*4.1. Qualitative Evaluation Method*

Among the results of qualitative studies on the effects of industrial heritage reconstruction and reuse, the "three-pillars approach" has been the main assessment method used to assess these effects from the trifold perspective of economic, social and environmental sustainability. For example, Corné de Broekert applied the "three-pillars approach" to explore the positive impact on the economic, social and environmental sustainability of industrial heritage reconstruction and reuse projects in postindustrial cities in the Netherlands, as well as the factors affecting the degree of added value generated [9]. As research has progressed, many researchers have come to believe that the "three-pillars approach" is insufficient to meet the complex challenges faced by modern society. In addition to economic, social and environmental sustainability, cultural sustainability is also an important dimension. As Sotiria Sarri's research demonstrated, cultural sustainability is a way to maintain cultural diversity and help build inclusive societies and strengthen economies [92]. In practice, an increasing number of governmental and nongovernmental organizations have used culture as a tool for accelerating economic growth, promoting social cohesion, stability and human welfare, and solving environmental problems [93]. Therefore, some researchers have proposed the "four-pillars approach" to meet the requirements of sustainable development. The "four-pillars approach" extends the evaluation to include culture and emphasizes that the cultural dimension is "integrated on an equal basis with the other three dimensions. This approach highlights culture as (re)source and considers components of culture to include heritage, identity, memory, creativity, human knowledge and skills, cultural practices, lifestyles, value systems and diversity, among others" [81].

In addition, some researchers have focused on specific aspects of industrial heritage reconstruction and reuse projects for their evaluation. For example, Nakai Yoko and Ito Hiroshi evaluated the effects of the reconstruction and reuse of the Kiryu sawtooth roof factory from the perspective of the protection of regional characteristics and local industries; they determined evaluation criteria according to the historical and industrial characteristics of Kiryu, including whether the textile factory was located in an area facing the river, whether the three facilities (sawtooth roof factory, residence and warehouse) still existed in one place, whether the space had remained vacant, and whether textile products were still being used. Highlighting regional characteristics was at the core of their evaluation of the effects of industrial heritage reconstruction and reuse [82]. Compared with the "three (four)-pillars approach", the results of an evaluation that focuses on one aspect are undoubtedly more targeted. Nevertheless, there were also shortcomings in this study because important dimensions were omitted, resulting in the "disconnection" between the actual effects of the project and the effects that could be achieved in theory.

#### *4.2. Quantitative Evaluation Method*

To solve the problem of how to precisely quantify externalities caused by reconstruction and reuse projects, many researchers have focused on research pertaining to quantitative evaluation methods in recent years. On the basis of the "three-pillars approach", Qian Yan, et al., introduced a weighted index in relation to stakeholder demands

and built a sustainability indicator system for industrial heritage reuse that includes social, economic and environmental dimensions to quantitatively evaluate the social, economic and environmental benefits of industrial heritage reconstruction and reuse projects [79]. Federico Dell'Anna estimated the economic impact of the reconstruction and reuse project implemented in the Turin's Aurora district (Northern Italy) and focused on the real estate market in the surrounding areas in recent years using an econometric model [83]. Similarly, Liu Guiwen [84], Zhao Qinna [85], Wei Xinna [86], etc., discussed the impact of industrial heritage reconstruction and reuse projects on surrounding housing prices. The research of Liu Guiwen and Zhao Qinna focused on one case or a group of cases. By using different analytical models, they concluded that reconstruction and reuse projects had a significant effect on the price of surrounding housing. Wei Xinna further explored the impact of different types of reconstruction and reuse projects on housing prices in the surrounding areas and concluded that reconstruction and reuse projects that are oriented toward commercial and cultural facilities can relatively improve housing prices in the region. In addition, Bäing and Wong used data analysis to assess the impact of the reconstruction and reuse project of Salford Quays in England on the community [38]. Ioannis Vardopoulos used the DEMATEL model to find out what elements of reconstruction and reuse projects can promote local sustainable development. He also evaluated the pattern and extent of interaction between these different factors [87]. Hence, it is predictable that quantitative evaluation methods have been prominent in this field.

#### *4.3. Individuals as Main Evaluation Target*

The results of the research conducted in the past five years on industrial heritage reconstruction and reuse have shown that individuals have become the main targets of the evaluation of the effects of these heritage projects; individual perception has become the main component of these evaluations, which is a shift from previous approaches that focused too much of projects themselves. This shift reflects changes in the concept of industrial heritage reconstruction and reuse. In the past, industrial heritage reconstruction and reuse were carried out as a way to protect heritage; nowadays, the main goal has become to promote social development and meet social needs via protection.

Based on the phenomenological method, Yasemin Mesda and Sevinc Kurt studied the spatial experience of individuals in the Nicosia Municipal Arts Centre, a museum that emerged out of the transformation of industrial architectural heritage in Cyprus. Through multisensory analysis, these scholars grasped the emotions and attitudes of individuals in that space to evaluate the effects of reconstruction and reuse [88]. Márton Berki also focused on the experience of individuals in the reused space. He focused on groups such as tourists. Through questionnaires, he studied how tourists understood and approached the venue and the ways in which they used the venue to assess the success of the reconstruction and reuse project [89]. Stanislav Martinat, et al., not only focused on tourists but also on how residents perceived a series of industrial brown land reuse projects, and they summarized people's experience in industrial heritage reconstruction and reuse projects [90]. Eujin Julia Kim and Patrick Miller also focused on residents' perception of industrial brownfields after reconstruction and reuse [91]. Hence, individuals' subjective experience has become an important starting point for most researchers to evaluate the effects of industrial heritage reconstruction and reuse projects, and tourists and residents have become important targets for researchers.


**Elke Tatjana Aristizabal Prada 1, Isabella Castellano 2, Eva Sušnik 1, Yuhong Yang 1, Lucie S. Meyer 1, Martina Tetti 3, Felix Beuschlein 1,4, Martin Reincke 1 and Tracy A. Williams 1,3,\***

Received: 15 February 2018; Accepted: 6 April 2018; Published: 9 April 2018

**Abstract:** Primary aldosteronism is the most common form of endocrine hypertension with a prevalence of 6% in the general population with hypertension. The genetic basis of the four familial forms of primary aldosteronism (familial hyperaldosteronism FH types I–IV) and the majority of sporadic unilateral aldosterone-producing adenomas has now been resolved. Familial forms of hyperaldosteronism are, however, rare. The sporadic forms of the disease prevail and these are usually caused by either a unilateral aldosterone-producing adenoma or bilateral adrenal hyperplasia. Aldosterone-producing adenomas frequently carry a causative somatic mutation in either of a number of genes with the *KCNJ5* gene, encoding an inwardly rectifying potassium channel, a recurrent target harboring mutations at a prevalence of more than 40% worldwide. Other than genetic variations, gene expression profiling of aldosterone-producing adenomas has shed light on the genes and intracellular signalling pathways that may play a role in the pathogenesis and pathophysiology of these tumors.

