# The Place of Descriptive Geometry in the Face of Industry 4.0 Challenges

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## Abstract

**:**

## 1. Introduction

- (a)
- The Purdue Spatial Visualization Test: Rotations (PSVT:R).
- (b)
- The Mental Rotation Test (MRT).
- (c)
- The Differential Aptitude Test: Space Relations (DAT:SR).
- (d)
- The Mental Cutting Test (MCT).

## 2. Materials and Methods

## 3. Results

#### 3.1. Study Case 1: Identification of Intersection Lines

#### 3.2. Study Case 2: Reinforcement or Nerve—Danilob Rib

#### 3.2.1. Option 1: Points A and C from the Ellipse Section Are Located on the Cylinder Top Base (Lid) Perimeter

#### 3.2.2. Option 2: Point B from the Ellipse Section Is Located on the Lid Perimeter

#### 3.3. Study Case 3: Bolt–Nut Head

#### 3.4. Study Case 4

- In view of the detailed engineering drawing, the different lines that are shown in the representations must be analyzed and questioned, along with their correspondence among the different views.
- Once the initial sketch or drawing has been analyzed and understood, the modeling of the part is carried out.
- After the modeling of the part, a detailed engineering drawing can be obtained, going from the 3D model to the 2D draft. Afterward, the 2D drawing needs to be “normalized”. The software gives a preview of the drawing, and further work needs to be performed by the user in order to choose the lines that have to be removed and those that need to be preserved, as well as any other line or symbol that should be added or changed to comply with the norm.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Rikalovic, A.; Suzic, N.; Bajic, B.; Piuri, V. Industry 4.0 Implementation Challenges and Opportunities: A Technological Perspective. IEEE Syst. J.
**2022**, 16, 2797–2810. [Google Scholar] [CrossRef] - Bajic, B.; Rikalovic, A.; Suzic, N.; Piuri, V. Industry 4.0 Implementation Challenges and Opportunities: A Managerial Perspective. IEEE Syst. J.
**2021**, 15, 546–559. [Google Scholar] [CrossRef] - Bakhtari, A.R.; Kumar, V.; Waris, M.M.; Sanin, C.; Szczerbicki, E. Industry 4.0 Implementation Challenges in Manufacturing Industries: An Interpretive Structural Modelling Approach. Procedia Comput. Sci.
**2020**, 176, 2384–2393. [Google Scholar] [CrossRef] - Franco, J.E.; Jiménez, J.A.; Hernández, S.; Bravo, M.G.; Camarillo, K.A.; Belman, C.E. Metodología Directiva de Las 4 Fases Para La Mejora y Migración Haci Ala Industria 4.0. DYNA
**2023**, 98, 228–233. [Google Scholar] [CrossRef] - Ninan, N.; Chacko Roy, J.; Rani Thomas, M. Training the Workforce for Industry 4.0. J. Homepage Int. J. Res. Soc. Sci.
**2019**, 9, 2249–2496. [Google Scholar] - Blanco Díaz, R.; Fontodrona Francolí, J.; Poveda Martínez, C. La Industria 4.0: El Estado de La Cuestión. Econ. Ind.
**2017**, 406, 151–164. [Google Scholar] - Morron Salmeron, A. Les Noves Tecnologies i el Mercat de Treball; Caixabank: Valencia, Spain, 2016; pp. 36–37. [Google Scholar]
- Frey, C.B.; Osborne, M.A. The Future of Employment: How Susceptible Are Jobs to Computerisation? Technol. Forecast. Soc. Chang.
**2016**, 114, 254–280. [Google Scholar] [CrossRef] - ICEMD. Instituto de Innovaciones ESIC Industria 5.0: Lo Que Significa y Sus Beneficios. Available online: https://icemd.esic.edu/knowledge/articulos/industria-5-0-lo-que-significa-y-sus-beneficios/#:~:text=La%20Industria%205.0%20es%20un,empresas%20diferenciarse%20de%20la%20competencia (accessed on 25 November 2023).
- Østergaard, E. Industria 5.0: La Nueva Era En El Sector de La Manufactura Mexicana. Available online: https://www.metalmecanica.com/es/noticias/industria-50-la-nueva-era-en-el-sector-de-la-manufactura-mexicana (accessed on 25 November 2023).
- Demir, K.A.; Döven, G.; Sezen, B. Industry 5.0 and Human-Robot Co-Working. Procedia Comput. Sci.
**2019**, 158, 688–695. [Google Scholar] [CrossRef] - Carro Suárez, J.; Sarmiento Paredes, S. El Factor Humano y Su Rol En La Transición a Industria 5.0: Una Revisión Sistemática y Perspectivas Futuras. Entreciencias Diálogos Soc. Conoc.
**2022**, 10. [Google Scholar] [CrossRef] - Molero Moreno, C.; Saiz Vicente, E.; Esteban Martínez, C. Revisión Histórica Del Concepto de Inteligencia: Una Aproximación a La Inteligencia Emocional. Rev. Latinoam. Psicol.
**1998**, 30, 11–30. [Google Scholar] - Guilford, J.P.; Lacey, J.I. Printed Classification Tests: Report No. 5.; US Government Printing Office: Washington, DC, USA, 1947; ISBN 2021993590. [CrossRef]
- McGee, M.G. Human Spatial Abilities: Psychometric Studies and Environmental, Genetic, Hormonal, and Neurological Influences. Psychol. Bull.
