloud-tocloud mean distance and SD when compared with the square nozzle. This is obvious as the circular nozzle provides more uniform curvature than the square nozzles. The cloud-to-cloud mean distance is very high for the samples printed with the square nozzle as the square nozzle creates twisted curvatures in the contour. Hence the contour deviations are higher for cylindrical objects when they are printed with square nozzles. Fig.9 shows the mean distance between cloud-to-cloud points, where three cylinders were printed using a circular nozzle, and two were printed with a square nozzle. Surface roughness is an important entity to measure the texture of the printed surface. In this study arithmetic surface roughness (Ra) and root mean square value (Rq) were used to determine the surface finish of the printed samples.
= (| 1 | + | 2 | + ⋯ + | |)/ (6) = [( 1 2 + 2 2 + ⋯ + 2 )/N] 1/2 (7) where N is the height of the printed sample, is the height from the mean line of the peak or valley in the printed construct.
The surface roughness of the samples measured from the SLS system in Fig. 10 shows that the samples printed with square nozzle have high Ra and Rq values as like the previous CloudCompare analysis. Since the square nozzle generates more deviation through every layer than the circular nozzle, the surface roughness is very high for them. Fig. 10 . Surface Roughness of the samples measured from the SLS system. Based on the three parameters, although the square nozzle imparts higher compression strength naturally, the surface roughness and the mean deviation is very higher. Also, the compression strength of the samples printed with a circular nozzle closer mechanical property with a smooth surface finish and lesser mean deviation from the CAD model. Hence for cylindrical objects, it is better to go for a circular nozzle rather than the square nozzle. The next stage of this research work will continue testing the same parameters for non-cylindrical, free form constructs.
In this study, three parameters namely compression strength, surface roughness and cloud-to-cloud mean distance were used to quantify the contour deviations and mechanical properties of the clay samples printed with circular and square nozzles. Using SLS system, the printed samples were scanned, and the point-cloud data generated from the system was compared with the CAD model to determine the contour deviations. The surface roughness of the printed constructs determined shows how critical it is to pre-determine the nozzle geometry before printing, as in this case, cylindrical construct had large contour deviation when printed with square nozzle than the circular nozzle. Although using a square nozzle increases the compression strength of the constructs by improving the density, it cannot be traded off for the external surface finish. Using the same parameters, the deviations and mechanical properties of the free form constructs can be determined which will be the future work from this research background. The work has provided a guideline of nozzle selection in 3D printing of clay constructs for civil infrastructures.