General Formula of Mobility Calculation for Planar Mechanism

Yang, Yan Dong; Zhang, Yi Tong

doi:10.4028/www.scientific.net/amr.562-564.654

Cited by 1 publication

(1 citation statement)

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“…New achievements have been presented that modified, 6 changed or completed [7][8][9] the G-K formula, or even put forward new formulae or methods. [10][11][12] The issue of overconstraint in planar mechanisms has generally been considered as part of a G-K calculation, so the key problem for mobility analysis has become how to identify and deal with these overconstraints. One way of doing this is based on the concept of a ''DOF substitute''.…”

Section: Introductionmentioning

confidence: 99%

Determination of overconstraint and mobility analysis for planar mechanisms

Zeng

Huang

2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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The mobility(or degree of freedom) analysis of planar mechanisms is traditionally calculated using the Grübler–Kutzbach formula. However, this method often fails in practice due to overconstraint, which is a core problem in all mobility analysis. Analyzing the cause of overconstraint, it is presented that overconstraint in closed-loop mechanisms can be recognized by analyzing the relative movements of the two elements in a rigidity re-closure. A solution to determine the overconstraint in multiloop mechanisms is also proposed. In this method, each loop is opened and the overconstraint can be calculated when the loop is reclosed. A mobility analysis must begin by determining the overconstraint. However, given that most planar mechanisms do not have any overconstraint, it is important to identify rapidly whether overconstraint exists in a mechanism. This paper proposes a concise technique to determine the existence of overconstraint based on the concept of “Assur groups”. To simplify the process of mobility analysis, three new concepts and four relevant theories are introduced. In this paper, the proposed methodology is applied to several types of planar mechanisms, producing results in accordance with the prototype. This shows that the proposed methodology makes performing the mobility analysis of planar mechanisms, including complicated planar mechanisms, accurate, convenient, and fast.

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