Didactic models for active and inquiry-based learning of machines and mechanisms

Abstract

Didactic models are invaluable resources for teaching Machines and Mechanisms, a crucial subject in the Engineering curriculum. This work investigates the impact of various types of models on learning outcomes across different instructional approaches, from traditional to active and inquiry-based learning methods. We analyzed a range of didactic models used in a second-year Theory of Machines and Mechanism (TMM) course at EUSS School of Engineering in Barcelona over the past decade, including: i) mechanical models built with “Meccano” parts, 3D-printed models, and kits simulating “fairground attractions”, introduced in traditional teaching settings; ii) real machines and student-developed models used in in TMM courses based on the “Study and Research Path” (SRP) approach, and iii) advanced didactic machines, created by fourth-year students. We discuss the educational benefits provided by these models, considering aspects like the theoretical concepts they mobilize, their construction (by teachers or students), design flexibility, materials used, complexity, and realism. Additionally, we examine how these models enrich the Media and Milieu dialectics, promote the development of both technical and transversal skills, and present a range of advantages and challenges in each TMM context. Our findings offer valuable insights into how models enhance the teaching and learning experience in Machines and Mechanisms, guiding instructors in selecting appropriate models and instructional strategies based on course objectives, student characteristics, and contextual constraints.

Introduction

The study of Machines and Mechanisms is an integral part of the Engineering curriculum in universities worldwide. Its primary objective is to comprehend the operational principles of mechanical systems by employing appropriate analytical and numerical techniques. From a broader perspective, this field encompasses the study of mechanical systems in a state of equilibrium (statics) as well as the study of machine kinematics and dynamics. The concepts and analytical tools related to Machines and Mechanisms are typically covered in courses such as “Theory of Machines and Mechanisms”, “Mechanics Applied to Machines”, or more comprehensive courses on “Mechanics for Engineers”.^1–4 The contents of this matter is found in textbooks such as J.J. Uicker, G.R. Pennock & J.E. Shigley, ⁵ F. Beer et al., ⁶ W. Riley & W. F. Sturges^7,8 or L.G. Meriam & J.L. Kraige. ⁹

In the field of Mechanical Engineering, models of mechanisms have been employed since ancient times for design and analysis, as well as for educational purposes. Didactic models constitute a widely used teaching resource in various disciplines, including Architecture, Medicine, ¹⁰ Geology, ¹¹ and, of course, Engineering.^12–14 These models serve as valuable resources for educators, enabling the teaching of complex systems in a tangible and interactive manner. ¹³ By integrating theoretical concepts with practical applications, students can develop a more profound comprehension of the subject matter through hands-on exploration. ¹³

In the history of machine science and technology, models developed rapidly specially during the Industrial revolution. ¹⁵ In the second half of the nineteenth century F. Releaux created a set of mechanisms for didactic use through the Voigt company, obtaining global success. ¹⁶ In the same period, there were also local initiatives for the development of models of mechanisms such as the collection of mechanism at the University of Dresden, Germany, ¹⁷ or Bauman Polytechnic of Moscow. ¹⁸ Recently, M. Ceccarelly and M. Cocconcelli reviewed the historical development of mechanism models in Italy. ¹⁹ Many of these historical models used in universities, made of wood, followed the classification of the mechanisms as proposed by F. Reuleaux ²⁰ and subsequent elaborations.^16,21 The main models referred to linkage mechanisms, cams, gear trains, friction-based mechanisms, wedge mechanisms, screw mechanisms, belt and chain drives, mechanisms containing pressurizing medium and step mechanisms.

More realistic, iron models have been also used to show the complexity of a real machine rather than a specific mechanism. They are models with cutaways to reveal the internal components. These models have been often used e.g., to show the work of different sorts of engines. ²² More recently, the advent of 3D printing has made available the possibility to create light and cheap models to demonstrate the principles of work of mechanisms. ²³

In traditional teaching, models of mechanisms were primarily used for demonstration purposes only. The models aimed to provide students with a practical implementation of the theoretical designs previously introduced in the course, to help them understand the operation principles of the mechanisms. Consequently, the models merely represented an integration of the technical drawings in textbooks. This demonstrative use of models is closely tied to the prevailing teaching methodology of Machines of Mechanisms, which has often relied on masterclasses and analytical solving of numerous machine examples, occasionally supported by demonstration of machines with physical or virtual models. ²⁴

However, in recent decades, active learning methods—where students engage in hands-on, problem-solving, and open inquiry activities—have been shown to be effective in achieving a deeper understanding and in developing non-technical skills in Engineering education. ²⁵ Problem-based learning, project-based learning (PBL) or inquiry-based approaches have proved to be excellent teaching – learning tools to guide engineering students towards their future work in industry. Moreover, activities in which students explore real-world challenges foster the student's creativity ²⁶ and increase their motivation.^13,27

In particular, in recent years, Study and Research Paths (SRPs)^28,29 have been proposed as an enriching, inquiry-based learning approach. SRPs were initially developed within the Anthropological Theory of the Didactic (ATD),^30,31 as a research methodology to model the processes through which an individual or community gains knowledge about an initial question. The SRP starts when the community of study considers an open-ended question (Q₀). The search for an answer to this generating question entails performing different study and inquiry activities, using multiple approaches. This process leads to a sequence of questions-answers, which can be modelled as a “Q-A map”. The interactions between the students and the different information and validation resources, modelled by the “Media-Milieu” dialectics,^29,32 produce a broadening of the community of study's knowledge about a subject. In ATD, “Media” refers to all the tools and methods used to convey knowledge (such as textbooks, digital tools, software, and interpersonal interactions), while the “Milieu” encompasses the broader educational context (including e.g., physical environments, cultural and social contexts, and institutional structures). The term “dialectics” captures the dynamic, reciprocal influence between Media and Milieu, where each continuously shapes and is shaped by the other. Understanding this interplay is essential to comprehend how knowledge is taught and learned, especially when introducing new teaching resources and methods, or adapting existing ones to new circumstances.

