Simulating the functioning of a mechanism requires programming languages which are used to calculate the dynamic equations of mechanics. One of the main limitations of this programming is the excessive run time the computer needs to generate these equations, even for simple problems. In this research they developed a set of techniques and algorithms that can be used with any formulation and with any type of coordinates and whose results are practically the same as those obtained with the best of the formulations.
Besides achieving optimum quality in the code generated, the main advantage of these techniques is that the equations obtained are optimized. "Since they are optimum, the computer takes less time to 'digest' them in order to subsequently work with them, and, therefore, the door is opened up for using computers with less computing power," said Plaza.
Another of the contributions of the research has been to eliminate the trigonometric simplification process to generate optimum symbolic equations. "The equations of mechanical systems are, in general, capable of being simplified," explained the researcher. "This simplification helps to reduce the size of the equations, but carrying this out involves extensive computing time. The technique proposed obtains the trigonometrically simplified equations directly without having to carry out this specification explicitly, which enables a piece of optimum code that is faster and with fewer memory resources to be generated."
Various applications
The engineer had the chance to put his proposal into practice in a collaboration project between the Applied Mechanical and Computational Engineering research group-IMAC of the NUP/UPNA, which he belongs to, and a company in the railway sector. A part of this project was to design the computational model of a locomotive to be used in various virtual experiments. "As it is a highly complex model, the computer took a long time to create it: about two and a half hours. That was partly because the model was developed using general purpose commercial software for symbolic calculations. As it was general and did not focus on mechanical models, it did not carry out the operations in the best way possible," he pointed out.
After applying the set of techniques and algorithms proposed in the research, the time to generate the equations was cut to ten minutes and the number of mathematical operations needed for the computer to "digest" this model was 0.3% with respect to the number of operations that it would need if it were generated by a piece of general software. What is more, it was not necessary to resort to general purpose commercial software, the use of which is restricted to those who purchase a licence.
This technique for obtaining equations can be applied to a whole range of mechanical systems. "Right now, for example, we are working on the model of a wind turbine. In the same way, we have produced models for cars, robots and vehicle suspensions in addition to other models we use for our research and even for teaching purposes," he said.
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