# Project-Based Curriculum for Teaching Analytical Design to Freshman Engineering Students via Reconfigurable Trebuchets

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## Abstract

**:**

## 1. Introduction

#### 1.1. Project-Based Learning via Trebuchets

#### 1.2. Previous Pedagogical Use of Trebuchets

#### 1.3. Transition from Seminar-Based Course

#### 1.4. Curriculum Overview

- Rank the design variables from 1 to 4 in order of importance;
- Identify variable ranges (min and max) that you would like to test using the physical trebuchet kit for guidance;
- Plan for a budget of eight total experiments with suggestions for space-filling experiments.

- Perform three predefined tests and report the distance;
- Answer the following question: “What is a good finger angle when sling length is 26 in and the pivot location is 4 in? Why?” (which is a single variable optimization problem);
- Rank the design variables from 1 to 4 in order of importance (repeat from the DOE activity);
- Plan for a budget of six total experiments for field day #2;
- (optional) Test more designs at home.

- Review of both quantitative and qualitative results from all of the project activities, including analysis of experimental results;
- Comparison of variable rankings based on student intuition (before and after the modeling lab);
- Discussion on the effectiveness of the launch day movement policies and comparison with multi-agent modeling results;
- Exploration of a comprehensive data set based on the trebuchet model to more fully understand the trebuchet design problem and the complex tradeoffs involved;
- Discussion on the explicit reasons for why engineering students take math and engineering analysis courses and how these topics are directly useful in engineering practice;
- Asking students their definitions of engineering intuition and judgment, and how course activities influenced their understanding of these ideas;
- Discussion on the value and potential problems with using modeling and simulation in engineering practice;
- Engaging students in a discussion on what they learned about developing a systems perspective for engineering design;
- Review of a variety of strategies for engineering design, including their different levels of analytical rigor, as well as the role of human creativity across all design strategies.

#### 1.5. Learning Objectives

## 2. Reconfigurable Trebuchet Kits

- Reproducibility across trebuchet kits for fair comparisons and use with a computer model;
- Reconfigurable capability to support rapid student adjustment of design variables (under 5 min);
- Streamlined assembly process, enabling most student groups to complete assembly process in less than 40 min given written instructions, components, fasteners, and tools;
- Portability (two college-level students can transport them small distances);
- Durability (multiple years of use, rain/weather protection);
- Reasonable cost (approximately $150 per kit, including all materials, hardware, tools, and manufacturing tools).

## 3. Interactive Computational Models

#### 3.1. Design for Maximum Range through Physics-Based Modeling

^{®}and SimMechanics

^{TM}software. The software interface for this simulation model is shown in Figure 7. The goal of providing students with a computer simulation model is to help them experience directly the importance of model-based design in the overall design process. It helps them to develop more accurate intuition through rapid creative exploration of the design space, and demonstrates through experience the value of rapid simulations when striving to solve a design problem quickly [31], and to identify better designs than can be achieved through slower physical testing.

^{®}/SimMechanics

^{TM}. These software tools simplify the process of modeling a complicated multibody dynamic system. Engineers specify the physical properties of the system, and then the equations of motion are constructed internally. These equations are then solved by numerical simulation. Even though a great deal of care is taken to model the trebuchet system in the MATLAB

^{®}/SimMechanics

^{TM}with as much as accuracy possible, certain physical aspects cannot be captured with complete accuracy—such as nonlinear friction between mechanical components, air resistance, and minor manufacturing variations across kits. We have ongoing research into these areas to improve the model through computer vision and system identification.

#### 3.2. Process Model for Field Day Logistics

^{®}to model the students behavior during the field day activities. This model is introduced to the students before the physics-based SimMechanics

^{TM}model so that the students can get familiar with the field day logistics through the animation demonstrated in Figure 11b, while learning important modeling principles and considerations, such as assumptions, constraints, required data, performance criterion, and protocols.

- Assigned stations — Each team is assigned a station and they rotate with other teams assigned to the same station;
- Random stations — Teams join a random queue without any thought;
- Shortest queue — When teams are ready, they join a station with the shortest line.

^{®}model. Model parameter estimation was performed using data obtained during a mock launch day conducted by student volunteers not in the class. Model parameters were estimated from physical tests such as time to adjust specific trebuchet design variables, total time to launch the projectile when on the throwing station, projectile retrieval time for a given number of projectiles and course staff members, and walking speed of the student groups with the trebuchets (which can be determined from the simulation output page in Figure 11c). Under the conditions during fall 2014, it is seen that the assigned station protocol results in the largest total number of throws but with moderate variability in the distribution of throws between groups. The shortest queue had a slightly smaller total number of throws but more uniformity between the groups. The random queue was substantially worse than the other two.

