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The engineering design process involves numerous steps that allow the engineer to reach his/her final design objectives to the best of his/her ability. This process is akin to creating a fine sculpture or a great painting where different approaches are explored and tested, then either adopted or abandoned in favor of better or more developed and fine-tuned ones. Consider the x-ray of an oil painting. X-rays of the works of master artists reveal the thought and creative processes of their minds as they complete the work. I am sure that some colleagues may disagree with the comparison of our modern engineering designs to art masterpieces, but let me ask you to explore the innovations and their brilliant forms, and maybe you will agree with me even a little bit.

Design Process

Successful design engineers must have the very best craft, knowledge and experience to generate work that is truly worthy of being incorporated in products that sell in the tens, or even hundreds, of millions. This is presently achieved by having cross-functional teams of engineers work on a design, allowing cross checking and several rounds of reviews, followed by multiple prototypes and exhaustive preproduction testing until the team reaches a collective conclusion that “we have a design.” This is then followed by the final design review and release of the product. This necessary and vital approach is clearly a time consuming and costly process. Over the years I have asked myself several times, “Did I explore every single detail of the design fully”? “Am I sure that this is the very best I can do?” And more importantly, “Does every component have the most fine-tuned value to render the best performance possible?” And invariably I am left with a bit of doubt. That brings me to a tool that has helped me in this regard.

A Great New Tool

I have used Maple for over 25 years to dig deeply into my designs and understand the interplay between a given set of parameters and the performance of the particular circuit I am working on. This has always given me a complete view of the problem at hand and solidly pointed me in the direction of the best possible solutions.

In recent years, a new feature called “Explore” has been added to Maple. This amazing feature allows the engineer/researcher to peer very deeply into any formula and explore the interaction of EVERY variable in the formula. 

Take for example the losses in the control MOSFET in a synchronous buck converter. In order to minimize these losses and maximize the power conversion efficiency, the most suitable MOSFET must be selected. With thousands of these devices being available in the market, a dozen of them are considered very close to the best at any given time. The real question then is, which one is really the very best amongst all of them? 

There are two possible approaches - one, build an application prototype, test a random sample of each and choose the one that gives you the best efficiency.  Or, use an accurate mathematical model to calculate the losses of each and chose the best. The first approach lacks the variability of each parameter due to the six sigma statistical distribution where it is next to impossible to get a device laying on the outer limits of the distribution. That leaves the mathematical model approach. If you take this route, you can have built-in tolerances in the equations to accommodate all the variabilities and use a simplified equation for the control MOSFET losses (clearly you can use a very detailed model should you chose to) to explore these losses. Luckily you can explore the losses using the Explore function in Maple.

The figure below shows a three dimensional plot, plus five other variables in the formula that the user can change using sliders that cover the range of values of interest including Minima and Maxima, while observing in real time the effects of the change on the power loss.

This means that by changing the values of any set of variables, you can observe their effect on the function. To put it simply, this single feature helps you replace dozens of plots with just one, saving you precious time and cost in fine-tuning your design. In my opinion, this is equivalent to an eight-dimensional/axes plot.

I used this amazing feature in the last few weeks and I was delighted at how simple it is to use and how much it simplifies the study of my approach and my components selection, in record times!

In this paper we will demonstrate the many differences of implementation in the modeling of mechanical systems using embedded components through Maplesoft. The mechanical systems are used for different tasks and therefore have different structure in its design; as to the nature of the used functional elements placed on them, they vary greatly. This diversity is reflected in approaches and practices in modeling.

The following cases focus on mechanical components of the units manufacturing and processing machines. We can generate graphs for analysis using different dynamic pair ametros; all in real-time considerations in its manufacturing costs from the equations of conservation of energy.
Therefore modeling with Maplesoft ensures the smooth optimum performance in mechanical systems, highlighting the sustainability criteria for other areas of engineering.



(in spanish)




Here the potential of maple 2015 to the quantitative study of the decomposition of a vector table is shown in two dimensions. Application for the exclusive use of engineering students, which was implemented with embedded components.


Lenin Araujo Castillo

Archivo Corregido:  Decomposició

My desk was covered with papers, a glass of water, and a big shipping container. Even though my chair was there, I was sitting on the floor with my laptop, having a bad hair day, and a robot was seated next to me.  This was a typical day at Maplesoft for an engineering co-op student.

For this project, at the request of my manager, I left my duties as Spanish translator and marketing assistant and I started to work with the robot NAO from Aldebaran Robotics. The purpose of this project was to program NAO using Aldebaran’s Choreographe software to make new movements and dances that I would later use to create new MapleSim models for Maplesoft’s Model Gallery. Maplesoft’s marketing team would then use these models in some of their promotional activities.

Given that NAO was going to travel to Taiwan in a short period of time, I wanted to focus on doing one elaborate dance and a couple of simple movements.Thanks to F.U.N. lab from the University of Notre Dame, I was able to focus on the detailed dance because they had an amazing Choreographe database of behaviour/movement code.   