**Keywords:** primary aldosteronism; aldosterone; aldosterone-producing adenoma; transcriptome profiing


**1. Introduction**

The fundamental freedom of design offered by different additive manufacturing (AM) technologies has stimulated a variety of lightweight structures in mechanical engineering over recent years. These lightweight components are often realized by lattice structures in different forms [1–4]. For instance, periodic structures consisting of unit cells [5–7] or gyroid gradients [8–11] have been utilized for eliminating or relocating material, thus saving weight while maintaining mechanical load capacity [12,13]. Sandwich or infill structures are used for load-dependent design of components for the aerospace industry, modulated for different tensile or compression conditions [14,15]. Based on both experimental studies and simulations, the maximum mechanical load has been correlated to the relative density of different lattice structures [11,16,17].

For metal AM, such as laser powder bed fusion of metals (PBF-LB/M), also referred to as selective laser melting (SLM), the achievable surface accuracy and roughness of components are, in general, inferior to conventional manufacturing methods, limiting applications with demanding requirements in terms of shape and surface conditions. In addition, surface defects and roughness influence mechanical properties such as, e.g., the tensile and fatigue strength. Hence, subtractive surface post-processing is essential for PBF-LB/M components to condition shape and surface properties. This, however, might be

**Citation:** Sommer, D.; Esen, C.; Hellmann, R. Static and Dynamic Mechanical Behaviour of Hybrid-PBF-LB/M-Built and Hot Isostatic Pressed Lattice Structures. *Materials* **2023**, *16*, 3556. https:// doi.org/10.3390/ma16093556

Academic Editors: Marcin Małek and Janusz Kluczy ´nski

Received: 5 April 2023 Revised: 3 May 2023 Accepted: 4 May 2023 Published: 6 May 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

challenging for lattice structures due to inaccessible, inner lying areas within the complex lattice arrangement.

In this respect, Zheng et al. and Sarkar et al. investigated the mechanical properties of PBF-LB/M-built components and demonstrated that these are, generally, inferior to conventionally fabricated components [18,19], while surface modifications can improve properties such as, e.g., the fatigue life [20–23].

To circumvent these disadvantages of PBF-LB/M, various hybrid additive manufacturing processes, generally consisting of an additive and a subtractive process, have been developed [24–26]. A very promising hybrid approach is the combination of regular PBF-LB/M as an additive process with high-speed-milling as a subtractive process, capitalizing the advantages of both technologies while evading the disadvantages of the PBF-LB/M-process. In particular, in situ high-speed milling integrated into the powder bed process fosters the capabilities of laser powder bed fusion towards superior surface quality and geometrical accuracy [27–29] with the unique advantage of providing access to component surfaces during the 3D-building phase which might be inaccessible after the component is finished.

In addition, with respect to the mechanical properties of metal structures built by PBF-LB/M, the effects of a post process heat treatment on the microstructure and porosity, hardness, yield and fatigue strength have specifically been addressed [20,30–38]. It has been revealed that a post PBF-LB/M heat treatment increases the mechanical load capacity [39–41]. In particular, solution and aging treatment [42,43] or hot isostatic pressing [44,45] have been proven to reduce porosity and positively modify the microstructure of PBF-LB/M-built parts, in turn leading to improved mechanical properties.

Against this background of optimizing PBF-LB/M of lattice structures for lightweight applications and applying heat treatments to metal AM components, the mechanical properties of body-centred cubic lattice structures are studied. Focussing on the maximum applicable static load and fatigue behaviour upon dynamic load, sole PBF-LB/M-structures are compared with a hybrid process, comprising PBF-LB/M and in-situ 3-axis micro milling. In addition, the effect of different heat-treatments, namely a solution and aging treatment as well as hot isostatic pressing, are investigated by studying porosity, hardness, and microstructure.

### **2. Materials and Methods**

### *2.1. Hybrid-PBF-LB/M Milling System*

Body-centred cubic lattice structures (cf. Section 2.2) are fabricated by additive and hybrid additive manufacturing using a Lumex Avance-25 (Matsuura Machinery GmbH, Wiesbaden, Germany). The machine combines conventional laser powder bed fusion with in situ three-axis high-speed milling, as schematically illustrated in Figure 1 and depicted in Figure 2.

For the milling process, the conventional PBF-LB/M process sequence is paused after several layers (typically ten), allowing access of the milling cutter to all contours of the specimen built thus far. This in turn allows the generation of finished components with superior surface roughness, including the machining of undercuts or internal structures.

The hybrid manufacturing process is conducted under nitrogen atmosphere with less than 3% oxygen level to avoid oxidation, with the build platform being kept at 50 °C to prevent deformation by curling due to thermal stress. The maximum build volume is 250 × 250 × 185 mm3 in width, depth, and height.

Since the PBF-LB/M-process does not fundamentally differ from industrial standard and this comparative study focuses on the tensile fatigue stress behaviour of the PBF-LB/Mand hybrid-built components, previously optimized and reported process parameters for this machine setup are applied for the manufacturing of the specimens (cf. Table 1) [29]. The machine is equipped with an Ytterbium fibre laser (SPI Lasers plc, Southampton, UK) operating at a wavelength of 1070 μm with a focal diameter of 200 μm.

**Figure 1.** Schematic illustration of the hybrid additive manufacturing unit.

**Figure 2.** Hybrid additive manufacturing unit, showing the build plate with the recoater and the milling spindle.

**Table 1.** Laser powder bed fusion parameters.

For high-speed milling, the integrated spindle operates at up to 45,000 revolutions per minute and a maximum torque of 1.31 Nm. In addition, a twentyfold tool magazine is available for the change of the milling device during operation. The milling cutters used in this study are solid carbide cutting tools with a nano coating, consisting of aluminium, titanium, and silicone for the reduction of tool wear (Mitsubishi Materials Corporation GmbH, Meerbusch, Germany). The wear characteristics reported in [46] are reinforced by virtue of the dry milling process. Due to the in situ application of the milling process inside the powder bed, no cooling lubricant can be used, leading to elevated temperature conditions and increasing tool wear [47–49]. To analyse the application of the lattice structures, previously determined milling parameters are used, given by Table 2 [29].