**1979**, 89, 889–918. [Google Scholar] [CrossRef] - Sorby, S.A. Developing 3-D Spatial Visualization Skills. Eng. Des. Graph. J.
**1999**, 63, 21–32. [Google Scholar] - Tartre, L.A. Spatial Orientation Skill and Mathematical Problem Solving. J. Res. Math. Educ.
**1990**, 21, 216–229. [Google Scholar] [CrossRef] - Maier, P.H. Räumliches Vorstellungsvermögen: Komponenten, Geschlechtsspezifische Differenzen, Relevanz, Entwicklung Und Realisierung in Der Realschule; Europäische Hochschulschriften/6: Psychologie; Peter Lang: Frankfurt, Germany, 1994; ISBN 9783631478257. [Google Scholar]
- Vazquez, S.M.; Noriega Biggio, M. Razonamiento Espacial y Rendimiento Académico. Interdisciplinaria
**2011**, 28, 145–158. [Google Scholar] - Linn, M.C.; Petersen, A.C. Emergence and Characterization of Sex Differences in Spatial Ability: A Meta-Analysis. Child Dev.
**1985**, 56, 1479–1498. [Google Scholar] [CrossRef] - Parrot, C.A. Visual Imagery Training: Stimulatin Utilization of Imaginal Processes. J. Ment. Imag.
**1986**, 10, 47–64. [Google Scholar] - Campos, A.; González, M.Á.; Pérez-Fabello, M.J. Características de La Imagen Mental y Rendimiento Académico. Rev. Galego-Port. Psicoloxía Educ.
**2011**, 5, 149–154. [Google Scholar] - Campos, A.; González, M.Á. Vivez de Las Imágenes Mentales y Rendimiento Académico En Estudiantes de Bellas Artes, Ciencias y Letras. Rev. Latinoam. Psicol.
**1994**, 26, 69–81. [Google Scholar] - Espíndola Jaime, E.M.; Martínez Hernández, A.; Navarrete Hernández, J.; Rojas Ordaz, C.; Santana Colchado, S.; Monroy Hernández, E.J. Habilidades Mentales Primarias En Universitarios: Fortalezas Y Debilidades. Rev. Electrónica Psicol. Iztacala
**2018**, 21, 1342–1370. [Google Scholar] - Katsioloudis, P.J.; Jovanovic, V. Spatial Visualization Ability and Impact of Drafting Models: A Quasi Experimental Study. Eng. Des. Graph. J.
**2014**, 78, 1–11. [Google Scholar] - Tsutsumi, E. Mental Cutting Test Using Drawings of Intersections. J. Geom. Graph.
**2004**, 8, 117–126. [Google Scholar] - Sorby, S.A.; Drummer, T.; Hungwe, K.; Charlesworth, P. Developing 3-D Spatial Visualization Skills for Non-Engineering Students. In Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition, Portland, OR, USA, 12–15 June 2005; pp. 4047–4057. [Google Scholar] [CrossRef]
- Guay, R.B. Purdue Spatial Visualization Test; Purdue Research Foundation: West Lafayette, IN, USA, 1977. [Google Scholar]
- Peter, L. College Entrance Examination Board-CEEB Special Aptitude Test in Spatial Relations 1939; Harvard University: Cambridge, MA, USA, 1939. [Google Scholar]
- Monahan, J.S.; Harke, M.A.; Shelley, J.R. Computerizing the Mental Rotations Test: Are Gender Differences Maintained? Behav. Res. Methods
**2008**, 40, 422–427. [Google Scholar] [CrossRef] [PubMed] - Mohler, J.L. A Review of Spatial Ability Research. Eng. Des. Graph. J.
**2008**, 72, 19–30. [Google Scholar] - Sanjuán, J.M.; Robles, C.L.; De Paula Montes Tubío, F. Spatial Skills of Students in New Technical Degrees. Case Study at the University of Granada (Spain). EGA Rev. Expr. Graf. Arquit.
**2014**, 19, 264–271. [Google Scholar] [CrossRef] - Sanjuan, J.M.; Robles, C.L.; Gordo, J.F.R. Methods for Training the Spatial Skills Pursuing Technical Careers. EGA Rev. Expr. Graf. Arquit.
**2015**, 20, 278–287. [Google Scholar] [CrossRef] - Vandenberg, S.G.; Kuse, A.R.; Vandenberg, S.; Kuse, A. Mental Rotation, a Group Test of Three-Dimensional Spatial Visualization. Percept. Mot. Ski.
**1978**, 47, 599–604. [Google Scholar] [CrossRef] - Campos-Juanatey, D.; Tarrio, S.; Dopico, J.Á.; Campos, A. Habilidad de Los Estudiantes de Arquitectura Para La Rotación de Mapas Urbanos || Ability of Architecture Students to Rotate Urban Maps. Rev. Estud. Investig. Psicol. Educ.
**2017**, 4, 106–111. [Google Scholar] [CrossRef] - Chomanski, B. On the Relation between Visualized Space and Perceived Space. Rev. Philos. Psychol.
**2018**, 9, 567–583. [Google Scholar] [CrossRef] - Bodner, G.M.; Guay, R.B. The Purdue Visualization of Rotations Test. Chem. Educ.