Although SRPs were first developed as an anthropological modeling tool, they evolved into an interesting, active and inquiry-based methodology. They were first adopted in the field of Mathematics education,^33–36 but they have since been applied in other areas.^33–36 In recent years, we have reported the benefits of SRPs for learning subjects of the Engineering curriculum, such as Strength of Materials,^37–40 Mechanics of the Continuous Media, ⁴¹ Information and Technology Communications (ITC), ⁴² and General Chemistry. ⁴³ In particular, we highlighted the advantages of incorporating the SRP methodology in Theory of Machines and Mechanisms (TMM). The designed TMM course instructed through the SRP methodology revolved around the study of different machines and mechanisms in a car.^44,45

We consider that the learning of Machines of Mechanisms through models will be influenced by various factors, including the type model and how it is introduced in teaching. Concerning the type of models, different sorts of kits may be distinguished, depending e.g., on the theoretical concepts they incorporate; whether the models are provided by the teachers or constructed by the students themselves; the degree of freedom students have in designing the models, the materials used, the proximity of the models to real systems, their complexity, etc. Furthermore, we consider that the effectiveness of learning will be influenced by the level of student interaction with the machines, and whether students are limited to observing or engaged in active-learning activities.

Therefore, in this work, we extensively analyze how the type of model and its integration into different learning methodologies impact TMM knowledge and skills development. The specific research questions (RQ's) that we address are as follows:

RQ1. What are the different types of models that can be used for teaching Machines and Mechanisms across various instruction modes, ranging from traditional to active-learning methodologies?

RQ2. How do models enhance the learning of Machines and Mechanisms based on their usage? In particular, in each case:

RQ2.1. In which ways and to what extend are the Media and Milieu enriched?

RQ2.2. Which are the specific and transversal skills mobilized (e.g., creativity, problem-solving, teamwork, autonomous learning etc)?

RQ2.3. What are the additional educational advantages and challenges that arise?

To investigate these questions, we studied a large number of different sorts of didactic models used in the teaching of TMM at the Escola Universitària Salesiana de Sarrià (EUSS) School of Engineering in Barcelona over the last decade (2013/14–2022/23). We analyzed and compared the use of these models in different educational contexts. Namely, we scrutinized: i) didactic kits introduced in the context of a traditional course, in practical lab assignments or projects; ii) different sorts of models studied in the context of SRP inquiry and active-based learning courses and; iii) two different sorts of advanced didactic machines, designed and constructed by 4^th year students during their final Bachelor's degree project.

Methodology

Course context and participants

Our study is based on the analysis of over 1100 model kits implemented in TMM courses at EUSS School of Engineering between the academic years 2013/14 to 2022/23 (Table 1). TMM is a 6 ECTS-credits, mandatory course in the second year of the Mechanical, Electricity and Electronics Engineering degrees offered at EUSS. The course lasts 17 weeks, with two sessions of 2 h and 3 h per week. The course is organized in two main parts, including the following chapters: I. Statics (1. Vector analysis, 2. Forces and moments, 3. Equilibrium in 2D and 3D, trusses, 4. Framework structures, 5. Load distributions, 6. Friction), and II. Dynamics (7. 2D kinematics, 8. 2D dynamics and 9. 3D kinematics).

Table 1.

Summary of TMM course setting, the activities where models were implemented, the number of participants each academic year, as well as the model types and number of models analyzed.

Course setting	Level	Activities with models	Years	# Students	Model types		#Models
Traditional TMM course with practical lab sessions	2nd year	3 “Meccano” models (T1) + “Fairground” project (T2)	2013–2016 2013/14 2014/15 2015/16 2016/17	421 118 105 106 92	T1	“Meccano” models	602
		3 “Meccano” models (T1)	2017–2018 2017/18 2018/19	186 113 73	T2	“Fairground” machines	94
		2 “Meccano” models (T1) + 3D printed machines (T3)	2019–2022 2019/20 2020/21 2021/22 2022/23	197 55 68 74 92	T3	3D printed machines	241
TMM - SRP course	2nd year	Q0 – How do Machines and Mechanisms in a car work? (S1-S6) Q01 – Gear Q02 - Trunk / 2D car hood Q03 - 3D car hood / bike-holder Q04 - Car jack / van roof Q05 - Crankshaft kinematics Q06 - Crankshat dynamics / garage door Q07 – Car window elevator Q08 - Car crane	2018–2022 2018/19 2019/20 2020/21 2021/22 2022/23	139 24 20 29 25 41	S1	Real machines	74
					S2	Real machines adapted for didactics	4
					S3	Toys	8
					S4	Commercial didactic models	3
					S5	Models using building blocks	28
					S6	Self-developed with own materials	54
Final Degree projects	4th year	Machines for TMM didactic purposes	2022–2023	1	F1	Chained effect machine	1
				1	F2	Garage door model	1

We analyzed the educational use of machine models introduced in various instruction modes, where students had different degree of autonomy of work. Table 1 summarizes the courses analyzed, learning methodology and number of participants in each case.

We first considered traditional TMM courses, where models were incorporated within laboratory assignments. From the academic years 2013/14 to 2018/19, this practical work involved studying various mechanical models built with commercial “Meccano” metal construction pieces, following the steps outlined in a guided lab script (see Supplementary Information (S.I.), section S1). Additionally, during the academic years 2013/14 to 2016/17, students were proposed to design, build and analyze models that mimicked a “fairground” attractions (see S2). Second, we analyzed models developed and studied in active, inquiry-based SRP-based TMM courses. In these courses, the entire six-month period was centered around a broad guiding question, “Q₀ – How do machines and mechanisms in a car work?” This approach led to the exploration of various sub-questions (Q_0i) about real systems found in cars, utilizing all available learning resources.