As reported before [27,46], the high-speed milling process starts after several built layers, interrupting the PBF-LB/M-process. In our study ten layers with a height of 50 μm

each are built before starting the milling process. Within the PBF-LB/M-process, a material allowance of *at* = 150 μm is added to the component structure, being removed gradually by the usage of two different milling cutters, realizing a roughing and a finishing sequence (cf. Figure 3b,c). At first, *a*1 = 120 μm of the material allowance are detached by the roughing cutter, machining the surfaces from the last built layers downwards. Afterwards, the finishing cutter removes the remaining *a*2 = 30 μm of the material allowance, improving the surface roughness and the final geometrical accuracy.

**Table 2.** Milling process parameters.

Contrary to the roughing cutter, the finishing cutter is working from the bottom to the top of the component as well as the last built layers are spared for the next process cycle. (cf. Figure 3a, where the finishing cutter has left several layers of *a*2). This geometrical shift of the milling processes is chosen to avoid thermal distortion as well as to optimize geometrical accuracy and superior surface quality. Due to the PBF-LB/M-process, a heat input is generated, evolving a thermal gradient within the built part. The upper layers exhibit a higher temperature than the layers below, which have already cooled down [50,51]. By virtue of the thermal conditions, a start at the bottom layers working upward is advised and the last built layers should be omitted [52–54].

**Figure 3.** Two stage milling process with two different milling parts for the hybrid system. (**a**) PBF-LB/M process; (**b**) Roughing process; (**c**) Finishing process.

### *2.2. Specimen Design and Material*

To study the effects of an improved surface quality provided by the hybrid process, a body-centred cubic unit cell has been chosen for the lattice structures, as it allows access of the milling cutter and as it represents an often chosen and well-studied structure. The dimensions of the unit cell are 5 × 5 × 5 mm, and the specimens are designed with 3 × 3 × 2 (width × height × depth) cells and a strut diameter of 1 mm, leading to a test specimen with about 13% relative density (cf. Figure 4b). Within the hybrid approach, the manufacturability of the specimens is determined by the three-axis milling system and the diameter of the used milling cutter. In this study, the used milling cutter has a diameter of 2 mm, exhibiting the geometry, shown in Figure 4a). Combined with the three-axis milling system, the milling cutter is machining the specimens on the top and besides (cf. Figure 4b), the undercut surfaces cannot be milled by virtue of the dimensions of the unit cell.

The study is performed processing maraging tool steel X3NiCoMoTi18-9-5 (1.2709, Matsuura Machinery GmbH, Wiesbaden, Germany), a high-nickel steel exhibiting a distinctive mixture of high strength and high hardness, combined with ease of welding. It is preferably employed in the die and tooling industry as well as in structural and aerospace applications [55,56]. The use of maraging steel in PBF-LB/M is also stimulated by the potential of generating cooling channels for the reduction of cycle times in injection moulding [57] of plastics and high-pressure casting of metals [58].

**Figure 4.** (**a**) Dimensions of the milling cutter, (**b**) milling of lattice structures.

### *2.3. Post-Processing Procedures*

As thermal post-processing of maraging steel, in general, improves mechanical properties of the built parts, the influence of solution treatment combined with aging treatment (SAT) as well as the impact of the hot isostatic pressing (HIP) are studied. For the SAT, a Nabertherm LH 120/12 batch furnace (Nabertherm, Lilienthal, Germany) is employed, enabling heat treatments up to 1200 °C with a maximum heat rate of 10 °C/min. The specimens, completely processed without process gas, are heated to 940 °C at the maximum heat rate, held for 30 min and cooled down to approximately 25 °C with a controlled cooling rate of 10 °C/min (solution treatment). Subsequently, for the aging treatment, the furnace is heated up to 550 °C, held for 4 h and followed by a natural cooling.

The HIP-process is conducted with a Quintus QIH (Quintus Technologies AB, Västeras, Sweden) with a maximum furnace temperature of 1400 °C and a maximum process pressure of 200 MPa. Argon gas is utilized as a process gas. The process starts with a heating up to 1035 °C with a heating rate of 15 °C/min, increasing the pressure to 150 MPa at the same time. This step is followed by a controlled cooling with 10 °C/min down to 940 °C, whereby the previously explained SAT procedure is finished.

The surface properties change within the different heat-treatment procedures (cf. Figure 5). For the SAT, the surface of the specimens shows an effect of blushing, while the HIP specimens obtain a dull appearance. In addition, at the as-built specimens as well as at the HIP specimens, the milling paths are visible, showing a frequent waviness.

**Figure 5.** Surfaces of milled specimens: (**a**) as-built, (**b**) SAT and (**c**) HIP.

### *2.4. Sample Characterization*

The mechanical behaviour of the built specimens is tested in the dependence of uniaxial static and dynamic load. For the compression tests with static load, an AG-X plus universal testing machine (Shimadzu, Kyoto, Japan) is used, applying a maximum force of 50 kN due to a precision ball-screw drive. For every state of the heat treatment, machined and PBF-LB/M-built, a batch of three specimens is tested, increasing the statistical significance.

The dynamic testing is executed with a StepLab UD020 (Step Engineering, Resana, Italy) with a maximum compression of 14 kN with a sinusoidal stress-time sequence at a maximum fatigue test frequency of 100 Hz. Analogous to the static tests, three specimens are tested for every level of amplitude, recording the number of cycles until failure.

For the characterization of the microstructure of polished and etched surfaces, a laser scanning microscope VX-2000 (Keyence, Osaka, Japan) is employed. For the examination of the microstructure, the specimens are acid treated with an etching agent according to Adler [59]. Fractographical analysis of cracks appearing during the mechanical testing is conducted with a scanning electron microscope (Maia-3, TESCAN, Dortmund, Germany), using the secondary electron detector (SE) and a SEM voltage of 3 kV.

### **3. Results and Discussion**

In the following, the results of the comparative study between PBF-LB/M-built and hybrid-built lattice structures are shown and discussed. Firstly, mechanical properties with respect to static and the dynamic load for the as built structures are discussed. Secondly, the influence of SAT and HIP is evaluated for both PBF-LB/M-built and hybrid-built lattice structures.

