{
  "id": "math/0505462",
  "version": "v2",
  "published": "2005-05-23T05:03:01.000Z",
  "updated": "2006-06-25T12:41:50.000Z",
  "title": "The configuration space of planar spidery linkages",
  "authors": [
    "Jun O'Hara"
  ],
  "comment": "33 pages, 41 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "The configuration space of the mechanism of a planar robot is studied. We consider a robot which has $n$ arms such that each arm is of length 1+1 and has a rotational joint in the middle, and that the endpoint of the $k$-th arm is fixed to $Re^{\\frac{2(k-1)\\pi}ni}$. Generically, the configuration space is diffeomorphic to an orientable closed surface. Its genus is given by a topological way and a Morse theoretical way. The homeomorphism types of it when it is singular is also given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-06-25T12:41:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "58E05",
      "57M20"
    ],
    "keywords": [
      "planar spidery linkages",
      "configuration space",
      "homeomorphism types",
      "rotational joint",
      "th arm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5462O"
    }
  }
}