Novasinergia 2025, 8(1), 19-32. https://doi.org/10.37135/ns.01.15.08 http://novasinergia.unach.edu.ec
Artículo de Investigación
Análisis estructural y cinemático del prototipo de una mesa plegable de
trabajo
Structural and kinematic analysis of the prototype of a folding work table
Isaac Simbaña1, Alexander Tirado2, Anderson Arias2, Xavier Vaca3
1Grupo de Investigación en Ingeniería Mecánica y Pedagogía de la Carrera de Electromecánica (GIIMPCEM), Instituto Superior
Universitario Sucre, Quito, Ecuador, 170601;
2Carrera de Tecnología Superior en Electromecánica, Instituto Superior Universitario Sucre, Quito, Ecuador, 170601;
3Grupo en Ingeniería, Productividad y Simulación Industrial (GIIPSI), Universidad Politécnica Salesiana, Quito, Ecuador, 170702;
michael22tirado@gmail.com; andersonarias2907@gmail.com; xvaca@ups.edu.ec
*Correspondencia: isimbana@tecnologicosucre.edu.ec
Citación: Simbaña, I.; Tirado,
A.; Arias, A. & Vaca, X., (2025).
Análisis estructural y
cinemático del prototipo de
una mesa plegable de trabajo.
Novasinergia. 8(1). 19-32.
https://doi.org/10.37135/ns.01.
15.08
Recibido: 10 abril 2024
Aceptado: 06 septiembre 2024
Publicado: 08 enero 2025
Novasinergia
ISSN: 2631-2654
Resumen: En esta investigación, se propuso el diseño de
una mesa plegable para el aprovechamiento de espacio en
un taller. Se utilizó un software CAD para el modelado 3D
de cada elemento estructural y el desarrollo del análisis
estático de la mesa sometida a una carga distribuida
establecida, al colocar como apoyos fijos al área de
contacto entre el suelo. Mediante la resolución del método
de elementos finitos por simulación computacional, se
generó un mallado con 390 558 elementos y 497 625 nodos,
con una calidad de malla excelente al alcanzar un
skewness de 0.2234, donde se obtuvo un esfuerzo de
209.36 MPa, consiguiendo un factor de seguridad de 1.84
al utilizar acero ASTM A36 como material. El estudio se
complementó realizando la configuración de restricciones
y desplazamientos para presentar una simulación
cinemática del rango de movimiento de la mesa, de esta
manera, se validó el diseño del prototipo de mesa plegable
propuesto.
Palabras clave: Análisis Estructural, Análisis Numérico,
Cinemática, Estructura plegable, Simulación.
Copyright: 2025 derechos
otorgados por los autores a
Novasinergia.
Este es un artículo de acceso abierto
distribuido bajo los términos y
condiciones de una licencia de
Creative Commons Attribution
(CC BY NC).
(http://creativecommons.org/licens
es/by-nc/4.0/).
Abstract: In this investigation, a folding table was proposed to
optimize space utilization in a workshop. Utilizing computer-
aided design (CAD) software, we performed 3D modeling for
each structural element and conducted a static table analysis
under an established distributed load. Fixed supports were
strategically placed at the contact area with the floor. Through
computational simulation using the finite element method, a
mesh consisting of 390 558 elements and 497 625 nodes was
generated with an excellent mesh quality, characterized by a
skewness of 0.2234. The analysis revealed a stress of 209.36
MPa, resulting in a safety factor of 1.84 when utilizing ASTM
A36 structural steel as the material. To further validate the
design, constraints, and displacements were configured, and a
kinematic simulation was conducted to showcase the table's
range of motion. This comprehensive study confirms the
feasibility of the proposed folding table prototype.
Keywords: Structural Analysis, Numerical Analysis,
Kinematics, Folding Structure, Simulation.