### *3.1.  In addition, the consecutive collapse of the three individual layers of the built lattice structure is clearly seen in the stress–straindiagram, until the entire specimen is densely compressed in test direction without entire rupture of the struts, in turn increasing the stress to the maximum applied load, as depicted in Figure 6 [23,33,54].

Comparing the sole PBF-LB/M-built and hybrid-built lattice structures, Figure 5 also shows that the in situ milled lattice structure withstands higher loads, consistently about 14–16% higher, before breaking the single layers than the PBF-LB/M-built structures. The strain and fracture behaviour of PBF-LB/M-built components is significantly influenced by the quantity and dimensions of surface defects [61–63]. Subsequently, the specific energy absorption (SEA) of the hybrid additive manufactured specimens is increased, scaling the applied load to the mass of the specimens [64–66]. While sole PBF-LB/M-built structures show a SEA of about 67.1 kJ/kg, the energy absorption can be raised to about 72.1 kJ/kg due to the surface finish. As shown in the SEM images in Figure 7, the PBF-LB/M-built surface reveals distinct irregularities and defects, associated by adhering powder particles, insufficiently molten regions and superficial cracks, which in turn weaken the mechanical resistance of the specimen. Contrary to this, the in situ machined parts do not show such large defects or cracks on the surface. While the surface roughness, in general, is superior to the PBF-LB/M-built surface roughness, the z-pitch of the milling process can be observed as an irregularity (Figure 7b). The surface quality can be improved to an average surface roughness of *Ra* = 1.5 –2 μm, as reported before [46], getting assigned to lead to the superior load capacity of the hybrid-built structures.

After heat treatment with the SAT process, the specimens reveal a distinctively different mechanical behaviour during static testing. As shown in Figure 8, instead of the layer-wise collapse of the different unit cells, the specimens fail completely at a maximum load of 75 MPa (unmachined) and at 81 MPa (machined), exhibiting typical shear fractures [54]. This difference in the mechanical behaviour can be attributed to a change in microstructure as it is expected after the SAT. The martensite (*α*) phase is dominant for the PBF-LB/M as-built state of maraging steel, indicating only a fractional amount of the austenite ( *γ*) phase [67]. During solution treatment, the *γ* phase completely merges into the *α* phase, converting back within aging. The ductile behaviour, observed for the as-built specimen, is significantly reduced and the performance during static load tests is dominated by the austenite phase, leading to a very strong but brittle material [68]. In addition, the hybrid-processed specimens reveal a superior stress–strain response as compared to

the sole PBF-LB/M-built parts, attesting the effect of an improved surface condition on the strain and fracture behaviour.

**Figure 6.** Stress–strain curve of the as-built lattice structures.

**Figure 7.** SEM images of (**a**) PBF-LB/M-built surface and (**b**) high-speed milled surface.

**Figure 8.** Stress–strain diagram for the comparison of Hybrid PBF-LB/M- and PBF-LB/M-built specimens for SAT lattice structures.

Qualitatively, a similar behaviour is found after HIP of the lattice structures, which fail at a maximum load of 79 MPa (sole PBF-LB/M-built) and 90 MPa (in situ milled), minimizing the ductile material structure as well as the SAT specimens (c.f. Figure 9). The increase in the maximum load of the hybrid-built specimens of about 12% shows an improvement, which is expected to arise from the superior surface quality [69]. In comparison to the SAT specimens, the maximum load for the failure has been increased with about 10 MPa, as reported by previous studies similarly for the comparison of SAT and HIP specimens [70]. The increase of the maximum load can be attributed to the improved material properties due to the HIP process, quantified by the porosity and the hardness of the tested material, measured additionally at cubic test specimens.

**Figure 9.** Stress–strain diagram for the comparison of Hybrid PBF-LB/M- and PBF-LB/M-built specimens for HIP lattice structures.

As shown in Figure 10a, the density of post processed components can be raised even though the porosity of as-built components is already high, being about 99.8%. Yet, the density of the SAT-processed specimen reaches about 99.84%, increasing marginally to almost 99.9% in succession of the HIP process. A more pronounced advancement in material properties, however, is achieved for the hardness (c.f. Figure 10b). While the hardness for the PBF-LB/M-built components is approximately at 345 MPa, post-processing improves this characteristic to about 550 MPa for the SAT specimen and to 570 MPa for the HIP specimen.

**Figure 10.** Comparing the as-built, SAT and HIP states for (**a**) density and (**b**) hardness.

While these experimental results indicate an improvement of the mechanical behaviour induced by the heat treatment, they simultaneously lead to a modification of the microstructure of the material [71]. The microstructure of the as-built specimens is unidirectional and dominated by a very fine-grain structure (Figure 11). Due to the different heat treatments, the microstructure changes, leading to a more coarse-grained structure and a dissipated alignment for both heat treatments [60].

**Figure 11.** Microstructure of the (**a**) as-built, (**b**) SAT and (**c**) HIP specimens.

### *3.2. Dynamic Testing*

Dynamic mechanical testing is performed according to Section 2.4 with a maximum load of 14 kN at a frequency of 50 Hz. For every level of amplitude, three specimens are tested until the final failure occurs, the average being depicted in a Wöhler diagram.

Figure 10 visualises the resulting Wöhler diagrams for the PBF-LB/M-built (Figure 12a) and the hybrid built (Figure 12b) lattice structures, comparing the specimens in the as-built state with the different heat treatment processes. The fatigue behaviour changes in dependence on the cycle number for the various batches of specimens, determining the areas of strength. For both, the PBF-LB/M-built and the hybrid-built lattice structures, the SAT- and HIP-treated specimen reveal a better performance in the low cycle fatigue (LCF) regime, decreasing to assimilable cycle numbers in the section of the high cycle fatigue (HCF). The heat-treated specimens prove a comparable performance for the very high cycle fatigue (VHCF), whereas the as-built structures demonstrate an inferior performance. As for the static load behaviour, the improved hardness and porosity of the heat-treated specimens, especially the HIP specimens, is advantageous for the LCF. With higher cycle numbers, the material performance of the as-built lattice structures is more ductile, raising the VHCF.

For the as-built specimens, the machined structures show a similar overall trend of fatigue behaviour, yet exhibiting an offset with higher cycle numbers for all different sections of strength. This difference can be attributed to the superior surface quality of the machined specimens, as stated before. Figure 13a depicts the crack-analysis for the as-built lattice structures, revealing an endurance failure (zone 1) as a beginning of the crack, including an internal void, possibly enabling the endurance failure. Further, a forced fracture (zone 2) is depicted, causing complete fracture of the specimen. Due to the ductile material structure of the maraging steel in the as-built state, an endurance failure can develop, weakening the structure with every cycle until its complete failure [72].

