Method for analytical description and modeling of the working space of a manipulation robot




manipulation robot, working space boundary, elementary surface, logic function


This paper reports a method, built in the form of a logic function, for describing the working spaces of manipulation robots analytically. A working space is defined as a work area or reachable area by a manipulation robot. An example of describing the working space of a manipulation robot with seven rotational degrees of mobility has been considered.

Technological processes in robotic industries can be associated with the positioning of the grip, at the required points, in the predefined coordinates, or with the execution of the movement of a working body along the predefined trajectories, which can also be determined using the required points in the predefined coordinates. A necessary condition for a manipulation robot to execute a specified process is that all the required positioning points should be within a working space.

To solve this task, a method is proposed that involves the analysis of the kinematic scheme of a manipulation robot in order to acquire a graphic image of the working space to identify boundary surfaces, as well as identify additional surfaces. The working space is limited by a set of boundary surfaces where additional surfaces are needed to highlight parts of the working space. Specifying each surface as a logic function, the working space is described piece by piece. Next, the resulting parts are combined with a logical expression, which is a disjunctive normal form of logic functions, which is an analytical description of the working space.

The correspondence of the obtained analytical description to the original graphic image of working space is verified by simulating the disjunctive normal form of logic functions using MATLAB (USA).

Author Biographies

Akambay Beisembayev, Satbayev University

PhD, Associate Professor

Department of Automation and Сontrol

Anargul Yerbossynova, Satbayev University

Doctoral Student

Department of Automation and Сontrol

Petro Pavlenko, National Aviation University

Doctor of Technical Sciences, Professor

Department of Applied Mechanics and Materials Engineering

Mukhit Baibatshayev, Satbayev University

Doctor of Technical Sciences, Associate Professor

Department of Automation and Сontrol


  1. Rastegar, J., Fardanesh, B. (1990). Manipulation workspace analysis using the Monte Carlo Method. Mechanism and Machine Theory, 25 (2), 233–239. doi:
  2. Ceccarelli, M., Liang, C. (2013). A formulation for automatic generation of workspace boundary of N-R manipulators. International Journal of Mechanisms and Robotic Systems, 1 (1), 2. doi:
  3. Madrid, E., Ceccarelli, M. (2014). Numerical solution for designing telescopic manipulators with prescribed workspace points. Robotics and Computer-Integrated Manufacturing, 30 (2), 201–205. doi:
  4. Cao, Y., Lu, K., Li, X., Zang, Y. (2011). Accurate Numerical Methods for Computing 2D and 3D Robot Workspace. International Journal of Advanced Robotic Systems, 8 (6), 76. doi:
  5. Liu, Z., Liu, H., Luo, Z., Zhang, X. (2013). Improvement on Monte Carlo method for robot workspace determination. Transactions of the Chinese Society for Agricultural Machinery, 44 (1), 230–235. doi:
  6. Burlіbay, A. A., Beisembaev, A. A., Wójcik, W. (2014). Description of the manipulator robot’s workspaces with three mobility degrees in the form of the logical expressions. PRZEGLĄD ELEKTROTECHNICZNY, 90 (8), 25–29. Available at:
  7. Li, J., Zhao, F., Li, X., Li, J. (2016). Analysis of robotic workspace based on Monte Carlo method and the posture matrix. 2016 IEEE International Conference on Control and Robotics Engineering (ICCRE). doi:
  8. Peidró, A., Reinoso, Ó., Gil, A., Marín, J. M., Payá, L. (2017). An improved Monte Carlo method based on Gaussian growth to calculate the workspace of robots. Engineering Applications of Artificial Intelligence, 64, 197–207. doi:
  9. Jauer, P., Kuhlemann, I., Ernst, F., Schweikard, A. (2016). GPU-based real-time 3D workspace generation of arbitrary serial manipulators. 2016 2nd International Conference on Control, Automation and Robotics (ICCAR). doi:
  10. Zhao, Z., He, S., Zhao, Y., Xu, C., Wu, Q., Xu, Z. (2018). Workspace Analysis for a 9-DOF Hyper-redundant Manipulator Based on An Improved Monte Carlo Method and Voxel Algorithm. 2018 IEEE International Conference on Mechatronics and Automation (ICMA). doi:
  11. Zhu, J., Tian, F. (2018). Kinematics Analysis and Workspace Calculation of a 3-DOF Manipulator. IOP Conference Series: Earth and Environmental Science, 170, 042166. doi:
  12. Fu, G., Tao, C., Gu, T., Lu, C., Gao, H., Deng, X. (2020). A Workspace Visualization Method for a Multijoint Industrial Robot Based on the 3D-Printing Layering Concept. Applied Sciences, 10 (15), 5241. doi:




How to Cite

Beisembayev, A., Yerbossynova, A., Pavlenko, P., & Baibatshayev, M. (2021). Method for analytical description and modeling of the working space of a manipulation robot. Eastern-European Journal of Enterprise Technologies, 6(7 (114), 12–20.



Applied mechanics