STABILITY ANALYSIS OF SOFTWARE MANIPULATOR MOVEMENTS USING MATHCAD

  • Natalya Sergeevna Ashchepkova Oles Honchar Dnipro National University
Keywords: MANIPULATOR, PROGRAM MOVEMENTS, CONTROL SYSTEM

Abstract

Abstract. The method of the stability analysis of the manipulator program movements with use of Mathcad applied programs package is offered. On the basis of the manipulator’s kinematic scheme, the matrices of homogeneous transformations of Denavit Hartenberg are formed and a mathematical model of the extended control object is drawn up. An outline of an extended object control system consisting of a manipulator and an actuator is presented. For example, the linear equations of the manipulator, actuators, meter and controller are considered. The task of synthesizing the manipulator control algorithm is to determine the coefficients of the matrix transfer function of the controller that satisfy the conditions of stability and quality of transients. Mathematical modeling of manipulator programmatic movements was performed using the Matchad application package. The analysis of simulation results allows us to evaluate: manipulator workspace, control system performance, grip positioning accuracy, dependence of grip positioning error on the nature of load and the law of motion. A change in the dynamic characteristics of an extended control object causes a change in the controllability of systems, for the considered example rang Q = 2, i.e. the system is fully controllable.

This method can be used to analyze the manipulation of the manipulator at the design stage; allows to determine the influence of design, kinematic and dynamic parameters on the manipulation of the manipulator and perform mathematical modeling of the manipulator motion. Calculation examples are given that confirm the expediency and effectiveness of using the Mathcad application software package to solve this type of problem.

References

Ащепкова Н. С. Моделирование и кинематический анализ кривошипно -шатунного механизма. Вісник НТУ “ХПІ”. Серія: Информатика и моделирование. Харків, 2014. № 62. С. 3 – 12.

Ащепкова Н. С. Метод кинематического и динамического анализа манипулятора с использованием Mathcad. Восточно-Европейский журнал передовых технологий. Харьков, 2015. № 5/7 (77). С. 54 – 63.

Ащепкова Н. С. Моделювання та аналіз точності позіціювання маніпулятора. Вісник НТУ “ХПІ”. Серія: Механіко-технологічні системи та комплекси. Харків, 2017. № 19 (1241). С. 34 – 42.

Зенкевич С. Л., Ющенко А. С. Основы управления манипуляционными роботами: учебник для вузов. Москва: Изд-во МГТУ им. Н. Э. Баумана, 2004. 480 с.

Колюбин С. А. Динамика робототехнических систем. Уч. пособие. Санкт-Петербург: Университет ИТМО, 2017. 117 с.

Шашихин В.Н. Современные проблемы автоматического управления. Санкт-Петербург: Изд-во Политехн. ун-та, 2017. 210 с.

Шахинпур М. Курс робототехники. Пер. с англ. Москва: Мир, 1990. 527 с.

Юревич Е. И. Основы робототехники. Санкт-Петербург: Питер, 2005. 252 с.

Maxfield B. Engineering with Mathcad: using Mathcad to create and organize your engineering calculation. Butterworth-Heinemann, 2016. 512 p.

Maxfield B. Essential Mathcad for Engineering, Science, and Math. Academic Press, 2009. 528 p.

Published
2019-12-30
How to Cite
Ashchepkova, N. S. (2019). STABILITY ANALYSIS OF SOFTWARE MANIPULATOR MOVEMENTS USING MATHCAD. Journal of Rocket-Space Technology, 27(4), 52-57. https://doi.org/10.15421/451908