**Figure 12.** Wöhler diagram for the (**a**) PBF-LB/M-built and (**b**) hybrid-built specimens, each comparing the as-built, SAT and HIP states.

**Figure 13.** Crack analysis for (**a**) as-built (zone 1: endurance failure, zone 2: forced fracture, getting divided by dashed line), (**b**) SAT and (**c**) HIP specimens for the same applied load.

The SAT structures exhibit almost identical numbers of cycles for the different loads, differing at the beginning of the low cycle fatigue but converging at the following high cycle fatigue, as shown in Figure 14b. Contrary to the as-built specimens, the fracture plain shows a big part of a forced fracture and excludes the endurance failure. The fracture surface only reveals an increased roughness without showing a structure or a development of the fracture (cf. Figure 14b). Due to the heat treatment, the material hardness increased, yet it became more fracturable, leading to a complete failure at a load that excels the maximum capacity.

**Figure 14.** Wöhler diagram for the (**a**) As-built, (**b**) SAT and (**c**) HIP specimens, comparing machined and unmachined specimens.

Similar to the SAT specimens, the HIP lattice structures demonstrate a big part of a forced fracture without any indication of a cyclic developing weakness (cf. Figure 13c). The endurance failure is, for small and high loads, not identifiable at the fracture plain, showing only a little number of porosities, subsequently increasing the maximum load for the lattice structures. Furthermore, the hybrid-built specimens excel the PBF-LB/M-built in the number of the cycles, retaining the offset during all sections of the fatigue testing. The load for the low cycle fatigue is about 10 MPa higher for the machined specimens as for the PBF-LB/M-built as well as the number of cycles in the high cycle fatigue differs about 25,000 at the same applied load (Figure 14).


**3. Software for integrated haptic rendering**

This section deals with the Computer Haptics aspects of the integrated force and tactile feedback, addressing, from one side, the physical and geometrical model of interaction, from the other, the computational challenges of the integrated rendering. The first part of this section is dedicated to a review of the models of contact, taking into account friction, soft finger representation and multiple finger interaction, both for kinesthetic and tactile feedback. The second part deals with architectural configurations of simulation and haptic rendering engines taking into account multi-rate and multi-resolution techniques.

critical since there is no need of gravity compensation. Moreover the single finger

One finger device has a superior level of complexity since the weights of the display has to be compensated by the kinaesthetic device. There are various implemented solutions that

Wagner in (Wagner, 2005) proposed the integration of kinaesthetic feedback with a shape display. Kheddar introduced the concept of a multilevel device for the different spatial level

In the case of multi-finger interaction a major problem has to be considered. For allowing the simulation of grasping of reduced thickness the fingers have to be free to get close each other. This results in very though requirements for the thickness of the tactile display in the palmar area of the fingertip. The display has to be as flat as possible in order to allow the finger of user to get close together during grasps of small virtual objects. There are no experiments that exactly establish what is the exact tolerable thickness of a display for supporting multi-finger interaction, but simple tests can demonstrate that it must be kept in

One possible way to get around this issue is to employ an electro-tactile display that can reach a very flat shape like in (Sato et al.,2007). However, electro-tactile displays show several disadvantages like large variation of perceived stimulus from subject to subject, dependence from wetness of the finger surface, employment of high voltage etc. Those unwanted feature made them hardly usable in the context of a virtual reality simulation. Other attempts has been done for obtaining mechanical tactile displays with flat shape.

Benali-Khoudja in (Benali-Khoudja et al., 2003) developed a pin-array display based on a multilayer approach that has been conceived for integration with kinesthetic feedback. In the European Project HAPTEX a system composed by a desktop haptic device and a piezo-electric pin-array display have been adapted for the integration and tested (Fontana et al., 2007).

Recently a novel pin-array display based on a customized solenoid transducer has been purposely developed by authors for the integration with a hand exoskeleton (Salsedo et

This section deals with the Computer Haptics aspects of the integrated force and tactile feedback, addressing, from one side, the physical and geometrical model of interaction, from the other, the computational challenges of the integrated rendering. The first part of this section is dedicated to a review of the models of contact, taking into account friction, soft finger representation and multiple finger interaction, both for kinesthetic and tactile feedback. The second part deals with architectural configurations of simulation and haptic

rendering engines taking into account multi-rate and multi-resolution techniques.

interaction puts no strict limits to vertical encumbrance of the display.

differ from the type of tactile display that is employed.

**3. Software for integrated haptic rendering**

of details (Kheddar, 2004). - Multiple Finger Spatial:

the range of few millimetres.

al.,2011).

The haptic rendering for object manipulation and exploration has the characteristic of combining the techniques from physics simulation with the principles of control and knowledge about human perception. Without losing generality haptic interaction scenarios can be represented by a physics simulation in which one or more virtual entities have the special role of exchanging haptic information with the user. These entities are called *proxies*. In some scenarios these virtual entities represent a user body part that directly interacts with other objects in the environment. A different type of representation is the one happening when the user interacts by means of a virtual tool as a stylus or a more complex tool. Examples of applications in the former type are exploration of surfaces, grasping, haptic rehabilitation and scenarios in which an avatar is employed. Examples of the latter type are drilling, simulation and even driving simulation. Clearly, the type of proxy depends on the type of haptic interface and the specific attachment to the user body part. For direct contact, like virtual finger exploration, the robotic endeffector applies forces on the fingers of the user using a rigid attachment to the user, or, following an encountered haptic approach. Instead devices in which the user holds a stylus or a handle are more suited for tool based proxies.

The type of proxy has effects, for the purpose of our discussion, in terms of the geometry and physical modeling of contact having to simulate, in one case, the contact between the finger or a body part with virtual objects, while in the other the contact of a virtual rigid object that transmits the contact to the user.

