Topology and the robot arm
type: Item
instance of: scholarly article
title: Topology and the robot arm
zbMATH Open document ID: 0652.57021
DOI: 10.1007/BF00047283
published in: Acta Applicandae Mathematicae
publication date: 1988-01-01T00:00:00Z
review text: A robot arm is in effect a smooth function from the space of positions of the arm to the space of positions of a coordinate frame attached to the end of the arm. For the most common robots built today, this means a map f: \(T^ n\to {\mathbb{R}}^ 3\times SO_ 3\). We describe the singularities of this map. The set of rotational singularities is the set of arm positions where the axes of the links are parallel to a plane. Thus, it is always two-dimensional. Also, we show that f is homotopic to a map which factors through a circle, and represents the generator of \(\pi_ 1(SO_ 3)\). The engineering implications of these statements are discussed.
Mathematics Subject Classification ID: 57R45
Mathematics Subject Classification ID: 93C30
Mathematics Subject Classification ID: 55Q05
zbMATH DE Number: 4064074
zbMATH Keywords: robot arm
zbMATH Keywords: space of positions of a coordinate frame
zbMATH Keywords: singularities
zbMATH Keywords: rotational singularities
zbMATH Keywords: set of arm positions
zbMATH Keywords: \(\pi _ 1(SO_ 3)\)
author: Daniel H. Gottlieb
MaRDI profile type: Publication
cites work: Q3779798
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description: scientific article; zbMATH DE number 4064074