Finally, we examined two different model machines designed, constructed and analyzed with a larger degree of autonomy by 4^th degree Mechanical Engineering students as part of their Final Degree Projects. The aim of these projects was to prospect the didactic potential of different models for future use in second-year TMM courses. They provided insights into how effectively the models support learning and engage students through various approaches, while also serving as pilot experiences to refine their application across different teaching methods. The students were mentored by a TMM teacher and defended their work in the 2022/23 academic year.

Data collection and analysis

To address our research questions, we gathered a variety of quantitative and qualitative data. In the case of Machines and Mechanisms taught through the traditional methodology, we analyzed the students’ reports submitted after each laboratory practical work. These reports were written in response to guided scripts (see S.I., sections S1 to S3). Additionally, we considered the teachers’ observations of the students’ work during the practical sessions. In years where a “fairground” project was required, we scrutinized the models presented, accompanying posters, and the teachers’ grading and annotations recorded during the poster sessions (see S2.2).

In the case of TMM instructed through SRP methodology, we examined the different sorts of model Machines and Mechanisms utilized by the students through the course. Each year the course was organized around 6–8 different Q₀'s. We analyzed the students’ productions (the written reports, so-called “Outputs”, delivered by each group after tackling each of the Q₀'s). We also considered the teacher's observations about the individual and collective work of students during 26 sessions per year. These notes were written by the teacher during the sessions on a ‘class diary’ sheet. We also considered the results of a survey, including questions about the practical nature of the SRP course (see S5). Moreover, qualitative information about the students’ perceptions during the SRP were obtained through interviews to 25 participants during one of the academic year 2018/19. ⁴³

Finally, in the case of the model kits prepared by Final Degree Project students, we examined the constructed models, the teacher's notes during the tutoring, the students’ thesis and their oral defense.

Results

Table 1 provides an overview of the various courses analyzed, and the main types of didactic models utilized in each course. To address our two research questions, for each TMM setting we first analyze the mechanical models, which have been categorized based on the type of mechanism and the concepts they represented, their construction (by the teacher or student), the materials used, and their realism and complexity. Additionally, we analyze the collected data to assess modifications in the Media-Milieu and the technical and transversal skills mobilized for each course setting and model used. We also discuss the advantages and challenges encountered in each case.

Traditional TMM teaching with practical work

T1. “Meccano” models: in academic years 2013/14 to 2018/19, the practical part of the course consisted on the study, following the steps of a guided lab script, of different kits built with “Meccano” pieces (see section S1). These were conceived by the teacher to complement the theory covered in class on specific chapters: Lab 1 consisted on the static analysis of Meccano cranes (Figure 1, T1a-b), to study vectors in the space, Free Body Diagrams (FBD) and pulleys. In Lab 2 students examined the truss structure of a different crane (Figure 1, T1c). Lab 3 consisted on the observation and analysis of the kinematics of a motor-actuated three-bar system (Figure 1, T1d). The model kits in these lab sessions represented the direct, practical implementation of an academic problem that students had previously learned to solve analytically, but as can be seen in Figure 1 (T1), they were far from realistic objects. The first two years, students were asked to construct the Meccano models by themselves, resembling the examples provided in the script, but each group had a different set of pieces in their lab box, and thus they had a certain degree of freedom in deciding how to build the model structures. During this process, students became conscious of how theoretical schemes on a drawing should look like in reality: for example, how to realize a rolling or a simple support, whether screws had to be fastened or not to represent link connections, different ways of implementing a similar FBD etc. These brought interesting debates within the students in the group, and interaction with the teachers. To fulfill the experimental part of the assignment, in Lab 1 and Lab 2 students had to measure the dimensions and draw schematic of the machines, making connections between how things look like in reality and how they are represented in a drawing. In Lab 3, in addition, they had to determine experimentally the angular speed of the bars and velocity of some points of the bar mechanism at certain instants of the movement, with the help of video recording. Then students were asked to compare these values with those obtained analytically using the compatibility equations and relative motion analysis tools learned in class (see section S1). The construction of the Meccano models developed the student's creativity, manual and engineering skills, as noted by teacher sessions’ observations. It is worth noting that at first, some students lacked the ability to assemble even simple structures. However, two practical problems arose: first, students did not always have the time to build the “Meccano” models and take the necessary measurements within the 2 h session, and second, the teachers found it time-consuming to guarantee every time that all the kit-boxes had the necessary pieces to construct the models. Therefore, since 2015 the crane models were directly provided by the teachers, and Lab 3 model was replaced by teacher-provided 3D printed machines (vide infra).

Figure 1.

Different types of mechanical models used in the traditional TMM courses with practical work analyzed: T1. Didactic “Meccano” models designed by the teacher; T2. Some examples of “fairground” projects (photo taken with permission of participants); T3. 3D printed machine models.

