### Abstract

We study the criteria under which an object can be gripped by a multifingered dexterous hand, assuming no static friction between the object and the fingers; such grips are called positive grips. We study three cases in detail: (i) the body is at equilibrium, (ii) the body is under some constant external force/torque, and (iii) the body is under a varying external force/torque. In each case we obtain tight bounds on the number of fingers needed to obtain grip. We also present efficient algorithms to synthesize such positive grips for bounded polyhedral/polygonal objects; the number of fingers employed in the grips synthesized by our algorithms match the above bounds. The algorithms run in time linear in the number of faces/sides. The paper may be of independent interest for its presentation of algorithms arising in the study of positive linear spaces.

Original language | English (US) |
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Pages (from-to) | 541-558 |

Number of pages | 18 |

Journal | Algorithmica |

Volume | 2 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1987 |

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### Keywords

- Force/torque
- Grip selection
- Positive grip

### ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics

### Cite this

*Algorithmica*,

*2*(1), 541-558. https://doi.org/10.1007/BF01840373