Алгоритм ейлера-лагранжа для проектування динамічної моделі.

Abstract

Urgency of the research. Nowadays robotics and mechatronics come to be mainstream. With development in these areas also grow computing fastidiousness. Since there is significant focus on numerical modeling and algorithmization in kinematic and dynamic modeling.

Target setting. By automation of whole process of dynamic model design the errors are eliminated as well as the time of designing significantly decreases.

Actual scientific researches and issues analysis. Designing of dynamic model by analytical way is very difficult especially in the cases considering high number of DOF. For hyper-redundant manipulators it is practically impossible. From this reason whole process is automatized.

Uninvestigated parts of general matters defining. The theory of Euler – Lagrange method is automatized by means of robotic view on this issue.

The research objective. In the paper, an algorithm for design of dynamic model was introduced.

The statement of basic materials. The paper deals with automatic design process of dynamic model for serial kinematic structure mechanisms. In the paper Euler – Lagrange formula is discussed. Analytical way of dynamic modeling should be difficult problem especially for mechanisms with high number of degrees of freedom. From this reason the paper shows the way of automatically designing of dynamic modeling in MATLAB. Our study shows dependence of computing time on increasing DOF. The relation is expressed by function of 3rd order. Subsequently the paper presents automatically generated inverse dynamic model in cooperation with inverse kinematic model as well as trajectory planning task.

Conclusions. The paper introduces automatically generated dynamic model for mechanisms with serial kinematic structure. The paper also established the time for designing of dynamic model for several mechanisms with changing DOF.