A Web-based Tool for Generating Bond Graphs and Differential Equations for Mechatronic Systems

Pradeep Radhakrishnan; David C Brown; Margaret E Earnest

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Conference: 2025 ASEE Annual Conference & Exposition
Location: Montreal, Quebec, Canada
Publication Date: June 22, 2025
Start Date: June 22, 2025
End Date: August 15, 2025
Conference Session: Mechanics Division (MECHS) Technical Session 1B
Tagged Division: Mechanics Division (MECHS)
Page Count: 13
DOI: 10.18260/1-2--55411
Permanent URL: https://peer.asee.org/55411
Download Count: 11

Paper Authors

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Pradeep Radhakrishnan Worcester Polytechnic Institute

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Dr. Pradeep Radhakrishnan is an Associate Professor of Teaching in Mechanical Engineering and Robotics Engineering at Worcester Polytechnic Institute. Dr. Radhakrishnan teaches fundamental courses in mechanics and design at the undergraduate level.

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David C Brown Worcester Polytechnic Institute

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David Brown is a Professor Emeritus in the Computer Science Department of Worcester Polytechnic Institute. He specializes in Human Computer Interaction and the uses of AI in Computational Design.

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Margaret E Earnest Worcester Polytechnic Institute

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Abstract

Bond graphs were introduced by Henry Paynter to describe dynamical mechanical or electrical systems and generate differential equations. Constructing a bond graph requires understanding a few rules. A node in a bond graph is called an element and an edge is referred to as a bond. An element can be one of the following: a source of flow (Sf) or effort (Se); an I-storage element; a C-storage element; an R-element; a transformer TF junction; a gyrator GY junction; a 0-junction; or 1-junction. A source of flow or effort is used to represent applied load or velocity. An I-element is used to represent an energy storing inertia element while a C-element is used to represent an energy storing spring or related stiffness member. An R-element is used to represent energy dissipation in the system. Any velocity change is represented using the transformer TF junction and energy transformation is represented using the gyrator GY junction. Velocity junctions and voltage junctions are represented using 1 and 0 junctions respectively.

The paper describes a web-based tool for generating bond graphs and differential equations from user-constructed system diagrams. The application was built using Blazor WebAssembly. The web application also includes features such as differential equation generation, an undo-redo system, exporting URLs and an interactive tutorial. The tool is designed to act in a way that it mimics the method of teaching bond graphs in lectures and related textbooks. Students can use the tool to verify the bond graphs generated by them as well as the differential equations. The web application was tested in a senior level course, and students had a positive reaction to the application with many wishing they had been able to use it earlier in the course. We found that over 91% of users were satisfied with the process of creating the system diagram along with saving and opening the same. All other features earned positive reactions from at least 95% of users. URL generation had the highest satisfaction rate, with favorable reception from 100% of users. Most student dissatisfaction came small user interface, and backend bugs. Students also requested improvement of a few features, such as labeling system diagram elements with hover text, and asked that some features, such as panning the graph, be added to the tutorial.

The paper will describe the various features of the application, back-end algorithms as well as results from user studies.

Citation
Format

Radhakrishnan, P., & Brown, D. C., & Earnest, M. E. (2025, June), A Web-based Tool for Generating Bond Graphs and Differential Equations for Mechatronic Systems Paper presented at 2025 ASEE Annual Conference & Exposition , Montreal, Quebec, Canada . 10.18260/1-2--55411

TY - CPAPER
AB - Bond graphs were introduced by Henry Paynter to describe dynamical mechanical or electrical systems and generate differential equations. Constructing a bond graph requires understanding a few rules. A node in a bond graph is called an element and an edge is referred to as a bond. An element can be one of the following: a source of flow (Sf) or effort (Se); an I-storage element; a C-storage element; an R-element; a transformer TF junction; a gyrator GY junction; a 0-junction; or 1-junction. A source of flow or effort is used to represent applied load or velocity. An I-element is used to represent an energy storing inertia element while a C-element is used to represent an energy storing spring or related stiffness member. An R-element is used to represent energy dissipation in the system. Any velocity change is represented using the transformer TF junction and energy transformation is represented using the gyrator GY junction. Velocity junctions and voltage junctions are represented using 1 and 0 junctions respectively.

The paper describes a web-based tool for generating bond graphs and differential equations from user-constructed system diagrams. The application was built using Blazor WebAssembly. The web application also includes features such as differential equation generation, an undo-redo system, exporting URLs and an interactive tutorial. The tool is designed to act in a way that it mimics the method of teaching bond graphs in lectures and related textbooks. Students can use the tool to verify the bond graphs generated by them as well as the differential equations.
The web application was tested in a senior level course, and students had a positive reaction to the application with many wishing they had been able to use it earlier in the course. We found that over 91% of users were satisfied with the process of creating the system diagram along with saving and opening the same. All other features earned positive reactions from at least 95% of users. URL generation had the highest satisfaction rate, with favorable reception from 100% of users. Most student dissatisfaction came small user interface, and backend bugs. Students also requested improvement of a few features, such as labeling system diagram elements with hover text, and asked that some features, such as panning the graph, be added to the tutorial.

The paper will describe the various features of the application, back-end algorithms as well as results from user studies.

AU - Pradeep Radhakrishnan
AU - David C Brown
AU - Margaret E Earnest
CY - Montreal, Quebec, Canada
DA - 2025/06/22
PB - ASEE Conferences
TI - A Web-based Tool for Generating Bond Graphs and Differential Equations for Mechatronic Systems
UR - https://peer.asee.org/55411
DO - 10.18260/1-2--55411
ER -