## Abstract

A configuration of a mechanical linkage is defined as regular if there exists a subset of actuators with their corresponding Jacobian columns spans the gripper's velocity space. All other configurations are defined in the literature as singular configurations. Consider mechanisms with grippers' velocity space ℝ^{m}. We focus our attention on the case where m Jacobian columns of such mechanism span ℝ^{m}, while all the rest are linearly dependent. These are obviously an undesirable configuration, although formally they are defined as regular. We define an optimal-regular configuration as such that any subset of m actuators spans an m-dimensional velocity space. Since this densely constraints the work space, a more relaxed definition is needed. We therefore introduce the notion of k-singularity of a redundant mechanism which means that rigidifying k actuators will result in an optimal-regularity. We introduce an efficient algorithm to detect a k-singularity, give some examples for cases where m = 2, 3, and demonstrate our algorithm efficiency.

Original language | English |
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Article number | 031015 |

Journal | Journal of Mechanisms and Robotics |

Volume | 9 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jun 2017 |

Externally published | Yes |

## ASJC Scopus subject areas

- Mechanical Engineering