## 4. Student Improvements in Trebuchet Comprehension and Engineering Judgment

#### 4.1. Setup

#### 4.1.1. Participants

#### 4.1.2. Instruments and Design—Four Course Activities

#### 4.2. Results and Discussion

#### 4.2.1. Design Variable Rankings

#### 4.2.2. Statistical Analysis of Field Day Launch Distances

- ${\mu}_{1}$: field day #1 launch distance (before model-based design activity);
- ${\mu}_{2}$: field day #2 launch distance (after model-based design activity and field day #1);
- ${H}_{0}:{\mu}_{1}={\mu}_{2}$; There is no difference between mean launch distances of day 1 and day 2;
- ${H}_{a}:{\mu}_{1}\ne {\mu}_{2}$; There is a difference between mean launch distances of day 1 and day 2.

#### 4.2.3. Qualitative Assessment of Student Reflections on Mathematical and Scientific Tools in Engineering Practice

How do mathematical and scientific tools, such as mathematical modeling and simulation, play an important role in engineering practice?

#### 4.2.4. Students vs. Optimization Algorithm

^{®}[36]. The other algorithm was gradient-free, namely patternsearch in MATLAB

^{®}[37]. Each data point in this comparison represents a distinct function call, i.e., a single execution of the trebuchet simulation (whether by student or optimization algorithm) for a unique trebuchet design. Optimization algorithm tolerances were loosened to allow faster termination, producing results that were better aligned with the number of tests performed by the students.