I started this project with zero knowledge about Choreographe, but with a good understanding of NAO´s MapleSim model that the Maplesoft engineers had previously created. After a few weeks with NAO and some YouTube tutorials, I discovered that programming NAO was really easy. I would move NAO’s joints to the positions I wanted to, and then I would tap its head to record and save them. I did this for a couple of weeks making sure that the sequence of movements wouldn’t make NAO fall or break a finger. At this point I was already a NAO expert.

After finishing up all the movements and dances it was time to move on to the next phase of the project: obtaining the data for the MapleSim model. The MapleSim model was created using the Denavit-Hartenber (DH) convention; therefore, I needed the values of the degrees of rotation of each joint while the robot performed a dance. These numbers were easily obtained using the “record” button in Choreographe and exporting them into a CSV file. This file was later attached to the MapleSim model, so it could be used in a time look up table. The input of NAO´s joints were then specified by using the values within this table.

I started by recording the simplest movements: NAO blowing kisses and doing the sprinkler. These were the best ones to start working on because in these examples, the robot only needs to move its upper body, meaning that the lower body didn’t need any flexibility. This gave me and Abtin Athari, Application Engineer at Maplesoft, the freedom to simplify the original model by removing unnecessary degrees of freedom on the lower body. Abtin and I also realized that at the beginning of some of the new movements the robot would have too much torque, so we extended some of the recorded position of the rotational joints so the robot could stay in the same position for a longer time. These modifications ensured that the model wouldn´t have any problems during any of the simulations.

To finish the project, I worked with the Marketing team to create some videos where we could display the real robot next to the MapleSim model doing the same movements. The purpose of these videos was to showcase the essence of the high-fidelity models that MapleSim allowed us to create. It was amazing to see how the MapleSim model corresponded so closely to the physical robot.

After three weeks of intense work and meetings, my days as a robot whisperer ended. I learned new things about robots, how to build models with MapleSim, and the processes behind developing videos. It was a project that allowed me to wear both an engineer’s and a marketer’s shoes.  I was able to put into practice my technical knowledge and problem solving skills; and at the same time I was able to enhance my creative and analytical skills by evaluating the quality and impact of my work.

Hello, Currently when I calculate something, for example R=U/A where R is resistance, U is voltage and A is current, I get the answer in Volt/Ampere in stead of ohm. How do I change that?

Then, if the result is something like 3.124*10^-4 , how do I make maple output this in an engineering way, this would be 10^3, 10^6, 10^9 etc. to begin with?

Sorry if I formulate this wrongly, English is not my first language and I could not find an answer to this after some research.

Thank you


UPDATE and solution: for future reference:

You don't need to type out the whole unit like this:


in stead you can do this:


I got the V and A from the SI Units palette on the left hand side,


To answer my own question about the engineering notation, this can be "forced" by clicking on "Format" -> "Numeric Formating..." -> Engineering and then choosing the number of decimals. apply and set as default. After you are going to have to copy and recalculate your math as the !!! wont do it.

In this work the theme of vector analysis shown from a computational point of view; this being a very important role in the engineering component; in civil and mechanical special it is why, using the scientific software Maple develops interactive solutions for long processes through MapleCloud calculations. At present the majority of professors / researchers perform static classes open source leaves; so that our students learn and memorize commands, thus generating more time learning in the area. Loading Bookseller VectorCalculus develop topics: vector algebra, differential operators, conservative fields, etc. Maplesoft making processes provide immediate calculations long operation Embedded Components displayed in line with MapleNet integrations. Today our future engineers to design solutions and will be launched in the cloud thus being a process with global qualification in the specialty. Significantly Maple is a scientific software which allows the researcher to design their own innovations and not use themes for their manufacturers.







In this paper of presents under a totally modern sound environment dynamics; using embedded components that gives us the Cybernet Company through its product Maple 2015. Using classical techniques vector equations describe the particle, particle system and solid bodies. We note that the solutions o ered by this software motivate students civil and mechanical engineering to nd optimal answers. Integrating algorithms own programming language and solid mechanics using buttons we relate the movement of translation and rotation with reference to its center of mass.
Choosing envelopes graphical methods, functional programming and mathematical computer display modeling reached alternatives to achieve the next generation of engineers. Therefore this work show that the use of
embedded components allow us to merge the traditional and the computer; It means that all these equations using physical and propose viable criteria we perform in a dynamic sheet; which they have a number of components; then generate simulations with real objects.

Congreso COMAP 2015.pdf

Study of the Dynamics of the Solid with Embedded Components in Civil Engineering with

(in spanish)


For the past thirty years, I have used several mathematical packages for problem solving and graphing. It all started with spreadsheet software that really helped speedup calculations compared to calculators. As many people do, once I had one tool I then started looking for another that would offer even more capabilities and features. I tested several of the very early math software but none really did all that I wanted until I came across Maple while I was working at SPAR Aerospace in Canada. For me, the rest is history. As long as I had a copy of Maple, it was all that I needed.