T2. “Fairground” models: from the 2013/14 to 2016/17 academic years, in addition to the three previously described labs, students were proposed to design, build, and analyze a model simulating a “fairground” attraction. They worked autonomously in groups of four. The assignment specified that the fairground model had to accommodate at least one passenger of the size of a “playmobil” doll, and had two include two degrees of movement, one of them being rotational (e.g., a “carousel”, involving a rotational and up-and-down movement; the “twister”, involving two, non-concentric rotational movements, etc), see S2.1. The models were fabricated outside the classroom. Students could choose to build up the model with Meccano pieces and motors, made available to them in the lab, during certain opening times, or use other alternative materials of their choice. Students had to deliver a video demonstrating the functioning of the model, and exhibited their projects during a collaborative, poster session (Figure 1, T2c). In the poster students had to explain the design of the fairground and how they achieved the two-fold degree of movement, the building of the attraction, the calculation of the velocity and acceleration of the “passenger” at a certain time of the movement, and improvement suggestions. The project and poster were assessed with the help of a rubric (see S2.2). Regarding the types of models presented, about 50% of the models were developed using the provided Meccano pieces and motors (Figure 1, T2a), while the remaining were fabricated using “Knex” (Figure 1, T2b) or recycled materials. Most of the designs did not mimic real fairground systems, but were rather implementations of 3D kinematics problems previously analyzed in class (similar to problems presented in Meriam textbook. ⁹ ) The students opted for a relatively narrow range of fairground designs, as they were cautious about making intricate designs that could present challenges during the analysis process. The project was mainly aimed to mobilize the student's knowledge on 3D kinematics. Students utilized solely the analytical tools learned in theoretical classes to determine the velocity and acceleration of the passenger. In addition, the project stimulated the students’ creativity, their fabrication skills, their ability to present and defend a project during a poster session, and teamwork. The Media and Milieu were expanded by peer interaction within the group, and discussions between students and with the teacher during the poster session. The “fairground” project offered several educational advantages that contributed to its effectiveness, such as a motivating learning environment and healthy competition among groups, as recorded by teachers’ annotations during the presentation of project and poster sessions. High levels of participation (94%), and excellent academic performance were recorded (the average score was 8.7/10). A disadvantage of the project organization was that educational teacher-student interactions occurred during the same poster session that served for the assessment, so there was no time for rectification, or way to grasp further learning progress.

Figure 2.

Simplified Q-A map developed in the SRP-based TMM course triggered by the question Q₀ - “How does a car window lift work?”. The question leads to the study of either a real or model car window, through experiments (left), simulation (center) and analytical calculations (right).

T3. 3D printed machine models: during years 2019/20 to 2022/23 the third Meccano lab assignment was substituted by the study of different model kits, designed and fabricated by the teachers by 3D printing. The models were aimed to mobilize the concepts about planar kinematics and dynamics previously learned in theoretical sessions. Five different motor-activated machines were prepared (Figure 1, T3): (a) a Maltese cross (also called Geneva unit), (b) a three-bar linkage saw, (c) a slotted bar and rack mechanism, (d) Jansen Legs, and (e) a rolling motion mechanism. Each pair of students analyzed a different machine during two separate 2-h lab sessions scheduled at the end of the semester. Following a guided script (see section S3), students were asked to: i) measure with the help of video-recording the speed and/or acceleration of certain parts of the machine, ii) simulate with “Working Model” (WM) software the motion, kinematics and dynamics of the machine, and iii) calculate analytically the velocity and acceleration of certain points of the machine, at given instants, using the theoretical tools learned in class. This practical work weighted a 15% of the total subject mark.

The Media and Milieu were enriched through the practical implementation of mechanical systems, providing students with hands-on experience that complemented their theoretical understanding. The practical assignment reinforced their knowledge of 2D kinematics and introduced the use of WM software for motion simulation and result verification. Additionally, this project fostered teamwork and improved reporting skills. The 3D printed models closely resembled the exercises taught in class and could be easily replicated for all groups. However, challenges emerged, including students’ unfamiliarity with the simulation program and difficulty in correlating theoretical concepts with experiments and simulations, as this methodology was introduced late in the course. The condensed course schedule, coinciding with exams from other subjects, added further strain.

Models studied in SRP-based TMM course

The SRP-based TMM course revolved around the generating question “Q₀ – How do machines and mechanism in a car work?”. This leit motiv led to inquiry about the functioning of different (Q_0i) real systems found in a car, such as: Q₀₁ – a gearshift lever, Q₀₂ – the equilibrium of a car hood, Q₀₃ – a car trunk / a bike rack, Q₀₄ – a car-jack, the pop-up roof of a van, Q₀₅ – the 2D kinematics, and Q₀₆ – 2D dynamics of a motor rod-crank system, Q₀₇ – a car window elevator system / wiper washer, and Q₀₈ – 3D kinematics of a car crane. The Q_0i questions were selected so as to: i) be linked to real machines in the car, ii) be either accessible, modelled or simulated in the laboratory; and iii) lead to the study of all the concepts of the course. Besides, each Q_0i sub-question was chosen so as to be potentially tackled through multiple approaches, including the study of the theoretical foundations behind the question, the analysis of similar problems, the search of information about the machine, the development of an analytical solution, the realization of computer simulations, the study of the real object at work, the construction of models, experimentation, consulting experts etc. ⁴⁴

The SRP-based course was typically structured in eight Q_0i study-blocks, each lasting two weeks, with the following structure: (i) at the start of each study-block the teacher introduced the Q_0i question and facilitated a brainstorming session to create a preliminary Q-A map of key questions. The teacher guided the discussion to ensure that students tackled all the relevant theoretical concepts; (ii) following this, working groups of five students were formed, where students examined the initial Q-A map, added new sub-questions, and determined their approach. During the sessions, students worked autonomously on the Q_0i questions and performed different types of tasks. The teacher circulated between groups, monitoring progress, team dynamics, offering assistance, and posing questions. Occasionally, the teacher provided explanations or worked through examples for the entire class; (iii) at the end of each study-block, groups presented a written “Output” report (structured as a sequence of Questions/Media used/Answers), summarizing their findings, see section S4. Assessment was based on the submitted “Outputs” (50%) and ongoing monitoring of students’ work (50%), evaluating both technical and transversal skills using rubrics. ⁴⁴

All SRP sessions took place in the Mechanical laboratory, a flexible environment equipped with tables, a blackboard, computers connected to Internet with engineering software installed (WM, Solid Works, CAD etc) and different materials and fab tools to build machines (e.g., Meccano pieces, a 3D printer, a milling machine and traditional laboratory tools).