## 5. Conclusions

## Supplementary Materials

- Manufacturing instructions;
- Assembly instructions;
- Launch day instructions given to the students to help them understand the logistics and safety of the launch day;
- DOE activity assignment;
- Model-based design activity assignment;
- CAD files of the various trebuchet parts;
- Short video of the events.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- What is Project Based Learning (PBL)? Available online: http://bie.org/about/what_pbl (accessed on 20 February 2016).
- Solomon, G. Project Based Learning: The Primer. Tech Learn. Mag.
**2003**, 23, 20–26. [Google Scholar] - Pilot, A.; Bulte, A.M.W. The use of “contexts” as a challenge for the chemistry curriculum: Its successes & the need for further development and understanding. Int. J. Sci. Educ.
**2006**, 28, 1084–1112. [Google Scholar] - Mills, J.E.; Freagust, D. Engineering education—Is problem-based or project-based learning the answer? Australas. J. Eng. Educ.
**2003**, 3, 1–16. [Google Scholar] - National Science Foundation. Systemic Engineering Education Reform: An Action Agenda; Technical Report; National Science Foundation: Arlington, VA, USA, 1997. [Google Scholar]
- Tempelman, E.; Pilot, A. Strengthening the link between theory and practice in teaching design engineering: An empirical study on a new approach. Int. J. Technol. Des. Educ.
**2011**, 21, 261–275. [Google Scholar] [CrossRef] - Savage, R.N.; Chen, K.C.; Vanasupa, L. Integrating project-based learning throughout the undergraduate engineering curriculum. J. STEM Educ.
**2007**, 8, 15–27. [Google Scholar] [CrossRef] - Dym, C.L.; Agogino, A.M.; Eris, O.; Frey, D.D.; Leifer, L.J. Engineering design thinking, teaching, and learning. J. Eng. Educ.
**2005**, 94, 103–120. [Google Scholar] [CrossRef] - Hadim, H.A.; Esche, S.K. Enhancing the engineering curriculum through project-based learning. In Proceedings of the 32nd Annual Frontiers in Education, Boston, MA, USA, 6–9 November 2002; Volume 2.
- Silk, E.M.; Schunn, C.D.; Cary, M.S. The impact of an engineering design curriculum on science reasoning in an urban setting. J. Sci. Educ. Technol.
**2009**, 18, 209–223. [Google Scholar] [CrossRef] - Wallace, K. (Ed.) Educating Engineers in Design; Royal Academy of Engineering: London, UK, 2005.
- Frost, R.B. A converging model of the design process: Analysis and creativity, the ingredients of synthesis. J. Eng. Des.
**1992**, 3, 117–126. [Google Scholar] [CrossRef] - Daly, S.R.; Yilmaz, S.; Christian, J.L.; Seifert, C.M.; Gonzalez, R. Design heuristics in engineering concept generation. J. Eng. Educ.
**2012**, 101, 601–629. [Google Scholar] [CrossRef] - Carberry, A.R.; McKenna, A.F. Exploring student conceptions of modeling and modeling uses in engineering design. J. Eng. Educ.
**2014**, 103, 77–91. [Google Scholar] [CrossRef] - Basili, V.R.; Shull, F.; Lanubile, F. Building knowledge through families of experiments. IEEE Trans. Softw. Eng.
**1999**, 25, 456–473. [Google Scholar] [CrossRef] - Evans, J.R. Engineering Design: Search and Evaluation; Coherence and Correspondence; Intuition and Analysis. M.S. Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 2009. [Google Scholar]
- Papalambros, P.Y.; Wilde, D.J. Principles of Optimal Design: Modeling and Computation; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Brice, L.L.; Catania, S. A pedagogical trebuchet: A case study in experimental history and history pedagogy. Hist. Teach.
**2012**, 46, 67–84. [Google Scholar] - Leifer, J. An Active Learning Design Project for a Junior-level Kinematics and Dynamics Class. In Proceedings of the 32nd Annual Frontiers in Education, Boston, MA, USA, 6–9 November 2002; Volume 1.
- Jahed, H. Trebuchet Design; ME380 Project Manual; University of Waterloo: Waterloo, ON, Canada, 2006. [Google Scholar]
- Brannan, K.P.; Murden, J.A.; Stout, R.H., Jr. The Great Trebuchet Project. In Proceedings of the 2002 ASEE Southeast Section Conference, Gainesville, FL, USA, 7–9 April 2002.
- Leonard, K.M.; Mastromonico, J.J., Jr. Integrating Engineering Design Heuristics into a First Year Engineering Course to Enhance Problem Solving and Team Building Skills. In Proceedings of the 2007 International Conference on Engineering Education, Coimbra, Portugal, 3–7 September 2007.
- Kenefic, R.; Lin, F.; Aschliman, D. Integrated design and analysis for a trebuchet using a high speed photographic measurement system and MATLAB. In Proceedings of the 2006 ASEE Illinois-Indiana and North Central Joint Section Conference, Fort Wayne, IN, USA, 31 March–1 April 2006.
- Slater, J. Making math and science exciting through engineering sport: The wright state university trebuchet competition. In Proceedings of the 2008 ASEE Annual Conference and Exposition, Pittsburgh, PA, USA, 22–25 June 2008. Number AC 2008-2221.
- Constans, E.; Constans, A. Treb-bot: Development and use of a trebuchet simulator. Phys. Teach.
**2015**, 53, 347–348. [Google Scholar] [CrossRef] - English, L.D.; Hudson, P.; Dawes, L. Engineering-based problem solving in the middle school: Design and construction with simple machines. J. Pre-Coll. Eng. Educ. Res.
**2013**, 3. [Google Scholar] [CrossRef] [Green Version] - Allison, J. Trebuchet Range Simulation and Optimization; MATLAB Central: Natick, MA, USA, 2012. [Google Scholar]
- Forrester, A.; Sobester, A.; Keane, A. Engineering Design via Surrogate Modelling: A Practical Guide; Wiley: Hoboken, NJ, USA, 2008. [Google Scholar]
- Bonabeau, E. Agent-based modeling: Methods and techniques for simulating human systems. Proc. Natl. Acad. Sci. USA
**2002**, 99, 7280–7287. [Google Scholar] [CrossRef] [PubMed] - Fishman, G. Discrete-Event Simulation: Modeling, Programming, and Analysis, 1st ed.; Springer Science & Business Media: Berlin, Germany, 2013. [Google Scholar]
- Thomas, E.W.; Marr, J.; Walker, N. Enhancement of Intuitive Reasoning through Precision Teaching and Simulations. In Proceedings of the Frontiers in Education Conference, Atlanta, GA, USA, 1–4 November 1995; Volume 2.
- Siano, D.B. Trebuchet Mechanics. Available online: http://www.algobeautytreb.com/trebmath356.pdf (accessed on 20 February 2016).
- Goebel, R.; Sanfelice, R.G.; Teel, A. Hybrid Dynamical Systems. IEEE Control Syst.
**2009**, 29, 28–93. [Google Scholar] [CrossRef] - Breslow, L. Methods of Measuring Learning Outcomes and Value Added; Online Report; Teaching and Learning Laboratory: Cambridge, MA, USA, 2007. [Google Scholar]
- fmincon: version R2014a; The MathWorks, Inc.: Natick, MA, USA. Available online: http://www.mathworks.com/help/optim/ug/fmincon.html (accessed on 20 February 2016).
- patternsearch: version R2014a; The MathWorks, Inc.: Natick, MA, USA. Available online: http://www.mathworks.com/help/gads/patternsearch.html (accessed on 20 February 2016).
- Mathison, S. Why Triangulate? Educ. Res.
**1988**, 17, 13–17. [Google Scholar] [CrossRef]

**Figure 1.**Space-filling Latin Hypercube sampling plan with three variables and eight sample points [28].

**Figure 2.**Reconfigurable trebuchet kit. (

**a**) CAD drawing of trebuchet illustrating the four design variables; (

**b**) measuring conventions for finger angle and pivot position.

**Figure 3.**Photographs of a student toolkit and a trebuchet. (

**a**) toolbox and select tools for assembly and design variable readjustments; (

**b**) assembled trebuchet.

**Figure 4.**Drawings illustrating steps 1–3 in the assembly instructions. Step (1) involves fastening of casters to the trebuchet base. Step (2) illustrates attachment of upright shoulders to the base. Step (3) involves assembly of the pivot mechanism and attachment of the counterweights.