On occasions when I did not have a copy of this amazing software, I resorted to spreadsheets once more to complete fairly large and complex projects involving large databases and large numbers of calculations, especially when performing What-If scenarios. One distinct disadvantage of using a spreadsheet was the cryptic form of equation writing. I had to divide one long equation into several sections in different cells and then add them all up, which clearly is not good for documentation of the calculations. It is also very confusing for other engineers to know what that equation is or what it does. The development of the full engineering spreadsheet took months to complete, debug and verify. During this process, when I had errors, it was often very difficult to track exactly where the problem was, making the debugging process time consuming and sometimes very frustrating.

Having worked with Maple before, I remembered how easy it was to enter equations in a very familiar, readable math format. The real power of this software is that it allows you to write the equation(s) anyway you like and solve for any given parameter, unlike spreadsheets where you have to solve the problem first, by hand, for the parameter you want and then get the spreadsheet to calculate the value. I remember one time a few years ago when I wrote nine or ten simultaneous differential equations all in symbolic form and asked Maple to calculate certain parameters in a fully symbolic form. To my utmost disbelief, the answer came back within few minutes. With results in hand, I was able to quickly finish my research, and the results were published at PCIM Europe 2005 in “Distributed Gate ESR and its Effect on Shoot Through Performance at the Die Level”. I would never have gotten the results I needed if I was using a spreadsheet.

Even with much simpler systems of equations, finding solutions with a paper and pencil was never an easy task for me. It took a very long time, and even then there was no guarantee that I did not make copying errors, accidentally leave out a term, or make a calculation error. After I found the correct solution, I then had the problem of plotting the results, which I often needed in 3-D. Plotting allowed much deeper insights into the interdependency of all the parameters and made it easy for me to concentrate on the important ones without wasting any time. I was very happy when I could pass all these tasks onto Maple, which could do them much faster and more reliably then I ever could. Maple is a software that allows me to go beyond routine engineering calculations and gives me the tools to reach levels of insight and understanding that were completely out of reach of the average engineer until a few years ago.

For the record, I have no business affiliations with Maplesoft. I’m writing this article because Maple makes such a difference in my work that I feel it is important to share my experiences so other engineers can get the same benefits.

We find recent applications of the components applied to the linear momentum, circular equations applied to engineering. Just simply replace the vector or scalar fields to thereby reasoning and use the right button.

(in spanish)



Developed and then implemented with open code components. It is very important to note this post is held for students of civil engineering and mechanics. Using advanced mathematical concepts to concepts in engineering.

(in spanish)









I'm an industrial engineering student who's running into problems with solving a simple system of non-linear equations.

Why do I get this error when issuing the solve command? I'm pretty sure I'm only passing two lists into the function?

Thanks a lot in advance,



Currently calculations: equations, regression analysis, differential equations, etc; to mention a few of them; are developed using traditional methods ie even are proposed and solved by hand and on paper. In teaching our scientists and engineers use the chalkboard as a way to reach students and enable them to solve their calculation. To what extent Maple contributes to research on new mathematical models applied science and engineering ?. Maplesoft appears as a proposal to resolve problems with our traditional proposed intelligent algorithms, development process, embedded components, and not only them but also generates type applications for Apple ipad tablets signature. Based on the computer algebra system Maple Maplesoft gives us the package which works exactly like we were on our work. I will show how mathematics is developed from a purely basic to reach modeling differential equations applied to education and engineering. Also visualizare current techniques for developing applications for mobile devices.





Lenin Araujo Castillo

Physics Pure

Computer Science

Today science professionals in engineering software used to only work on the desktop and even just looking to download and use mobile apps math; but they are not able to design their own applications.Maplesoft to set the solution to it through its Maple package; software supports desktop and mobile; solves problems of analysis and calculation with Embedded Components. To show this we have taken the area of different mathematical topics; fixed horizontally to a certain range of parameters and not just a constant as it is customary to develop. This paper shows how the Embedded Components allow us to develop mathematics in all areas. Achieving build applications that are interactive in mobile devices such as tablets; which are used at any time. Maple gives us design according to our university or research need, based on contemporary and modern mathematics.With this method we encourage students, teachers and researchers to use graphics algorithms.




Lenin Araujo Castillo

Physics Pure

Computer Science

Presentations of the first national congress of civil engineering developed at the University Cesar Vallejo. From 10 to 12 November 2014.



(in spanish)

Lenin Araujo Castillo

Physics Pure

Computer Science





The Embedded Components are containers that currently use industries for modeling complex systems to find viable solutions in real time and thus avoid huge wait times and overload our computer; by this paper should show you how to implement a dynamic worksheet through Embedded Components in Maple; it goes from finding solutions to ordinary differential equations partial; which interact with the researcher using different parameters.
Using graphical programming will find immediate solutions to selected problems in science and engineering criteria of variability and boundary conditions evolving development with buttons on multiple actions.



(in spanish)


Lenin Araujo Castillo

Physics Pure

Computer Science


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