### 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) |
---|---|

Pages (from-to) | 541-558 |

Number of pages | 18 |

Journal | Algorithmica (New York) |

Volume | 2 |

Issue number | 1-4 |

DOIs | |

State | Published - Nov 1987 |

### Fingerprint

### Keywords

- Force/torque
- Grip selection
- Positive grip

### ASJC Scopus subject areas

- Applied Mathematics
- Safety, Risk, Reliability and Quality
- Software
- Computer Graphics and Computer-Aided Design

### Cite this

*Algorithmica (New York)*,

*2*(1-4), 541-558. https://doi.org/10.1007/BF01840373

**On the existence and synthesis of multifinger positive grips.** / Mishra, Bhubaneswar; Schwartz, J. T.; Sharir, M.

Research output: Contribution to journal › Article

*Algorithmica (New York)*, vol. 2, no. 1-4, pp. 541-558. https://doi.org/10.1007/BF01840373

}

TY - JOUR

T1 - On the existence and synthesis of multifinger positive grips

AU - Mishra, Bhubaneswar

AU - Schwartz, J. T.

AU - Sharir, M.

PY - 1987/11

Y1 - 1987/11

N2 - 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.

AB - 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.

KW - Force/torque

KW - Grip selection

KW - Positive grip

UR - http://www.scopus.com/inward/record.url?scp=28444496141&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28444496141&partnerID=8YFLogxK

U2 - 10.1007/BF01840373

DO - 10.1007/BF01840373

M3 - Article

VL - 2

SP - 541

EP - 558

JO - Algorithmica

JF - Algorithmica

SN - 0178-4617

IS - 1-4

ER -