The study of each sub-question led students to the study of the related theory, search for information from various resources (such as the Internet, books, and videos) about the machine's operation, and analyze the Q_0i machine (see Figure 2). Each group could choose to analyze a real object, a didactic model, and/or construct a self-developed machine. Additionally, they could study the machine using one or more of the following approaches: (i) observation and experimentation, (ii) simulations (using WM or other software), and/or (iii) analytical calculations. During the SRP, a rich variety of different model systems were analyzed, sometimes brought by the teacher, but must of the time proposed by the students. We discuss in the following the observed educational benefits and challenges observed during the use of these different types of models.

S1. Real machines: in some cases, students opted to directly study real objects. For instance, some students conducted measurements of the forces required to manipulate a gear (Figure 3, S1) or examined different types of car hoods and their supports. Engineering students, in particular, demonstrated high motivation to explore real machines as this provided a “sense” to the subject, as expressed in the course surveys. During interviews and surveys (see S.I., section S5), students expressed this positive feedback with comments such as: “It is a very good idea to base the course on real machines and see that what you study relates to real life”, “You learn how things in the real world work; what you learn is ‘tangible’”, “You learn how different mechanisms work,” and “I liked Engineering-oriented cases”. On average, 72% of students across the 2018/19 through 2022/23 courses indicated that machine-centered projects helped clarify the utility of TMM.

Figure 3.

Different types of mechanical model systems analyzed during SRP-based TMM courses. Top: S1. Real and, S2. Adapted machines and mechanisms; Middle: S3. Toys, S4. Commercial didactic machines; Bottom: Self-developed models using, S5. Different types of commercial construction elements (e.g., Meccano, Lego, Knex), and S6. Constructed using different materials, such as wood, cardboard, recycled materials, 3D printing.

Engaging with real machines through experimentation enhanced the students’ observation abilities, allowing them to grasp the true magnitudes of various machine parameters. Additionally, they honed their ability to simplify objects and make analytical approximations for studying them. Most often, the study of these real objects took place outside the classroom, utilizing measuring tools borrowed from the lab or constructed by the students themselves. A disadvantage of the real machines was that sometimes they were difficult to disassemble to explore their inside. Other students found them too complex to analyze in the given time, and opted for a simplified model.

S2. Real machines adapted for didactic purposes: an alternative option was to study a machine specifically modified by the teacher for didactic purposes. For instance, a “gear and crank” system from a motorcycle was selected, with a cross-sectional cut to show the motion of the bars (Figure 3, S2). This approach provided an intermediary solution between examining a real machine and constructing a model. It offered a close approximation to reality, allowing students to grasp the machine's functioning, and it could be studied within the classroom. However, this method required prior preparation by the teacher, and limited the availability to a single machine. Although it spared students the time of constructing a model, it was not frequently chosen, see Figure 4, due to the challenges of disassembling the machine and measuring complex-shaped components.

Figure 4.

Histogram summarizing the types of models studied in the SRP-based TMM courses between 2018/19 and 2022/23, as a function of the machine-related Q_0i question.

S4. Toys: sometimes, students chose to study a toy that resembled the real machine Q_0i, even though the former was not originally designed for educational purposes. For instance, some students examined the stability of toy car hoods, or the functionality of scissor jack elevators in toy garages (see Figure 3, S3). By utilizing this resource, students had to establish a connection between the abstract concept of a machine and the objects available in their surroundings. Notably, it was frequently observed that students maintained an emotional attachment to these objects, with which they had played during their childhood, and this factor contributed to their motivation.

S4. Didactic commercial models: in certain instances, students brought commercially available machines specifically designed for educational purposes to the classroom. For example, robotic arms with various degrees of movement were utilized for studying 3D kinematics (refer to Figure 3, S4). The advantage of these models was that they were already tailored for educational use, saving students time that would have been spent on constructing the machine, but it limited the development of their creativity skills. Students found these didactic commercial models motivating, enjoyable, and easily transportable for use in the classroom or at home. On the downside, not all of these models could be disassembled for analysis, and the availability of these models relied on the resources accessible to the group.

S5. Machines developed with commercial building blocks: students frequently constructed model systems using various types of building blocks, including Meccano pieces available in the lab, as well as their own collection of commercial construction pieces like Lego, Knex, or Plastidecan (see Figure 3, S5). This approach offered notable advantages in terms of versatility, allowing students to create a wide range of machines and fostering their creativity. It provided significant flexibility in designing models that could closely resemble real machines or be simplified versions. Moreover, it enhanced students’ engineering and building skills. They often embarked on multiple trials, repeatedly assembling and disassembling the machines until they found functional solutions. Another advantage of this approach was the ability to disassemble the pieces for making measurements (e.g., weighting the machine elements). However, the feasibility of this option was again subject to the resources available to the students.

S6. Self-developed machines, constructed with own material: (Figure 3, S6) it was quite common for students to opt for building simplified models of the Q_0i machine using a variety of materials such as cardboard, wood, ABS 3D printed pieces, and recycled materials. This approach offered several notable advantages, including fostering creativity, encouraging engineering skills, and providing an opportunity to utilize design programs like Solid Works. Moreover, prior to assembly, the individual pieces could be measured for later use in the analysis. Observations revealed that within each group, some students enjoyed the fabrication task while others were more inclined towards calculations, resulting in a natural division of roles. In some groups, roles were interchanged from one project to the next, but in cases where this did not occur, teacher intervention was sometimes required. It was also noted that the composition of the group and the unique abilities of individuals influenced the collective development of the machine: for example, some students contributed by designing components in Solid Works, or incorporating moving parts using Arduino. However, there were a few disadvantages to consider. The fabrication process required time, and it was somewhat dependent on the students’ access to resources such as fabrication tools and workshop facilities outside the classroom.