The general aim of the proxy is to be respectful of the physical properties of the virtual world, meaning that its behavior will avoid penetration with other objects. There is anyway a caveat. In real world the user moves the haptic interface end-effector specifying in this way a requested virtual position for the proxy. This requested position and orientation is a virtual entity called *haptic handle*. When the proxy touches an object like a virtual wall, the haptic interface produces a force to represent the opposition of the wall to penetration but this force is not always able to prevent the motion of the user in real space into the space where the virtual object is located. The discrepancy between proxy position and haptic handle position is a key element of haptic rendering. The common to rendering approach is to simulate the presence of a virtual spring between the proxy and the handle with a factor proportional to the stiffness of the object in contact. This approach is called penalty based because force is proportional to the penalty of entering with the handle into the object. This spring can introduce some instability and for this reason it can be replaced by a damped spring. Please note how, in this discussion, we have not taken into account the effect of the force produced by the spring on the proxy.

Moreover, we have not made distinctions between impedance and admittance interfaces. In the formers the low level controller receives forces to be applied to the user at the endeffector, and in most of the cases such force is computed on the side of the computer performing simulation and collision. In the latters the low level controller specifies a position to be held with a given stiffness, up to the maximal force of the device.


**Author details**

John R. Castro-Suarez, William Ortiz-Rivera, Nataly Galan-Freyle, Amanda Figueroa-Navedo, Leonardo C. Pacheco-Londoño and Samuel P. Hernández-Rivera *ALERT DHS Center of Excellence, Department of Chemistry University of Puerto Rico-Mayagüez, Mayagüez, PR*


**1. Introduction**

Developments in manufacturing technologies by introducing systems based on cyber– physical concepts, Internet of Things (IOTs), and artificial intelligence (AI) are considered as Industry 4.0. The concept features two main aspects: integration and interoperability [1,2]. Linked with several applications and software, Industry 4.0 enables sustainability in production and service [3,4]. Developed countries are creating their own version of Industry 4.0-related strategies like "China 2025" in China [5], "Industry 4.1J" in Japan [6], and "Advanced Manufacturing Partnership (AMP 2.0)" in the USA [7]. However, this concept is still in its embryological stages in developing countries, specifically Pakistan. There is considerably less access to modern technologies and a collective reluctance in adopting its application, as indicated by its global ranking on various indices. Therefore, an evaluation of the maturity of developing countries in adopting Industry 4.0 poses a significant challenge. Pakistan, for instance, ranks 110th out of 141 countries in terms of global competitiveness. According to Khan [8], there is a significant decline in growth of the textile industries of Pakistan, which will impact the Key Index, i.e., the GDP of Pakistan, which was 4.24% [9], as the share of the industrial sector in terms of GDP is 12.4% of whole GDP. To increase the GDP, the manufacturing industry should shift toward Industry 4.0 in terms of large- and small-scale manufacturing systems [10]. Industries are also facing a shortage of skilled workers and knowledge sets [11]. The logistic network of the country is also deficient compared with other neighboring countries like India, China, and Bangladesh [12]. To tackle this issue, the use a framework involving evaluating the readiness level of individual companies using maturity models. The term "maturity" denotes a "state of being complete, ready or perfect" and implies development. The established seriousness models are generally used as tools to assess and measure the inclination of an organization or a process [13]. Readiness models are exclusively designed to secure a first perspective and to enable the start of the development route [14]. These models are established by renowned expert firms worldwide and have proven effective in assessing the manufacturing sector. By utilizing such

**Citation:** Khan, U.; Ahmad, W.; Sajjad, A.; Jawad, M. Preliminary Maturity Level Assessment of Industry 4.0 in the Context of Pakistani Industries. *Eng. Proc.* **2023**, *45*, 29. https://doi.org/10.3390/ engproc2023045029

Academic Editors: Mohammad Javed Hyder, Muhammad Mahabat Khan, Muhammad Irfan and Manzar Masud

Published: 12 September 2023

models, countries can gain insights into their current state and take necessary measures to embrace Industry 4.0 technologies and practices. Several countries have developed unique models to assess their Industry 4.0 state, including the IMPULS model by the German Association of Mechanical Engineers (VDMA), the Singapore Smart Industry 4.0 Readiness Index, and the Smart Manufacturing Readiness Model formed by the National Institute of Standards and Technology (NIST) in the United States of America. These models have been tailored to suit the specific situations and circumstances of technologically advanced nations. However, a challenge arises when applying these models in developing countries, as they have not been extensively utilized in such contexts [10]. These developed models are comprehensive, detailed, and resource-intensive. Thus, it is necessary to assess the preliminary maturity stage of Industry 4.0 in the manufacturing sector of Pakistan using the limited resources and a cost-effective way to provide a preliminary understanding of the adoption of Industry 4.0. A questionnaire was developed to frame close-ended questions related to the Industry 4.0 concept and its awareness, willingness, and maturity level. It will provide a basic understanding and conceptualization of the readiness level to implement Industry 4.0 in Pakistan's industrial sector.

#### **2. Methodology**

The current report is exploratory and not based on any previously developed framework and primarily emphasizes an evaluation of the industrial sector of Pakistan, as well as the profiling of industrial concepts. The outcome of this study will be helpful and will provide guidelines for the development of strategies in Pakistani industries in the future. Close-ended questions are considered the most suitable way to conduct qualitative research. First, a comprehensive literature review was conducted to obtain a clear understanding of the Industry 4.0 paradigm. To find a suitable model for assessing Industry 4.0 readiness and maturity of manufacturing enterprises in Pakistan, the method in Figure 1 was adopted. It contains four steps to analyze the industrial sector of Pakistan [10]: the first step comprises the questionnaire development and its dissemination; the second step consists of data collection from industrial experts, top management, decision makers, and AI experts of the Pakistani industrial sector through a questionnaire; in the third step, the data are processed using statistical software; the last step consists of a data analysis, the findings, and the conclusions upon obtaining the answers and feedback.

**Figure 1.** Steps adopted to analyze maturity and readiness.

#### *2.1. Questionaire Development*

The questions were in line with the major issues identified from the literature review and validated by the industrial and academic experts. The questionnaire consists of 9 questions, as given in Appendix A, with a complete set of data having the following three parts:

Part 1: Basic knowledge of Industry 4.0 (Questions 1–3); Part 2: Readiness for Industry 4.0 (Questions 4–6); Part 3: Maturity level (Questions 7–9).

#### *2.2. Dissemination and Data Collection*

In this step, an online survey was developed and disseminated through email, WhatsApp, and other social media platforms. The developed survey was filled out by industrial experts, production engineers, consultants, and top management from selected 20 industries. The sample size was calculated using random sampling (Equation (1)).

$$P = 1 - (1 - \left(\frac{1}{N}\right))n.\tag{1}$$

where *n* = sample size; *N* is the population size, which was 400; and *P* is the probability, which was 5% in this study.

