### Analysis of the working area of the robot DexTAR - dexterous twin-arm robot

#### Abstract

The paper proposes and experimentally compares two approaches to the task of determining the working area of parallel robots using the example of a flat Dextar robot with two degrees of freedom. The considered approaches are based on the coupling equations. In the first case, the original coupling equations are used in the six-dimensional space of two coordinates describing the position of the output link and the four rotation angles of the bars with the subsequent projection of the solution onto a two-dimensional plane. In the second, the system of inequalities connecting the coordinates of the manipulator output link, which is solved in the twodimensional Euclidean space, is derived from the coupling equations. The algorithm of the proposed approaches is the nonuniform covering method, which allows to obtain external and internal approximation of the set of systems solutions for each approach with a given accuracy. Approximation is a set of parallelepipeds. It is shown that in the first case it is more efficient to use interval estimates that coincide with the extremums of a function on a parallelepiped, in the second it is a grid approximation, in connection with the multiple occurrence of variables in expressions.

#### Full Text:

PDF (Russian)#### References

Merlet J. P. Parallel Robots. — Springer Publishing Company, Incorporated, 2010.

Rybak L. A. Erzhukov V. V. Chichvarin A. V. Jeffektivnye metody reshenija zadach kinematiki i dinamiki robota stanka parallel'noj struktury. — M. : Fizmatlit, 2011.

Glazunov V.A. Koliskor A.Sh. Krajnev A.F. Prostranstvennye mehanizmy parallel'noj struktury. — M.: Nauka, 1991.

Kun S. Gosselin K. Strukturnyj sintez parallel'nyh mehanizmov. — M. : Fizmatlit, 2012.

Sergiu-Dan Stan Vistrian Maties, Balan Radu. Optimization of a 2 dof micro parallel robot using genetic algorithms // Frontiers in Evolutionary Robotics. — 2008. — P. 465–490.

Evtushenko Yu G. Numerical methods for finding global extrema (case of a non-uniform mesh) // USSR Computational Mathematics and Mathematical Physics. — 1971. — Vol. 11, no. 6. — P. 38–54.

Evtushenko Yury, Posypkin Mikhail. A deterministic approach to global box-constrained optimization // Optimization Letters. — 2013. — Vol. 7, no. 4. — P. 819–829.

Jaulin Luc. Applied interval analysis: with examples in parameter and state estimation, robust control and robotics. — Springer Science & Business Media, 2001. — Vol. 1.

Numerical method for approximating the solution set of a system of non-linear inequalities / Yuri G Evtushenko, Mikhail A Posypkin, Larisa A Rybak, Andrei V Turkin // International Journal of Open Information Technologies. — 2016. — Vol. 4, no. 12. — P. 1–6.

Approximating a solution set of nonlinear inequalities / Yuri Evtushenko, Mikhail Posypkin, Larisa Rybak, Andrei Turkin // Journal of Global Optimization. — 2017. — P. 1–17.

Posypkin Mikhail, Usov Alexander. — Basic numerical routines, 2018 (accessed May 21, 2018). — URL: https://github.com/mposypkin/ snowgoose.

Evtushenko Yuri, Posypkin Mikhail, Sigal Israel. A framework for parallel large-scale global optimization // Computer Science-Research and Development. — 2009. — Vol. 23, no. 3-4. — P. 211–215.

### Refbacks

- There are currently no refbacks.

Abava FRUCT 2019

ISSN: 2307-8162