Workspace analysis of parallel mechanisms by considering active joints ranges of motion using a method based on interval analysis

IF 1.9 3区工程技术 Q3 MECHANICS

Meccanica Pub Date : 2025-04-07 DOI:10.1007/s11012-024-01892-1

Fatemeh Pourkariman, Mehdi Karimi, Payam Varshovi-Jaghargh, Mehdi Tale Masouleh

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引用次数: 0

Abstract

The parallel robots workspace plays an important role in their design and construction. In this paper, a new algorithm is presented based on the concepts of interval analysis to determine the parallel robots workspace by considering joints ranges of motion. The proposed algorithm is based on the kinematics equations, interval arithmetic computations and refinement method. In this algorithm, the system of interval nonlinear equations obtained from kinematic analysis is solved simultaneously and the refinement operation is carried out to accurately calculate the intervals of the equations. A type of refinement operation, namely the slope form, is used in this method to eliminate the excess width of intervals of equations. The proposed algorithm is implemented on 3 and 4-DOF Delta parallel robots of Human and Robot Interaction Laboratory of Tehran university. The workspace of 3-DOF Delta parallel robot and the constant-orientation workspace of 4-DOF Delta parallel obtained from the proposed method for the different active joints ranges of motion are compared with the results of the method based on interval analysis without refinement operation and the geometric method. The results show that the proposed algorithm calculates the parallel robot workspace with appropriate accuracy.

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考虑活动关节运动范围的并联机构工作空间分析

并联机器人的工作空间在其设计和制造中起着重要的作用。本文基于区间分析的概念，提出了一种考虑关节运动范围确定并联机器人工作空间的新算法。该算法基于运动学方程、区间算法计算和细化方法。该算法同时求解由运动学分析得到的区间非线性方程组，并对方程组进行细化运算，精确计算出方程组的区间。该方法采用了一种细化运算，即斜率形式，来消除方程区间的过量宽度。该算法在德黑兰大学人机交互实验室的三自由度和四自由度Delta并联机器人上实现。将该方法得到的三自由度Delta并联机器人在不同活动关节运动范围下的工作空间和四自由度Delta并联机器人的恒定方位工作空间与基于区间分析而不进行细化运算的方法和几何方法的结果进行了比较。结果表明，该算法能较好地计算出并联机器人的工作空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Meccanica 物理-力学

CiteScore

4.70

自引率

3.70%

发文量

151

审稿时长

7 months

期刊介绍： Meccanica focuses on the methodological framework shared by mechanical scientists when addressing theoretical or applied problems. Original papers address various aspects of mechanical and mathematical modeling, of solution, as well as of analysis of system behavior. The journal explores fundamental and applications issues in established areas of mechanics research as well as in emerging fields; contemporary research on general mechanics, solid and structural mechanics, fluid mechanics, and mechanics of machines; interdisciplinary fields between mechanics and other mathematical and engineering sciences; interaction of mechanics with dynamical systems, advanced materials, control and computation; electromechanics; biomechanics. Articles include full length papers; topical overviews; brief notes; discussions and comments on published papers; book reviews; and an international calendar of conferences. Meccanica, the official journal of the Italian Association of Theoretical and Applied Mechanics, was established in 1966.