Novasinergia 2025, 8(1), 19-32 20
1. Introduction
The evolution of the industry prompts the adoption of novel strategies, incorporating
materials like structural steel for various applications (Ostergaard et al., 2020). In any
industry, ensuring safety and comfort in the work area is paramount, with special
consideration for confined spaces that demand meticulous organization (Schrogl et al.,
2020). Folding structures find utility in temporary facilities or those requiring relocation.
Comprising rigid elements interconnected by sets of nodes, these mechanisms facilitate
expandable and contractible movements. Typically, these nodes are positioned at the ends
of the elements, usually rigid bars, and occasionally at their midpoints, providing a certain
degree of freedom to the components (Yamaoka et al., 2019). Regarded as one of the most
efficient approaches, collapsible structures excel in terms of installation, transportation, and
functionality.
Bhooshan et al. (2020) conducted a comprehensive particle study on folding work tables,
highlighting their versatility as furniture adaptable to various environments, ranging from
office spaces to workshops. The standout feature of these tables lies in their foldability,
facilitating convenient storage and transport. Constructed with robust materials, these
tables ensure stability and durability. In idle moments, they efficiently fold up, minimizing
spatial requirements, an especially advantageous trait in constrained environments. Cruz
(2019) affirms that there are several design methodologies for folding structures, suggesting
the potential development of traction graphical methods to enhance motion control
simulations. Addressing challenges like the intersection problem during the folding and
unfolding process necessitates employing thickness adaptation techniques in the design
field. Resolving such issues is imperative for advancing prefabricated structural systems.
The overarching goal of designing folding structural systems is to optimize limited space,
involving comprehensive studies on the materials used. Furthermore, proposing innovative
folding techniques inspired by improvements in people's daily lives is a valuable avenue
for exploration (Epp, 2020).
Preedawiphat et al. (2020) conducted mechanical investigations on A36 structural steel, an
alloy composed of iron and carbon with a percentage ranging from 0.8 to 2 %. This low-
alloy steel is extensively utilized in construction and various industrial applications,
meeting the specifications set by the American Society for Testing and Materials (ASTM).
Due to its alloy composition, A36 structural steel exhibits a remarkable capacity to support
structures in diverse spaces where its use is required. Carneiro et al. (2019) delved into the
service life and properties of A36 structural steel, highlighting its tensile strength of 400
MPa. Known for its commendable weldability and formability, A36 structural steel is well-
suited for a variety of applications. Beyond its common use in structures like buildings,
bridges, platforms, and other infrastructure, it finds application in manufacturing
machinery and equipment components, such as beams, plates, and structural sections. The
combination of versatility, strength, and ease of forming renders it a favored choice in the
construction and manufacturing industry.
Computer-aided design (CAD) serves as a versatile tool across various engineering
domains. Specifically, architectural modeling software within the CAD framework is
Novasinergia 2025, 8(1), 19-32 21
employed for the creation and modification of three-dimensional and two-dimensional
models representing real-world objects. In a study by Erazo-Arteaga (2022), the focus was
on investigating computer-aided design and digital manufacturing methodologies in
product development within the Latin American context. CAD software facilitates the
virtual construction and modification of new parts or products swiftly, eliminating the need
for physical prototypes. This tool significantly expedites work processes, concurrently
minimizing errors in the product design, thereby enhancing efficiency and overall quality.
Notably, designs created within the CAD platform can be stored and transported
electronically, facilitating easy manipulation and visualization at any time. On the other
hand, Computer-Aided Engineering (CAE), as defined by Khan & Rezwana (2021), serves
as a tool for creating and developing elements through comprehensive evaluations. These
evaluations span static, dynamic, fluid, thermal, electromagnetic, and acoustic analyses, all
performed using computers. In a study by Berselli et al. (2020), CAD and CAE tools were
scrutinized in the context of project-based learning, underscoring the importance of
studying mechanical devices in a parametric environment. This emphasis on education
aligns with its subsequent practical application in the industry.