**Figure 5.**Drawings illustrating steps 3–6 in the assembly instructions. Step (4) illustrates how the finger assembly is to be installed. The throwing arm assembly is then attached to the trebuchet body via the fulcrum in Step (5). Step (6) shows how to attach the sling. The end of the sling cord with a loop is first slid over the finger (part F), and then the other end of the sling is threaded through the clamp mechanism (part E). This clamp mechanism allows rapid adjustment of sling length without the need to untie or tie knots, and also prevents sling cord damage.

**Figure 10.**Coupling between finger angle and sling length for two fixed pivot position values. (

**a**) ${x}_{3}\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}4.1$ in; (

**b**) ${x}_{3}=8$ in.

**Figure 11.**Field day logistics model built with AnyLogic

^{®}. (

**a**) parameter page; (

**b**) screenshot of live animation of the field day logistics model; (

**c**) simulation output page.

**Figure 14.**Student tests with computational model compared with optimization algorithms (both gradient-based and gradient-free).

Meeting | Week | Type | Name |
---|---|---|---|

1 | 1 | Hands-on | Trebuchet Assembly |

2 | 2 | Hands-on | Trebuchet Assembly and DOE Activity |

3 | 4 | Lecture | Process Design Overview |

4 | 6 | Hands-on | Field Day #1 |

5 | 7 | Lecture | Trebuchet Physics Overview |

6 | 7 | Hands-on | Model-based Design Activity |

7 | 8 | Hands-on | Field Day #2 |

8 | 11 | Lecture | Project Analysis and Reflection |

**Table 2.**Reconfigurable design variables for trebuchet kits, with lower and upper bound specifications.

Name | Type | LB | UB | |
---|---|---|---|---|

${x}_{1}$ | Sling Length | Continuous | 5 in | 35 in |

${x}_{2}$ | Finger Angle | Continuous | −40° | 40° |

${x}_{3}$ | Pivot Position | Continuous | 0 in | 8 in |

${x}_{4}$ | Wheels | Discrete | On | Off |

Variable | DOE Activity | MBD Activity | Instructor |
---|---|---|---|

Sling Length | 2.3 | 2.2 | 1 |

Finger Angle | 2.0 | 1.8 | 2 |

Pivot Position | 1.8 | 3.4 | 4 |

Wheels | 3.9 | 2.5 | 3 |

Quantity | $\overline{x}$ | σ | ${\text{SE}}_{\overline{x}}$ | 95% CI | T | ${D}_{f}$ |
---|---|---|---|---|---|---|

ΔRange (day 1 - day 2) | 15.652 | 38.745 | 3.298 | (9.130, 22.174) | 4.746 | 137 |

Source | Type III Sum Sq. | ${D}_{f}$ | Mean Square | F | p |
---|---|---|---|---|---|

Corrected Model | 90972${}^{a}$ | 45 | 2022 | 3.2 | 0 |

Intercept | 1152161 | 1 | 1152161 | 1827.0 | 0 |

Group | 40067 | 22 | 1821 | 2.9 | 0 |

Day | 25845 | 1 | 25845 | 41.0 | 0 |

Group × Day | 23328 | 22 | 1060 | 1.7 | 0.031 |

Error | 171530 | 272 | 631 | ||

Total | 1537276 | 318 | |||

Corrected Total | 262503 | 317 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Herber, D.R.; Deshmukh, A.P.; Mitchell, M.E.; Allison, J.T.
Project-Based Curriculum for Teaching Analytical Design to Freshman Engineering Students via Reconfigurable Trebuchets. *Educ. Sci.* **2016**, *6*, 7.
https://doi.org/10.3390/educsci6010007

**AMA Style**

Herber DR, Deshmukh AP, Mitchell ME, Allison JT.
Project-Based Curriculum for Teaching Analytical Design to Freshman Engineering Students via Reconfigurable Trebuchets. *Education Sciences*. 2016; 6(1):7.
https://doi.org/10.3390/educsci6010007

**Chicago/Turabian Style**

Herber, Daniel R., Anand P. Deshmukh, Marlon E. Mitchell, and James T. Allison.
2016. "Project-Based Curriculum for Teaching Analytical Design to Freshman Engineering Students via Reconfigurable Trebuchets" *Education Sciences* 6, no. 1: 7.
https://doi.org/10.3390/educsci6010007