### Abstract

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a linearly actuated quadratic spherical parallel manipulator. An alternative formulation of the kinematic equations of the quadratic spherical parallel manipulator is proposed. The singularity analysis of the quadratic spherical parallel manipulator is then dealt with. A new type of singularity of parallel manipulators-leg actuation singularity-is identified. If a leg is in a leg actuation singular configuration, the actuated joints in this leg cannot be actuated even if the actuated joints in other legs are released. A formula is revealed that produces a unique current solution to the FDA for a given set of inputs. The input space is also revealed for the quadratic spherical parallel manipulator in order to guarantee that the robot works in the same assembly mode. This work may facilitate the control of the quadratic spherical parallel manipulator. © 2011 American Society of Mechanical Engineers.

Original language | English |
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Article number | 011007 |

Journal | Journal of Mechanisms and Robotics |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - 6 Jan 2011 |

### Keywords

- Forward displacement analysis
- Parallel mechanism
- Quadratic parallel mechanism
- Singularity analysis
- Spherical parallel mechanism

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## Cite this

*Journal of Mechanisms and Robotics*,

*3*(1), [011007]. https://doi.org/10.1115/1.4003079