**1997**, 2, 1–17. [Google Scholar] [CrossRef] - Rahmawati, Y.; Dianhar, H.; Arifin, F. Analysing Students’ Spatial Abilities in Chemistry Learning Using 3d Virtual Representation. Educ. Sci.
**2021**, 11, 185. [Google Scholar] [CrossRef] - Maturana Muñoz, H.F.; Curbeira Hernández, D. La Formación de Habilidades Espaciales Desde La Matemática En Los Estudiantes de Cuarto y Quinto de Básica Primaria. Rev. Conrado
**2018**, 15, 190–195. [Google Scholar] - Atit, K.; Power, J.R.; Veurink, N.; Uttal, D.H.; Sorby, S.; Panther, G.; Msall, C.; Fiorella, L.; Carr, M. Examining the Role of Spatial Skills and Mathematics Motivation on Middle School Mathematics Achievement. Int. J. STEM Educ.
**2020**, 7, 38. [Google Scholar] [CrossRef] - Hegarty, M.; Keehner, M.; Cohen, C.; Montello, D.R.; Lippa, Y. The Role of Spatial Cognition in Medicine: Applications for Selecting and Training Professionals. In Applied Spatial Cognition: From Research to Cognitive Technology; Psychology Press: New York, NY, USA, 2007; pp. 285–315. [Google Scholar]
- Langlois, J.; Wells, G.A.; Lecourtois, M.; Bergeron, G.; Yetisir, E.; Martin, M. Spatial Abilities of Medical Graduates and Choice of Residency Programs. Anat. Sci. Educ.
**2015**, 8, 111–119. [Google Scholar] [CrossRef] [PubMed] - Kalun, P.; Dunn, K.; Wagner, N.; Pulakunta, T.; Sonnadara, R. Recent Evidence on Visual-Spatial Ability in Surgical Education: A Scoping Review. Can. Med. Educ. J.
**2020**, 11, 111–127. [Google Scholar] [CrossRef] - Gittler, G.; Glück, J. Differential Transfer of Learning: Effects of Instruction in Descriptive Geometry on Spatial Test Performance. J. Geom. Graph.
**1998**, 2, 71–84. [Google Scholar] - Leopold, C.; Górska, R.A.; Sorby, S.A. International Experiences in Developing the Spatial Visualization Abilities of Engineering Students. J. Geom. Graph.
**2001**, 5, 81–91. [Google Scholar] - Suzuki, K. Activities of the Japan Society for Journalistic Studies. J. Geom. Graph.
**2002**, 6, 221–229. [Google Scholar] [CrossRef] - Sorby, S.; Gorska, R. The Effect of Various Courses and Teaching Methods on the Improvement of Spatial Ability. In Proceedings of the 8th International Conference on Engineering Design Graphics and Descriptive Geometry, Austin, TX, USA, 31 July–3 August 1998; pp. 252–256. [Google Scholar]
- Stachel, H. What Is Descriptive Geometry For; Institute of Geometry, Vienna University of Technology: Vienna, Austria, 2006; pp. 327–336. [Google Scholar]
- Bokan, N.; Ljucović, M.; Vukmirović, S. Computer-Aided Teaching of Descriptive Geometry. J. Geom. Graph.
**2009**, 13, 221–229. [Google Scholar] - Fleisig, R.V.; Robertson, A.; Spence, A.D. Improving the Spatial Visualization Skills of First Year Engineering Students. In Proceedings of the Canadian Design Engineering Network Conference, McGill University, Montreal, QC, Canada, 29–30 July 2004; pp. 10–11. [Google Scholar] [CrossRef]
- Di Paola, F.; Pedone, P.; Pizzurro, M.R. Digital and Interactive Learning and Teaching Methods in Descriptive Geometry. Procedia-Soc. Behav. Sci.
**2013**, 106, 873–885. [Google Scholar] [CrossRef] - Moreno, R.; Bazán, A.M. Automation in the Teaching of Descriptive Geometry and CAD. High-Level CAD Templates Using Script Languages. In IOP Conference Series: Materials Science and Engineering; IOP Publishing: Bristol, UK, 2017; Volume 245. [Google Scholar] [CrossRef]
- Kotarska Lewandowska, B. Between Descriptive Geometry and CAD 3D. J. Biul. Polish Soc. Geom. Eng. Graph.
**2018**, 31, 15–20. [Google Scholar] - Ilić, M.; Kosić-Jeremić, S.; Stavrić, M. Descriptive Geometry and Spatial Ability-Correlation and Mutual Impact at Engineering Students. Teh. Vjesn.
**2020**, 27, 2001–2007. [Google Scholar] [CrossRef] - Prado-Velasco, M.; Ortiz Marín, R.; García Ruesgas, L.; Del Río Cidoncha, M.G. Graphical Modelling with Computer Extended Descriptive Geometry (CEDG): Description and Comparison with CAD. Comput. Aided. Des. Appl.
**2021**, 18, 272–284. [Google Scholar] [CrossRef] - Papaz, D.; Jeremić Kosić, S.; Ilić, M. Impact of Descriptive Geometry on the Improvement of Spatial Abilities of Architecture Students. In Proceedings of the International Conference on Contemporary Theory and Practice in Construction XV, Banja Luka, Bosnia, 16–17 June 2022; pp. 181–190. [Google Scholar]