When faced with a specific Q_0i question, students were given the freedom to choose from the aforementioned S_i model approaches. Their decision-making process was influenced by factors such as time constraints, cost, availability of resources, and the ease of analysis. This fostered the development of their decision-making and planning skills. The analysis of their choices reveals that, depending on the nature of the Q_0i object, students tended to lean towards a particular type of model. The histogram shown in Figure 4 summarizes the distribution of model types employed for the study of the different Q_0i machines.

The analysis of the Media-Milieu dialectics reveals a significant expansion of resources utilized to generate, validate, and integrate knowledge within the SRP, surpassing those of the traditional course. To address the Q_0i questions, students engaged in a variety of study and inquiry activities, utilizing multiple sources of information. They conducted independent research on the Internet, studied theory from prepared materials, textbooks, and online resources. Problem-solving training was facilitated through textbooks, video tutorials, and teacher assistance. Working in sub-groups, students discussed and explained problems to enhance learning. Each group solved 10–15 problems per Q_0i case, presenting the results in the “Output”. Working Model software was used for 2D motion simulation, while Solid Works and CAD software aided in 3D modeling and schematics. Numerical calculations were performed using Excel or programmable calculators. To understand machine functioning, students measured forces and explored real-world examples or built their own models. The analytical, numerical, and practical analyses were interconnected, validating results through cross-checking with different media. Students engaged in rich discussions within and between groups, seeking expertise from teachers, higher-level students, family members, and engineers.

The SRP for this TMM course was specifically designed so as to combine the training of technical and other transversal skills. ⁴⁴ The analysis of the implemented SRPs shows how this methodology expanded and interconnected the technical skills acquired by the students. Beyond solving traditional machine problems analytically, as typically done in the traditional setting, students were introduced to a diverse array of machines, mechanisms, and their practical applications. They designed and constructed their own machines and analyzed them using both analytical and simulation methods. Moreover, the SRP proved to be effective in fostering various transversal competences among the students. This is demonstrated by the results of surveys conducted from 2018/19 through 2022/23 (see S.I., section S5), which align with the findings from interviews of the first SRP edition. ⁴⁴ Firstly, teamwork skills were emphasized and valued by the students, who recognized the importance of collaborating and coordinating with others. They appreciated the opportunity to distribute tasks, roles, and communicate effectively within the group. The SRP also fostered autonomous learning, with students encouraged to find answers independently using various sources beyond the teacher. The teacher's role shifted towards guiding students through questioning and providing hints rather than directly answering their questions. Problem-solving skills, including initiative, decision-making, and creativity, were actively practiced in the SRP. Students enjoyed the freedom to explore different resources and approaches to solve problems, which stimulated their creativity. The fabrication of model machines further encouraged their inventive thinking. Additionally, planning and project management skills were developed as students organized and managed their tasks, roles, and workload. They recognized the importance of effective project management, adjusting their work dynamics to avoid bottlenecks and inconsistencies. In fact, an analysis of the SRP-based TMM course using Failure Mode and Effect Analysis (FMEA) quality tool revealed that studying the theory associated to the Q_0i-machine, and planning adequately the different tasks were key for the successes of the project. ⁴⁵ The use of Q-A maps was found to be a valuable tool for organizing the project, distributing tasks, and gaining an overview of the inquiry process. Lastly, the SRP promoted orientation towards quality, as students were required to deliver high-quality “Output” reports based on specific criteria. Continuous feedback from the teacher allowed for ongoing improvement, resulting in progressively better outputs over time.

On the other hand, the SRP successfully transformed the study processes and addressed some problematic issues identified in previous traditional courses. ⁴³ One of the identified problems was the students’ lack of a ‘sense’ for the subject. The SRP shifted the focus of TMM towards understanding real machines, providing an intrinsic objective and enhancing student motivation. Indeed, in the interviews 80% of students expressed that the SRP helped them understand the purpose of TMM and its relevance to real-life applications. Furthermore, they appreciated the practical hands-on learning experience with real-world machines. Another identified issue was the overreliance on algorithmic problem-solving. In contrast, analysis of the SRP “Outputs” produced by students reveals that they encountered a wide range of diverse problems that could not be solved through a standard approach. In addition to traditional analytical methods, students tackled non-standard problems that required original thinking and the combination of different approaches. Regarding the prevention of knowledge atomization, examination of the Q-A maps and “Outputs” demonstrates that the Q_0i approach facilitated the integration of concepts typically found in separate chapters. For example, in the study of Q₀₃ (car hood), the concepts of equilibrium, distributed loads, and the center of mass were interconnected, promoting the integration of theory and practice.

Didactic models designed by final degree project students

We also analyzed two different didactic models developed by Final Degree Mechanical Engineering students. The objective of their projects was to design, construct and analyze a didactic mechanical model using a threefold approach (by calculations, simulation and experimentation), and to prospect its potentiality for learning TMM.

F1. Chain reaction machine: in this model, the initial release of a pendulum triggers the chain movement of a series of objects and mechanisms, in the following sequential order: there is a collision between balls, a pulley, a rolling ball on an inclined plane, a free fall, a crank-slider mechanism, gears, and a mechanism of bars with slots. ⁴⁶ The movement occurs entirely within the vertical plane. The model was aimed at learning the kinematics of these mechanical elements, very frequent in the field of Engineering. Although the specific theoretical elements were agreed in advance with the TMM teacher, the materials and the chained functioning of the machine was fully developed by the student. The mechanical elements are ordered in increasing degree of difficulty. Thus, the first elements mobilize theoretical notions typically studied in General Physics (particle kinematics and dynamics, elastic collisions, energy conservation), while the last ones involve concepts typically studied in TMM (planar kinematics and dynamics of rigid bodies and mechanical systems, bar systems, compatibility equations, relative motion and “dragging-relative” methods). The kinematics of each mechanical element of the model was analyzed by three methods (see Figure 5, F1): empirically (using video-recording), theoretically, using analytical calculations, and through WM simulations. Some of the elements afforded theoretical analysis by different approaches (e.g., by kinematic equations or energy methods). The Media and Milieu was expanded through the observation of the machines in motion, the experimental determination of the speed and acceleration of certain machine parts, and the use of WM to design the chained movement of the machine and validate the results of analytical calculations. Comparing the experiment with theoretical calculations helped the student realize about factors affecting real machines, such as friction or non-elastic collisions, which are often neglected in academic exercises. In addition, the gradual increase in the complexity of the elements allowed the student to get familiar with WM the simulation program and the threefold analysis approach. The “chain reaction machine” produces a highly attractive visual effect, and results playful and motivating, despite having no connection with real systems. We deem this model could be ideal for shaping a long-term practical assignment within a traditional-based TMM course.

