### Abstract

In this paper, the dynamics formulation of a general Stewart platform manipulator (SPM) with arbitrary geometry and inertia distribution is addressed. Based on a structured Boltzmann-Hamel-d'Alembert approach, in which the true coordinates are for translations and quasi-coordinates are for rotations, a systematic methodology using the parallelism inherent in the parallel mechanisms is developed to derive the explicit closed-form dynamic equations which are feasible for both forward and inverse dynamics analyses in the task space. Thus, a singularity-free path programming of the SPM for the minimum actuating forces is presented to demonstrate the applications of the developed dynamics model. Using a parametric path representation, the singularity-free path programming problem can be cast to the determination of undetermined control points, and then a particle swarm optimization algorithm is employed to determine the optimal control points and the associated trajectories. Numerical examples are implemented for the moving platform with constant orientations and varied orientations.

Original language | English |
---|---|

Pages (from-to) | 705-730 |

Number of pages | 26 |

Journal | Advanced Robotics |

Volume | 22 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2008 Jun 1 |

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### Keywords

- Boltzmann-Hamel-Alembert formulation
- Parallel mechanism
- Particle swarm optimization
- Singularity
- Stewart platform manipulator

### ASJC Scopus subject areas

- Software
- Control and Systems Engineering
- Human-Computer Interaction
- Hardware and Architecture
- Computer Science Applications

### Cite this

**Optimal path programming of the Stewart platform manipulator using the Boltzmann-Hamel-d'Alembert dynamics formulation model.** / Chen, Chun Ta; Liao, Te Tan.

Research output: Contribution to journal › Article

*Advanced Robotics*, vol. 22, no. 6, pp. 705-730. https://doi.org/10.1163/156855308X305281

}

TY - JOUR

T1 - Optimal path programming of the Stewart platform manipulator using the Boltzmann-Hamel-d'Alembert dynamics formulation model

AU - Chen, Chun Ta

AU - Liao, Te Tan

PY - 2008/6/1

Y1 - 2008/6/1

N2 - In this paper, the dynamics formulation of a general Stewart platform manipulator (SPM) with arbitrary geometry and inertia distribution is addressed. Based on a structured Boltzmann-Hamel-d'Alembert approach, in which the true coordinates are for translations and quasi-coordinates are for rotations, a systematic methodology using the parallelism inherent in the parallel mechanisms is developed to derive the explicit closed-form dynamic equations which are feasible for both forward and inverse dynamics analyses in the task space. Thus, a singularity-free path programming of the SPM for the minimum actuating forces is presented to demonstrate the applications of the developed dynamics model. Using a parametric path representation, the singularity-free path programming problem can be cast to the determination of undetermined control points, and then a particle swarm optimization algorithm is employed to determine the optimal control points and the associated trajectories. Numerical examples are implemented for the moving platform with constant orientations and varied orientations.

AB - In this paper, the dynamics formulation of a general Stewart platform manipulator (SPM) with arbitrary geometry and inertia distribution is addressed. Based on a structured Boltzmann-Hamel-d'Alembert approach, in which the true coordinates are for translations and quasi-coordinates are for rotations, a systematic methodology using the parallelism inherent in the parallel mechanisms is developed to derive the explicit closed-form dynamic equations which are feasible for both forward and inverse dynamics analyses in the task space. Thus, a singularity-free path programming of the SPM for the minimum actuating forces is presented to demonstrate the applications of the developed dynamics model. Using a parametric path representation, the singularity-free path programming problem can be cast to the determination of undetermined control points, and then a particle swarm optimization algorithm is employed to determine the optimal control points and the associated trajectories. Numerical examples are implemented for the moving platform with constant orientations and varied orientations.

KW - Boltzmann-Hamel-Alembert formulation

KW - Parallel mechanism

KW - Particle swarm optimization

KW - Singularity

KW - Stewart platform manipulator

UR - http://www.scopus.com/inward/record.url?scp=46249108313&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46249108313&partnerID=8YFLogxK

U2 - 10.1163/156855308X305281

DO - 10.1163/156855308X305281

M3 - Article

AN - SCOPUS:46249108313

VL - 22

SP - 705

EP - 730

JO - Advanced Robotics

JF - Advanced Robotics

SN - 0169-1864

IS - 6

ER -