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

## Authors

• Akambay Beisembayev Satbayev University, Kazakhstan
• Anargul Yerbossynova Satbayev University, Kazakhstan
• Petro Pavlenko National Aviation University, Ukraine
• Mukhit Baibatshayev Satbayev University, Kazakhstan

## Keywords:

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

## Abstract

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

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2021-12-21

## 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. https://doi.org/10.15587/1729-4061.2021.246533

## Section

Applied mechanics