Figure 5.

Didactic machines developed by final degree project students. Top: Chain reaction machine (F1). Each element is studied experimentally, through (a) video-recording, (b) analytically and (c) by WM simulations; Bottom: Garage door fabricated by 3D printing and controlled by Arduino (F2). (a) Research of garage doors in the market, (b) design in Solid Works, (d) theoretical analysis and (d) WM simulation.

F2. Garage door: the aim of this project was to develop a garage door model, using one of the mechanisms available in the market. ⁴⁷ Thus, after a research on different types of existing garage doors (composed of one or two blades; manually or motor actuated; including counter-weights or not; with lateral or vertical elevation etc), the student, in agreement with the tutor, decided to build the single-blade garage door shown in Figure 5, F2. This system closely resembles a typical linked-bar system. The project included the design in Solid Works, the fabrication of door elements by 3D printing, the development of the Arduino-activated endless screw mechanism elevating the door, and the resistance study of the most critical parts using Finite Element Method (FEM) simulations. Once constructed, the student analyzed the velocity and acceleration of the different parts of the door using three approaches (analytical calculations, WM simulations, experiments), and the forces and moments involved using the first two. The analytical study of the door, involving three linked bars (Figure 5, F2c), implied solving a system of 9 equations with 9 unknowns, for which the student developed an Excel-based matrix solver. We believe this model could be ideally integrated in an SRP-based TMM course, or alternatively, used as didactic support in a more traditional setting.

Discussion and conclusions

In the following section, we discuss the findings obtained concerning our two research questions.

RQ1. Which different types of models can be used for teaching Machines and Mechanisms across various instruction modes, ranging from traditional to active-learning methodologies?

We have shown that different types of models can be beneficially used for the learning of TMM across different settings. The employed models may be classified depending on the notions mobilized, whether they are student or teacher provided, the materials chosen, the closeness to reality of the model and its degree of complexity. The majority of utilized models were introduced in the course to reinforce theoretical notions on machine kinematics, which is considered one of the most challenging parts of the TMM curriculum.

It is worth mentioning the rather distinct way in which didactic models appear in the analyzed traditional and SRP instruction mode settings, as illustrated in Figure 6. In the traditional TMM course, theoretical knowledge and pen-and-paper problems are taught in the first place, and models are designed by the teachers to exemplify the work of particular mechanisms and reinforce concepts. Thus, usually there exists a univocal correlation between theoretical notions and the developed model-machine. The inclusion of other means of analysis, such as experimentation or simulation appear subordinated to analytical calculations (Figure 6(a)). On the contrary, in the SRP approach the real machines are at the center of the subject and provide a “raison d’être” (“sense of existence”) to the TMM course (Figure 6(b)). Within the Anthropological Theory of the Didactic (ATD), developed by Yves Chevallard, the term “raison d'être” refers to the fundamental purpose or essential reason behind the existence of an educational practice, content, or institution. ⁴⁸ The curiosity surrounding the operation of a machine prompts students to explore the underlying mechanisms of its functioning. This exploration involves experimentation with the machine and creating models to study its behavior in a simplified manner. With the guidance of a teacher, students delve into theoretical concepts, analytical techniques, and simulation tools, enabling them to comprehensively analyze the machine. We note also that the study of a particular machine often requires proficiency in various theoretical notions. (For example, tackling the Q₀₁ – gear question may involve concepts such as 3D vectors, forces, moments, and equilibrium). It is then the responsibility of the teacher to guide the students in narrowing down their focus within the limited time allocated for studying a specific topic, or breaking the trigger question in multiple study-blocks. For example, the question regarding the “connecting rod-crank” was typically divided in two sub-questions Q_0i, one focusing on the kinematics and another on the dynamics of the system.

Figure 6.

Schematics showing the introduction of models and connection with theoretical notions in (a) traditional TMM course setting with practical work, and (b) SRP-based TMM course.

Teacher-provided models provide targeted coverage of specific curriculum areas and can be prepared in advance or replicated in large quantities to ensure there are enough specimens for all students in the class. However, this approach often lacks opportunities for students’ creativity or the development of construction skills, and the models tend to be practical representations of academic examples already covered in class. Conversely, when students fabricate the models themselves, they engage in various tasks thereby fostering the development of a diverse range of technical and transverse competencies. Students engage in researching machine information, participate actively in the design and construction processes, exercise problem-solving abilities, and unleash their creativity. Having the freedom to create is highly motivating for Engineering students, as expressed in interviews. Throughout the process, we observed intriguing discussions among students as they worked towards finalizing their designs. They also honed their drawing skills by sketching their machine designs and developed their abilities in using design software, 3D printing, and construction techniques. Interestingly, imposing certain restrictions, such as creating a double-rotating movement with a single motor, served as catalysts for fostering creativity. The development of models also trained the students’ planning skills, as they were responsible for sourcing materials, and allocating time for both building and analyzing the machine. Model development often involves applying knowledge from various disciplines beyond TMM, such as Graphical Expression, Physics, Information Technology, and Strength of Materials. However, it is worth noting that managing this approach can pose additional challenges for the teachers, as they need to provide guidance and support to each group working on a unique object. In our experience, the SRP methodology applied to TMM should be limited to a cohort of maximum 20–25 students per teacher.