Numerical analysis involves the exploration of algorithms that mathematically model the
numerical outcomes of problems across diverse domains of human knowledge (Benzi,
2021). Simulation, on the other hand, involves the emulation of the operation and evolution
of real-world processes or systems over time. From the perspective of numerical analysis
for the current millennium, Upadhyay et al. (2021) emphasize the extensive use of
simulation in industry. This approach enables the identification, development, and
controlled testing of the various processes integral to industrial operations. Furthermore,
modeling holds significant value in terms of repeatability, allowing identical or varied
launches in diverse executions. A design analysis system, as outlined by De Holanda et al.
(2019), offers simulation solutions encompassing linear and nonlinear statics, frequencies,
bending, thermal conditions, fatigue, pressure vessels, buckling, dynamics, as well as linear
and nonlinear optimization and analysis. Complementing this, computer-aided design
plays a pivotal role in generating 2D drawings and 3D parts and assemblies. It provides an
extensive toolkit spanning all stages of the product improvement process, inclusive of
design, simulation, manufacturing, publication, and back-end document design (Charmi et
al., 2021).
Keshavan (2022) defines a folding structure as a mechanical system, consisting of
interconnected elements with movable joints that transform velocities, trajectories, and
forces into energies. Within this mechanical system, rigid or semi-rigid elements form
mechanisms, where one component, typically the frame, remains fixed to prevent
movement. Movement occurs at joints, also known as kinematic pairs (McCracken et al.,
2020).
Foster-Vázquez et al. (2021) exemplify optimization in a hospital bed lifting mechanism by
modifying joints and links to reduce actuator force. In the context of folding structures, a
mechanism refers to the elements and connections enabling folding, unfolding, or
adjustments. Various joint types exist, with hinges allowing rotational movement between
structure parts being a primary example. Telescoping joints, enabling sections to slide into
Novasinergia 2025, 8(1), 19-32 22
each other, reduce the overall length when folded (Ramezani & Dietz, 2019). Accordion
folds represent a common mechanism, extending and contracting to fold or unfold the
structure. Engineering folding structures involves a diverse field encompassing creative and
functional solutions.
This investigation focuses on designing a folding work table, utilizing numerical analysis in
CAD software to improve workshop space utilization. The document is organized as
follows: the Methodology outlines the research stages, the Results section presents graphical
information from simulations, and the Conclusions section synthesizes and analyzes the
obtained results, explaining the scope of this work.
2. Methodology
The applied investigation approach was chosen as it aims to generate knowledge
directly applicable to problem-solving in the manufacturing sector (Canales et al., 2017).
This method was complemented by the analytical approach, viewing analysis as a mental
process that dissects complexities into parts and properties, facilitating the mental
deconstruction of the whole into its various relationships. Conversely, synthesis involves
uniting the analyzed parts and identifying relationships and general characteristics derived
from the analysis results (Falcón & Serpa, 2021). Subsequently, the analytical-synthetic
method was employed to address the primary research objective, which focused on
designing a folding table for optimal space utilization. In addition, computational numerical
analysis was applied to generate a 3D model and conduct simulations, encompassing
structural statics and kinematics of the folding table (Flores et al., 2019). The design required
a kinematic analysis of displacement and translation in the components of the table
mechanism. In the case of simple rotational motion, the angular position (θ) of the link is
expressed as a function of time (t) by equation (1) as indicated by Ouyang et al. (2021):
(1)
Where, θ0 and ω0 represent the initial angular position and angular velocity, respectively,
while α denotes the constant angular acceleration. Furthermore, the angular displacement
(Δθ) is defined as the change in angular position between two points in time. This
displacement is determined by integrating equation (2) of angular velocity concerning time:
(2)
It is clear that to analyze trajectories and displacements effectively, it must begin by
determining the speed at which the link moves. Angular velocity is thus defined as the rate
of change of angular displacement concerning time, while angular acceleration represents
the rate at which this angular velocity changes over time. Equations (3) and (4) have been
applied by Ochilovich & Sadirovich (2022) to conduct the analysis:
(3)
Novasinergia 2025, 8(1), 19-32 23
(4)
The degrees of freedom represent the minimum number of independent generalized
velocities necessary to define the kinematic state of a mechanism or mechanical system. This
quantity corresponds to the number of equations required to describe the motion. For two-
dimensional mechanisms, where displacement exclusively occurs in those two dimensions,
the number of degrees of freedom (GL) is computed using the equation (5) as outlined by
Senapati & Chatterjee (2020):
(5)
Where n is the number of links, j1 and j2 correspond to the number of joints of 1 and 2 degrees
of freedom, respectively. It is imperative to establish the displacement range of the supports.