The industries are categorized as the textile, automotive, and manufacturing industries, as tabulated in Table 1.

**Table 1.** List of companies.

#### *2.3. Data Processing*

To process the data, Microsoft Excel was used to preprocess, compile, analyze, and visualize the responses. The collected data were analyzed to remove any blank entries and redundant data. Then, the data were compiled in such a way as to make it suitable for statistical analysis. The assembled data were modelled by amassing personal opinions about each variable into clusters to obtain a response rating distribution of these groups as a suitable means of reviewing the data.

#### *2.4. Data Analysis*

To investigate and assess deviations in the data, standard deviation (SD) is a useful tool in statistics. It is the distribution of a dataset compared with its normal value. Data points that are distant from the mean indicate a higher deviation within the dataset. As a result, the data become more dispersed, leading to an increased value for the standard deviation. An SD cannot be negative as it is calculated by squaring the parameter. Mean is the average of a certain set of observations. A one-way analysis of variance (ANOVA) was conducted to measure the inconsistency in the collected data. A *p*-value less than 0.05 depicts the significance of the data. A *p*-value of 0.003 was obtained in the comparison of data obtained directly from interviews and those obtained indirectly from mail.

#### **3. Results and Analysis**

In total, 150 responses were recorded and received from the 20 sampled industries. The average results of these responses are summarized in Table 2. The complete results regarding basic knowledge of, readiness/adaptability for, and level of understanding/maturity regarding Industry 4.0 were determined using a Microsoft Excel sheet and verified using SPSS 28.0.1; the overall average for the results is 1.9, as shown in Table 2. This means that the overall readiness/adaptability in the selected industries is below average. As far as awareness is concerned, the average score is 2.4, which means the bulk of industries in Pakistan are conscious of Industry 4.0 and only a few of them do not know about Industry 4.0. For example, cement manufacturing companies work manually via ordinary labor, as they work with ordinary methods and there are no digital manufacturing processes.

**Table 2.** Summary of averages for the results from the survey responses.

Total number of questions = 9, number of respondents = 20, total score (rating) = 5, any data that were not known took a value of zero, 0 = least effective, 5 = most effective.

The commutative aggregate of the ratings of these three major categories are illustrated in Figures 2–4. It is depicted in Figure 1 that the number of peaks above average are more than below average, which means that most companies are aware of the basic idea of Industry 4.0, the suitability of Industry 4.0 technology for production, and that it is better than manual production systems. The rating for readiness for Industry 4.0 is shown in Figure 3. It can be noticed that the number of below-average peaks are greater than the number of above-average peaks, which clearly explains the lack of readiness of industries due to a preference for manual work rather than Industry 4.0 technology. Industries are assuming that conventional methods are better for manufacturing their products. Therefore, industries have less awareness about the efficiency of Industry 4.0 production processes, and they resist converting their conventional production systems into digital systems. The maturity levels of Industry 4.0 in selected industries are shown in Figure 4. It is evident that the number of below-average peaks are much greater than the number of above-average peaks, which depicts a lack of Industry 4.0 maturity for industries due to a greater adaptability to manual work than to Industry 4.0 technology. Industries assume that conventional methods are easier to use in manufacturing processes. Thus, industries are more adaptable to manual work, consider the quality of production through Industry 4.0 to be less, and believe that there are safety risks in the context of the modern paradigm.

**Figure 2.** Basic concept of Industry 4.0 in Pakistan.

**Figure 3.** Readiness/adaptability.

**Figure 4.** Maturity level of Industry 4.0.

A one-way analysis of variance (ANOVA) was carried out to assess the unevenness in data collected from industrial experts, production engineers, consultants, and top management. A *p*-value less than 0.05 depicts the significance of the data. The grouped data were modelled by amassing individual observations of a variable into groups, so that a response rating distribution of these groups was obtained. A variable was only significant when its f-stat was greater than 4 (>4) and its probability was less than 5% (<5%). Here, we can see that the variable under "within people", i.e., between treatments, is a major determinant in estimating Tukey's equal variances, having an f-stat of 20.4 and a probability of 0.001. Therefore, any variation in "between treatments" will cause a major variation in the dependent variable.

The result details are written in Table 3.

#### **4. Discussion**

The results of this sectoral survey and its analysis reveal that the score for the first group in awareness of the basic concept is 1.96 out of 5 (40%), which is very low compared with the results of similar international industrial markets. The main reason behind this is the fact that management of main industrial sectors are significantly not related in terms of educational backgrounds and there is a loose arrangement in the job selection process. However, it also expresses that the respondents realize that Industry 4.0 technology is not suitable for their current production setups, as they feel more comfortable with manual work. These results correspond with those of with previous research [8]. The result for Group 2 is 2.1 out of 5 (42%). The readiness level is also below average. The main reason for this is that most industries prefer manual processing rather than digitization. The conventional methods are more suited for manufacturing the products. The result for maturity level (group 3) is 1.75 out of 5 (35%), which indicates that industries in Pakistan are not mature enough to embrace Industry 4.0, which corresponds with the outcomes of Hameed et al. [12]. Industries are adaptable to manual work, consider the quality of production through Industry 4.0 to be less, and believe that there are safety risks in the context of the modern paradigm. So, we can say that this maturity and readiness assessment research has critical value in the field of assessment of Industry 4.0 with regard to checking the fundamental knowledge, readiness, and maturity of Pakistani industries. Major stakeholders such as the Government of Pakistan and industrialists should take urgent measures to promote the use of this technology and to embrace the concept of Industry 4.0 in the manufacturing, hospital, and agriculture sectors as an increase in industry development means growth in the GDP of the country.