In terms of materials used, the teacher-designed models were created using either Meccano pieces (T1) or 3D printing (T3). The Meccano option presented the opportunity for students to construct the machines themselves, but it required significant time and effort to ensure the availability of the necessary pieces for all study groups. Additionally, the bulky nature of Meccano pieces made them sometimes incompatible with educational motors. On the other hand, 3D printing provided teachers with the advantage of producing dedicated models, easily actuated with low-power motors. However, this approach limited students’ creativity and building skills, as they were not actively involved in the fabrication process. Conversely, in the case of models developed within an active-learning context, such as the SRP-course (S1-S6), the “fairground” project (T2), and Final Degree projects (F1-F2), a wide variety of materials were utilized. These included commercial blocks, cardboard, wood, ABS 3D printed pieces, and recycled materials, among others. Notably, in the SRP-based TMM course, a diverse array of model designs emerged, showcasing the students’ creativity and resourcefulness.

When selecting a didactic model for teaching TMM, a dual relationship emerges between the model's proximity to reality and the complexity of its analysis, as depicted in Figure 7. On one end of the spectrum, the study of real machines (S1) greatly motivates Engineering students, as it provides a tangible sense of purpose. However, analyzing real machines often involves complexities that necessitate approximations, and involve consideration of factors such as friction or complex shapes. Real machines adapted for didactic purposes (S2) offer a good balance, reducing complexity while maintaining a close resemblance to reality. Within the SRP, a diverse array of models appeared, spanning from those closely resembling real machines to those further removed from reality, with associated levels of complexity (Figure 7). Meccano models (T1), 3D printed models (T3), and the components of the “chained effect machine” (F1) represent recreations of theoretical concepts encountered in theory, albeit being more distant from real machines. The complexity of these models ranged from simple static systems to moderately complex mechanisms with a maximum of three moving elements. The “fairground” (T2) and garage door (F2) models drew inspiration from existing real machines, igniting students’ motivation and inspiring exploration into their inner workings, although for obvious practical reason the models differed from their real-life counterparts. The complexity of the “fairground” models varied based on the students’ choice of movement degrees.

Figure 7.

Complexity versus proximity to reality (each rated on a scale from 0 to 10) of TMM mechanical models analyzed in this study.

RQ2. In which ways do the models improve the learning of TMM, depending on their usage?

The introduction of didactic models expanded the Media-Milieu across various TMM settings, though to varying extents depending on the teaching approach, as schematized in Figure 8. Here, ‘Media-Milieu expansion’ refers to the broadening of available resources and the increased diversity of ways students engage with them to learn. The integration of models (S1-S6) within the SRP methodology brings along the most extensive broadening of the Media and Milieu, involving activities such as researching real machine information online, utilizing various written resources, performing theoretical calculations using analytical and numerical procedures, designing models using different software tools, and participating in frequent discussions with teachers, external experts, and peers. The garage model (F2) and “chained effect” models incorporate all the aforementioned learning elements except peer discussion, as each machine was developed by a single Final Degree student. In the case of 3D printed models (T2), provided by the teachers, the learning environment was broadened by the comparison of analytical results with WM simulations and the experimental determination of instant speed and accelerations. The “fairground” models prompted the search of other machines on Internet, the design of prototypes as well as intragroup discussions. In fact, learning through peer discussion was reinforced in all activities conducted in groups. In the case of the practical work using Meccano models (T1), the learning environment was widened through model assembly, observation and experimentation.

Figure 8.

Increasing expansion of Media-Milieu in different practical TMM activities involving the study of didactic models.

Likewise, the incorporation of models into the learning process enhanced the acquisition of technical competences related to Machines and Mechanisms, as well as other essential transversal skills, depending on the instructional approach employed. In general, analytical tools were applied to comprehend the functioning of machines, but simulation programs were also utilized in many cases, for purposes such as validating analytical results, designing new machine prototypes, or examining the effects of varying machine parameters on performance. As mentioned earlier, approaches in which students themselves developed the models (SRP, “fairground” project, garage model and chained-effect machine) facilitated the development of their design and construction skills. Analytical and problem-solving abilities were nurtured through all activities involving models. Moreover, the SRP active-learning methodology particularly fostered the development of other transversal skills essential for future Engineers, including teamwork, autonomous learning, project management, and continuous improvement.

In conclusion, didactic models offer a multifaceted approach to learning about Machines and Mechanisms. By providing hands-on experiences, model kits bridge the gap between theory and practice, allowing learners to engage with the subject matter in a tangible way and gaining deeper understanding. Our study shows how the different types of models and the way they are introduced in instruction modes with different degrees of active-learning result in varying impacts on the expansion of the Media-Milieu, and the learning outcomes.

The results of our research provide valuable insights into how the utilization of models can enhance the teaching and learning experience in the field of Machines and Mechanisms. Our findings can assist instructors in selecting the most appropriate types of models and instructional approaches, taking into account the specific objectives of the course, the students’ characteristics and the contextual limitations imposed by the course, institution or circumstances.

While this study focuses on a TMM course, future research could explore the application of didactic models and SRP-based active learning in other Engineering disciplines, such as Electricity, Electromagnetism, and Electromechanics, which could also benefit from these approaches.

Supplemental Material

sj-pdf-1-ijj-10.1177_03064190241310053 - Supplemental material for Didactic models for active and inquiry-based learning of machines and mechanisms

Supplemental material, sj-pdf-1-ijj-10.1177_03064190241310053 for Didactic models for active and inquiry-based learning of machines and mechanisms by E Bartolomé in International Journal of Mechanical Engineering Education