Given the design criterion for the table to exhibit an inversely constant angular trajectory,
the trajectory, expressed as a function of the table angle, as Ponsioen et al. (2020) determined
using equation (6):
(6)
Where θ0 and θf are the initial and final angle of the table, and φ0 and φf are the initial and
final angle of the motion, respectively. It's worth noting that hinge couplings were chosen,
as they enable rotational movement around a fixed axis. The restriction simply involves
ensuring the equality of angles between the connected links. Figure 1 illustrates the
schematic design of the prototype to be analyzed, incorporating the established dimensions.
Figure 1: 3D modeling and dimensions of the table.
This process involves numerical analysis, a scientific discipline dealing with the
construction, analysis, and application of computer methods to obtain a numerical or
approximate solution for a given problem. To predict the behavior of an element under
loads, the finite element method (FEM) is employed, a numerical technique for solving field
problems described by a set of partial differential equations (Abueidda et al., 2019). Within
mechanical engineering, FEM is extensively utilized to address structural, vibration, and
thermal issues. The procedure encompasses discretizing the element, creating a mesh that
Novasinergia 2025, 8(1), 19-32 24
divides the geometry into relatively small and simple units known as finite elements. These
elements are named to emphasize that they are small relative to the total size of the model,
rather than infinitesimally small (Yu et al., 2021). When working with finite elements, the
software utilizes a set of simple solutions for individual elements to approximate the
desired solution, such as load or stress, for the entire model. In Figure 2a, the meshing of
the element is illustrated, featuring dominant tetrahedra chosen for their adaptability to
special geometries and showing a detail. Figure 2b displays the mesh validation metrics. To
achieve an excellent mesh, Simbaña et al. (2024) specifies that the skewness must be below
0.25, indicating that the tetrahedra closely resembles the ideal shape. In this instance,
employing various meshing techniques resulted in an average skewness of 0.2234.
a)
b)
Figure 2: Meshing of the folding table, a) generated in the element, b) metric.
The proposal involves the development of structural static analysis, a method employed to
ascertain a structure's response to internal loads and forces. This analysis plays a crucial role
in engineering design, ensuring the safety of an element under specified loads (Seralathan
et al., 2020). A widely utilized technique in this context is load analysis, which entails
calculating forces and moments acting on a structure under static conditions. In this
analysis, the structure is considered to be in equilibrium. To address this, Slusarenko &
Rojas (2021) proposed equations (5) and (6):
(5)
(6)
Where F is the force in the x-axis and y-axis, and M is the moment. The Von Mises stress is
characterized as the uniaxial stress capable of producing equivalent distortion energy to the
actual combination of applied stresses. This approach enables the treatment of combined
multiaxial forces, encompassing both normal and shear stresses, s if they were pure axial
stresses (Wang et al., 2021). The calculation of the stress (σ) to which the structure is
subjected involves the application of equation (7):
(7)
Novasinergia 2025, 8(1), 19-32 25
Where F is the point load applied on the table and AT is the cross-sectional area of the
structure. The factor of safety establishes a relationship between the maximum allowable
stress for a given material and the stress value obtained during the analysis (Ruge et al.,
2022). The factor of safety (Fs) is determined using equation (8):
(8)
3. Results
Figure 3 illustrates the Von Mises stress values obtained in the simulation, with a
maximum recorded stress of 209 MPa. Fixed supports were positioned in the area where the
structure contacts the ground and a load of 200 kg was applied, accounting for the
simultaneous work of two individuals and the use of specific equipment or tools. A36
structural steel, with a minimum yield strength of 250 MPa and a tensile strength of 400
MPa, allows for an elongation of 20 % (Moreno-Pallares & Quinga-Morales, 2022). In this
instance, the stress of 209 MPa falls below the minimum yield strength for A36 structural
steel, indicating a positive outcome. This suggests that the material should be capable of
withstanding the applied load without undergoing permanent deformations. Nevertheless,
it is decisive to acknowledge that practical applications may introduce additional factors,
including structural design, loads, environmental conditions, and other relevant
considerations.