#### **5. Conclusions**

The motive behind this questionnaire-based survey was to assess the preliminary readiness and maturity level of Pakistan's industrial sectors with reference to Industry 4.0. It is concluded that the basic conceptualization of Industry 4.0 can be suitably checked using the designed questionnaire. Further, the distribution of responses in various industrial sectors such as the textile, automotive, and manufacturing industries also adds credibility. The questionnaire was validated using a statistical analysis. It was revealed that there is an awareness of the basic concept of Industry 4.0 across major Pakistani industries, but they are reluctant to adopt digitization and still prefer conventional production systems. A possible reason for this may be their better adaptability to conventional or manual technology and the low financial requirements. The current study provides a theoretical contribution to the subject in terms of assessments and has managerial implications as it can be used by top management involved in promoting the acceptance of Industry 4.0 processes. The findings of this research can be used for decision-making processes when converting conventional factories into smart manufacturing systems or when implementing Industry 4.0 processes. **Author Contributions:** Conceptualization, U.K. and W.A.; methodology, U.K.; software, U.K.; validation, A.S. and M.J.; formal analysis, U.K.; data curation, U.K., M.J. and A.S.; writing—original draft preparation, U.K.; writing—review and editing, W.A. and A.S.; visualization, A.S. and M.J.; supervision, W.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A. Questionnaire on Basic Knowledge, Readiness, and Maturity Level**

#### **References**


*2.3. The Foot Force Distribution*

When analysing the foot force distribution, the slippage between the foot endpoint and the ground is neglected [13]. For the sagittal motions, the lateral forces of the foot endpoints can be ignored, and the ground reaction forces of each leg can be divided into a normal and a tangential component.

The ground reaction force can cause many negative effects like structural damages and control difficulties; therefore, the value of the ground reaction force must be minished. Here, the minimization of norm of the foot force method is used to minimize the norm solution of the foot force and to reduce the compact between the ground and the robot [14].

A coordinate frame {*Ob*} is established at the geometric center of the body. The *x* axis points to the direction of the motion. The direction of the *z* axis is vertical to the ground and points upwards. The *y* axis is defined by the right-hand rule. The static force diagram is illustrated in Figure 3. Here, we assume the RF and LH (left-hind) legs are in the stance phase. *FG* = [ *fRF*, *fLH*] *T* is the ground reaction force vector which contains the ground reaction force of the RF and LH legs, where *fRF* = [ *fRF*,*x*, *fRF*,*z*] *T* and *fLH* = [ *fLH*,*x*, *fLH*,*z*] *T*. The vector *V* = [*Fx*, *Fz*, *Ty*] *T* contains the forces and moment acting on the robot COM in sagittal plane. Under these conditions, the forces and moment balance equations can be written as follows:

$$F\_{\mathbf{x}} = f\_{RF,\mathbf{x}} + f\_{LH,\mathbf{x}} \tag{17}$$

$$F\_z = f\_{RF,z} + f\_{LH,z} \tag{18}$$

$$T\_y = f\_{RF,x}z\_{RF} - f\_{RF,z}x\_{RF} + f\_{LH,x}z\_{LH} - f\_{LH,z}x\_{LH} \tag{19}$$

**Figure 3.** The static force diagram of SCalf.

*Appl. Sci.* **2019**, *9*, 1771

The Equations (17) to (19) can be written in a matrix form as follows:

$$B \cdot \mathbf{F}\_G = V \tag{20}$$

where

$$\mathbf{B} = \begin{bmatrix} 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 \\ z\_{RF} & -\mathfrak{x}\_{RF} & z\_{LH} & -\mathfrak{x}\_{LH} \end{bmatrix} \tag{21}$$

In Equation (21), {*xRF*, *zRF*} and {*xLH*, *zLH*} are the coordinates of the support foot endpoints in {*Ob*}. In Equation (20), there are 4 unknowns but only 3 equations. Here, we use the least squared method to realize the minimization of norm of the foot force method. The result is shown as follows.

$$F\_G = \mathbf{B}^T (\mathbf{B}\mathbf{B}^T)^{-1} \mathbf{V} \tag{22}$$

In Equation (22), the matrix *B*+ = *BT*(*BBT*)−1 is also the pseudoinverse matrix of *B*. As the third component of *V* (*Ty*) is zero, the parameters in the last column of *B*+ can be neglected. The value of *B*+ is shown as follows.

$$\mathbf{B}^{+} = \begin{bmatrix} \frac{b\_{11}^{+}}{2\Lambda} & \frac{b\_{12}^{+}}{2\Lambda} & \times \\ & \frac{b\_{21}^{+}}{2\Lambda} & \frac{b\_{22}^{+}}{2\Lambda} & \times \\ & \frac{b\_{31}^{+}}{2\Lambda} & \frac{b\_{32}^{+}}{2\Lambda} & \times \\ & \frac{b\_{41}^{+}}{2\Lambda} & \frac{b\_{42}^{+}}{2\Lambda} & \times \\ & \frac{b\_{41}^{+}}{2\Lambda} & \frac{b\_{42}^{+}}{2\Lambda} & \times \end{bmatrix} \tag{23}$$

where

$$b\_{11}^{+} = (\mathbf{x}\_{RF} - \mathbf{x}\_{LH})^2 + 2z\_{LH}^2 - 2z\_{LH}z\_{RF} \tag{24}$$

$$b\_{12}^{+} = (\mathbf{x}\_{RF} + \mathbf{x}\_{LH})(z\_{RF} - z\_{LH}) \tag{25}$$

$$b\_{21}^{+} = (\mathbf{x}\_{RF} - \mathbf{x}\_{LH})(z\_{RF} + z\_{LH}) \tag{26}$$

$$b\_{22}^{+} = (z\_{RF} - z\_{LH})^2 + 2\mathbf{x}\_{LH}^2 - 2\mathbf{x}\_{LH}\mathbf{x}\_{RF} \tag{27}$$

$$b\_{31}^{+} = (\mathbf{x}\_{RF} - \mathbf{x}\_{LH})^2 + 2z\_{RF}^2 - 2z\_{LH}z\_{RF} \tag{28}$$

$$h\_{32}^{+} = (\mathbf{x}\_{RF} + \mathbf{x}\_{LH})(z\_{LH} - z\_{RF}) \tag{29}$$

$$b\_{41}^{+} = (\mathbf{x}\_{LH} - \mathbf{x}\_{RF})(z\_{RF} + z\_{LH}) \tag{30}$$

$$b\_{42}^{+} = (z\_{RF} - z\_{LH})^2 + 2\mathbf{x}\_{RF}^2 - 2\mathbf{x}\_{LH}\mathbf{x}\_{RF} \tag{31}$$

$$\mathbf{A} = (\mathbf{x}\_{RF} - \mathbf{x}\_{LH})^2 + (z\_{RF} - z\_{LH})^2 \tag{32}$$

The Jacobian matrix in Equation (16) can be written as follows:

$$J\_G = \begin{bmatrix} J\_F & \mathbf{0} \\ \mathbf{0} & J\_H \end{bmatrix} \tag{33}$$

In Equation (33), *JF* and *JH* are the Jacobian of the RF and LH legs respectively.