Singularity analysis of 3T2R parallel mechanisms using Grassmann–Cayley algebra and Grassmann geometry

Amine, Semaan; Masouleh, Mehdi Tale; Caro, Stéphane; Wenger, Philippe; Gosselin, Clément

doi:10.1016/j.mechmachtheory.2011.11.015

Cited by 52 publications

(35 citation statements)

References 37 publications

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“…Limb singularities can be characterized by a loss of DOF locally, while a gain of DOF or a lack of stiffness is known as a parallel singular configuration (Amine et al, 2011), (Amine et al, 2012). …”

Section: Singularity Analysismentioning

confidence: 99%

Kinematic Analysis of Lower Mobility Cooperative Arms by Screw Theory

2012

Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics

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Section: Singularity Analysismentioning

confidence: 99%

Kinematic Analysis of Lower Mobility Cooperative Arms by Screw Theory

2012

Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics

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“…First, the designer only has to focus on the selection of a parallel architecture with adequate singular configurations, instead of having to select a parallel mechanism and afterward a configuration. Second, the designer can benefit from the knowledge of singularity analysis for many parallel manipulators [16,18]. It is then easy to obtain mechanisms that can achieve particular mobilities with parallel architectures for the sake of stiffness.…”

Section: Introductionmentioning

confidence: 99%

Using Singularities of Parallel Manipulators to Enhance the Rigid-Body Replacement Design Method of Compliant Mechanisms

Rubbert

Caro

Gangloff

et al. 2014

Journal of Mechanical Design

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The rigid-body replacement method is often used when designing a compliant mechanism. The stiffness of the compliant mechanism, one of its main properties, is then highly dependent on the initial choice of a rigid-body architecture. In this paper, we propose to enhance the efficiency of the synthesis method by focusing on the architecture selection. This selection is done by considering the required mobilities and parallel manipulators in singularity to achieve them. Kinematic singularities of parallel structures are indeed advantageously used to propose compliant mechanisms with interesting stiffness properties. The approach is first illustrated by an example, the design of a one degree of freedom compliant architecture. Then the method is used to design a medical device where a compliant mechanism with three degrees of freedom is needed. The interest of the approach is outlined after application of the method. IntroductionCompliant mechanisms are monolithic structures taking advantage of elasticity to produce movements. The absence of backlash and friction allows the production of very accurate movements making them suitable for medical devices [1-3], micropositioning [4,5] and space applications [6]. One challenge is to design compliant mechanisms with multiple degrees of freedom that have adequate stiffness performances, i.e. that demonstrate low stiffnesses along the desired degrees of freedom (DOF), high stiffnesses in the other directions, and that fulfill other design criteria such as compactness. There are different ways to design compliant mechanisms. The most common synthesis approaches, described in [7], are the kinematic-based approaches, the building blocks approaches and the structural optimizationbased approaches. Among the kinematic-based approaches, the FACT method does not require knowledge of existing

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“…This improvement enhanced the application of Grassmann-Cayley Algebra for limited dof parallel manipulators. The method was later expanded to represent the wrenches in a projective space, named wrench graph by Amine et al [21][22][23]. The wrench graph depicts all geometrics properties between the constraint and actuation wrenches of manipulators and highlight points at infinity in a superbracket.…”

Section: Introductionmentioning

confidence: 99%