Figure 3: Static structural analysis on the folding table.
Unit strain serves as a metric for gauging the relative extension of a material under a load,
often expressed as a percentage (Gutiérrez Rodríguez et al., 2021). In Figure 4, the data
visualizes the values and locations of deformations occurring under the specified loading
conditions, with a maximum recorded unit strain of 1.46 %. This unit strain value, when
applied to A36 structural steel, is notably low and typically falls within the elastic limits of
the material.
Novasinergia 2025, 8(1), 19-32 26
Figure 4: Unit deformation under the determined loads.
The factor of safety is a critical measure in engineering and design, ensuring that a
component or structure can endure loads and service conditions without failure (Craig &
Taleff, 2020). Figure 5 illustrates the factor of safety obtained through simulation, reaching
a value of 1.84. This safety factor implies that the component is designed to withstand 1.84
times the maximum load it is expected to encounter when using A36 structural steel.
Consequently, the design exceeds the strict necessities for fulfilling its function, offering an
additional margin of safety. In the context of chair and table structures, a safety factor
should have a minimum value of 1.69. Thus, a higher value indicates greater component
strength, a crucial consideration in safety-critical applications.
Figure 5: Safety factor for the folding table.
Under typical conditions, operators commonly work individually, with it being rare to see
two people working together. Consequently, the load is defined as half the weight of a
person, along with a load of objects and tools placed at one end of the table, totaling 50 and
25 kg, respectively, with a combined point load of 25 kg. Figure 6 displays the stress results
obtained by applying these conditions to a structural support, reaching a value of 92.74 MPa,
which does not exceed the yield limit, thus confirming the table's structural integrity.
Novasinergia 2025, 8(1), 19-32 27
Figure 6: Stress analysis with a point load applied to a support.
Additionally, Figure 7a shows a maximum stress of 106.5 MPa when this point load is
applied under the same conditions at the edge of the foldable section. Figure 7b illustrates
how the table structure deforms, with a deflection of 1.27 mm, representing the most critical
point of the cantilever structure. This indicates a design that will not fail under the specified
conditions.
Figure 7: Analysis of applying a 75 kg point load on the table cantilever a) stresses, b) deformations.
Furthermore, an alternative design of the table was analyzed using a different material for
the supports. Aluminum was selected due to its density being approximately 2.5 times
lower than that of structural steel. Figure 8 presents the results of applying a distributed
load of 200 kg on the table surface with this modification in the material of the supports.
The yield limit for the selected aluminum is 503 MPa, and with a maximum stress of 312.6
MPa reached, a safety factor of 1.6 was obtained. By using aluminum for the supports, the
mass was reduced to 38.57 kg, making it 14% lighter than with steel. However, the economic
factor is significant, as costs increase with the acquisition of raw materials and the welding
processes for the supports.
Novasinergia 2025, 8(1), 19-32 28
Figure 8: Stress simulation using aluminum for structural supports.
