A semi-analytical approach towards determining the largest collision-free sphere in R3 inside the effective regular workspace of a 6-6 Stewart-Gough platform manipulator corresponding to a given orientation workspace

IF 5.9 1区工程技术 Q1 ENGINEERING, MECHANICAL

Mechanism and Machine Theory Pub Date : 2026-04-01 Epub Date: 2026-01-09 DOI:10.1016/j.mechmachtheory.2025.106331

Bibekananda Patra, Nishanth Adithya Chandramouli, Sandipan Bandyopadhyay

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Abstract

This article focusses on the problem of interference among the links of a parallel robot, namely, the Stewart-Gough platform manipulator. The geometry of the legs is approximated by capsules, leading to the detection of collision among any pair of legs in terms of tangency of the corresponding capsules. Analytical conditions for the said cases of tangency are derived in closed-form, which manifest geometrically as certain quadrics in space. Through a thorough study and explicit characterisation of these surfaces, novel analytical methods are developed to find the largest spheres in space which are tangent to these surfaces. Such spheres are free of possibilities of link collisions, and they can be derived analytically for a given orientation of the moving platform of the manipulator. The analysis is subsequently extended to the orientation workspace of the manipulator by repeating the above-mentioned computations over a large number of discrete samples. The results obtained are verified numerically by comparing them with those generated from other sources. A parametric study is performed to demonstrate the utility of the proposed analysis in practice.

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6-6 Stewart-Gough平台机械臂在给定方位工作空间下的有效规则工作空间内R3中最大无碰撞球面的半解析方法

本文主要研究Stewart-Gough平台型并联机器人各环节间的干扰问题。腿的几何形状由胶囊近似，从而根据相应胶囊的切线检测任意一对腿之间的碰撞。这些切线的解析条件以封闭形式导出，在几何上表现为空间上的某些二次曲线。通过对这些表面的深入研究和明确表征，开发了新的分析方法来寻找与这些表面相切的空间中最大的球体。这种球体不存在连杆碰撞的可能性，并且可以在给定的机械手运动平台方向下解析导出。通过在大量离散样本上重复上述计算，将分析扩展到机械臂的定向工作空间。将所得结果与其他来源的结果进行了数值验证。进行了参数化研究，以证明所提出的分析在实践中的效用。

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

Mechanism and Machine Theory 工程技术-工程：机械

CiteScore

9.90

自引率

23.10%

发文量

450

审稿时长

20 days

期刊介绍： Mechanism and Machine Theory provides a medium of communication between engineers and scientists engaged in research and development within the fields of knowledge embraced by IFToMM, the International Federation for the Promotion of Mechanism and Machine Science, therefore affiliated with IFToMM as its official research journal. The main topics are: Design Theory and Methodology; Haptics and Human-Machine-Interfaces; Robotics, Mechatronics and Micro-Machines; Mechanisms, Mechanical Transmissions and Machines; Kinematics, Dynamics, and Control of Mechanical Systems; Applications to Bioengineering and Molecular Chemistry