Research and developing methods of solving engineering optimization problems for parallel structure robots

Artem D. Maminov, Mikhail A. Posypkin


We consider the optimization of the key design parameters of the 2-RPR parallel robot in this paper. Optimization is carried out according to two criteria: the area of the workspace of the 2-RPR robot and the controllability index - global dexterity index (GDI). In the process of analyzing the robot, the direct and inverse kinematic problems are solved, the Jacobi matrices of the input and output parameters are found, and the final complete Jacobi matrix is constructed. We use Monte Carlo method to compute the area of the workspace. The GDI index is calculated by approximating the integral to the sum of the values on a uniform grid. As a result, the Pareto-optimal set  is calculated for one of the parameters of the robot, which is the solution of the problem. There was created software package, which includes visualization of the robot workspace, the dependence of the robot condition number on various parameters of the 2-RPR robot and plot of Pareto-optimal solution.

Full Text:

PDF (Russian)


Huang T. et al. Optimal kinematic design of 2-DOF parallel manipulators with well-shaped workspace bounded by a specified conditioning index //IEEE Transactions on Robotics and Automation. – 2004. – T. 20. – #. 3. – S. 538-543.

Gosselin C., Angeles J. A global performance index for the kinematic optimization of robotic manipulators //Journal of Mechanical design. – 1991. – T. 113. – #. 3. – S. 220-226.

Gosselin C., Angeles J. Singularity analysis of closed-loop kinematic chains //IEEE transactions on robotics and automation. – 1990. – T. 6. – #. 3. – S. 281-290.

Gallant M., Boudreau R. The synthesis of planar parallel manipulators with prismatic joints for an optimal, singularity-free workspace //Journal of Robotic Systems. – 2002. – T. 19. – #. 1. – S. 13-24.

Merlet J. P. Parallel robots. - Springer Science and Business Media, 2006. – T. 128.

Malyshev D. I. i dr. Analiz rabochej oblasti robota DexTAR-dexterous twin-arm robot //International Journal of Open Information Technologies. – 2018. – T. 6. – #. 7.

Stan S. D., Maties V., Balan R. Optimization of a 2 dof micro parallel robot using genetic algorithms //Frontiers in Evolutionary Robotics. – IntechOpen, 2008.

Jeffektivnost' po Pareto // Vikipedija. [2018—2018]. Data obnovlenija: 07.06.2018. URL: B. Smith, “An approach to graphs of linear forms (Unpublished work style),” unpublished.

Nam Y. J., Park M. K. Workspace optimization and kinematic performance evaluation of 2-DOF parallel mechanisms //Journal of mechanical science and technology. – 2006. – T. 20. – #. 10. – S. 1614-1625.

Oliphant, T.E., 2006. A guide to NumPy, Trelgol Publishing USA.

Biblioteka Math. URL:

Biblioteka Matplotlib. URL:

Biblioteka Shapely.


Biblioteka Descartes.


Podinovskij V. V., Nogin V. D. Pareto-optimal'nye reshenija mnogokriterial'nyh zadach. – Fizmatlit, 2007.

Bushenkov V. A., Lotov A. V. Metody i algoritmy analiza linejnyh sistem na osnove postroenija obobshhennyh mnozhestv dostizhimosti //Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki. – 1980. – T. 20. – #. 5. – S. 1130-1141.


  • There are currently no refbacks.

Abava  Кибербезопасность FRUCT 2023

ISSN: 2307-8162