Conclusively, the study was augmented with the kinematic analysis of the table, verifying
that the displacement of its components aligns with the specified trajectories. The
calculation began with determining the angular velocity, averaging approximately 1 rad/s,
under the premise that a relatively gentle motion should be maintained to prevent damage
to the mechanism and ensure user safety. Additionally, the motion assumed constant
acceleration, resulting in an angular acceleration of 0.1 rad/s². This factor accounted for the
influence of gravity, stemming from the weight of the components, which could affect
velocity but remained within the control of the user. Figure 9 illustrates the table design,
showcasing its folded configuration for storage and its fully unfolded state for utilization.
Figure 9: Design of the table, folded and functional.
4. Discussion
An essential aspect to consider, and the reason behind initiating the design, was the
complexity of the folding mechanism. While the primary alternative for space optimization
would be a rectangular table, its geometry proved challenging to divide into sections and
ensure proper coupling for laying completely flat. Furthermore, more structural elements
were needed, as it had to consist of at least four sections, thereby increasing the weight of
the designated area. Equally crucial, design parameters focusing on ergonomics were taken
into account, as explored by Ron et al. (2018), which analyzed height and usable area
dimensions for a work table. This information is significant since poor posture during
extended work periods is associated with various health issues and can also reduce work
performance, as detailed in the study by Cercado-Bajaña et al. (2021). As outlined by
Novasinergia 2025, 8(1), 19-32 29
Mínguez-García (2018) in their exploration of folding structures' impact on contemporary
design, the significance of incorporating a folding table lies in the ease of maneuvering these
mechanisms. With articulated joints linking the components, the structure gains flexibility,
facilitating straightforward transportation and storage, akin to the compact nature of an
umbrella when folded, yet providing substantial coverage when unfolded.
Furthermore, computer-aided design streamlines analysis via the finite element method,
enabling both 2D and 3D modeling, alongside various static and dynamic simulations. The
analytical approach and results presented in this study are juxtaposed with the
methodology adopted by Calvo-López et al. (2022), who investigated loads and stresses on
a CNC milling machine worktable. Additionally, to validate the derived values for the
permissible stress of A36 structural steel, computational numerical analysis conducted by
Páez-Redrován & Guerrero-Cuasapaz (2022) was referenced, yielding a relative error of
approximately 7 %. Thus, the necessity of employing folding mechanisms and designing
them using FEM is underscored, facilitating estimations closely aligned with reality and
offering predictive insights into the structure's behavior under specified conditions.
5. Conclusions
The significance and benefits of folding structures are underscored through a
synthesis of information gleaned from scholarly sources. While these structures facilitate
efficient operation within confined spaces, a design capable of withstanding specific loads
is imperative. For this study, a maximum load of 200 kg was chosen, factoring in the
combined mass of two individuals and the essential tools typically used in a mechanical
workshop. The design and modeling of the folding structure were executed using CAD
software, resulting in a 3D model with 390 558 elements and 497 625. This included the
distributed load and trajectory analysis definition, ultimately yielding a maximum stress
value of 209.36 MPa, utilizing a 38.1 mm circular pipe section. Through load analysis, the
utilization of a 38.1 mm (1 ½ in.) diameter round profile in A36 structural steel, with a yield
stress of 400 MPa, was determined. A static simulation was conducted to derive results for
the Von Mises stress and factor of safety. The design was validated as the Von Mises stress
fell below the maximum steel stress, and a safety factor of 1.84 was obtained, confirming
that the design withstood the established conditions. Lastly, the folding structure's design
was validated through kinematic, mobility, and trajectory analyses, affirming its capability
to be fully deployed for use and then retracted to reduce its space for storage.
Authors' contributions
In accordance with the internationally established taxonomy for the assignment of
credits to authors of scientific articles (https://casrai.org/credit/). Authors declare their
contributions in the following matrix:
Novasinergia 2025, 8(1), 19-32 30
Simbaña, I.
Tirado, A.
Arias, A.
Vaca, X.
Conceptualization
Formal analysis
Research
Methodology
Resources
Validation
Writing - revision and editing
Interest conflict
The authors must declare that there are no conflicts of interest of any nature or, failing
that, declare the type of conflict of interest that the author (or authors) has with this research.
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