**Figure 1.**Drawings A1 and B1 correspond to raw CAD outcomes when going from 3D to 2D views. A2 and B2 refer to frequent mistakes made by students related to outer and inner intersection lines. A3 and B3 display the rightful form of the drawing depending on whether it relates to a semi-cut or total cut.

**Figure 2.**Perspectives showing the piece with a quarter cut or total cut, depending on the case. Red areas highlight the piece faces that generate the front lines the students tend to miss.

**Figure 4.**Misrepresentations of reinforcements. In (

**A**), the intersection line shown in the front view between the cylinder and the nerve would produce a different top view, where the top surface of the cylinder enlarges to meet the nerve; in (

**B**), the intersection line between the nerve and the cylinder is wrongly placed at the end of the horizontal diameter since it would originate a symmetric void space on each side of the horizontal axis that would change how the top view is displayed; in (

**C**), the end of the line that represents the nerve is wrongly located inside the top circular surface, which would remove part of the cylinder material at that point, showing an incomplete circumference of the cylinder top surface.

**Figure 5.**Ellipse section produced in a cylinder by an inclined plane. Points A, B, and C belong to the ellipse.

**Figure 6.**Resulting projections when A and C belong to the lid perimeter (top base of the cylinder).

**Figure 12.**Error caused by taking the distance between the hexagon opposite vertices as the diameter of the directive circle.

**Figure 13.**Correct modeling by taking the distance between faces (e/c) as the diameter of the directive circumference.

**Figure 16.**Capture and verification of points 1, 2, 3, etc., that belong to the intersection curves A, B, and C.

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## Share and Cite

**MDPI and ACS Style**

Ladrón-de-Guevara-Muñoz, M.C.; Alonso-García, M.; de-Cózar-Macías, Ó.D.; Blázquez-Parra, E.B.
The Place of Descriptive Geometry in the Face of Industry 4.0 Challenges. *Symmetry* **2023**, *15*, 2190.
https://doi.org/10.3390/sym15122190

**AMA Style**

Ladrón-de-Guevara-Muñoz MC, Alonso-García M, de-Cózar-Macías ÓD, Blázquez-Parra EB.
The Place of Descriptive Geometry in the Face of Industry 4.0 Challenges. *Symmetry*. 2023; 15(12):2190.
https://doi.org/10.3390/sym15122190

**Chicago/Turabian Style**

Ladrón-de-Guevara-Muñoz, M. Carmen, María Alonso-García, Óscar D. de-Cózar-Macías, and E. Beatriz Blázquez-Parra.
2023. "The Place of Descriptive Geometry in the Face of Industry 4.0 Challenges" *Symmetry* 15, no. 12: 2190.
https://doi.org/10.3390/sym15122190