Determination of particular singular configurations of Stewart platform type of fixator by the stereographic projection method

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2021-08-08 DOI:10.1080/17415977.2021.1960325

D. Dönmez, I. Akcali, E. Avşar, A. Aydın, H. Mutlu

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引用次数: 1

Abstract

Hexapod-type external fixators based on a general 6-6 Stewart platform structure are extensively used to manage orthopaedic disorders. While implementing these robotic devices, a practical visual aid is needed to quickly identify their uncontrollable states referred to as singularities. Thus, a visible correlation between the singularity of hexapod-type external fixators and their particular configurations has been explored geometrically in this work. A novel method called stereographic projection is utilized for that purpose. A mathematical procedure has been established to determine the characteristic values of the singular states. It is found that in case four- out of six-rod directions intersect each other at a common point, two different singular robot configurations result. Besides, if four joint angles at the top and bottom rings of the hexapod are equal, rings being parallel, then five-rod directions are intersected by two lines each passing through the end joints of the fifth rod.

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用立体投影法确定Stewart平台型固定器的特殊奇异构型

基于6-6 Stewart平台结构的六足外固定架广泛用于骨科疾病的治疗。在实现这些机器人设备时，需要一种实用的视觉辅助来快速识别它们的不可控状态，即奇点。因此，在这项工作中，六足型外固定架的奇异性与其特定构型之间的可见相关性已经在几何上进行了探索。一种称为立体投影的新方法被用于这一目的。建立了确定奇异态特征值的数学方法。研究发现，当六杆方向中的四杆在公共点相交时，会产生两种不同的奇异机器人构型。此外，如果六足体上下环的四个关节角相等，环平行，则五杆方向由两条线相交，每条线穿过第五杆的末端关节。

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

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.