Cardminder mobile linkage
Section 4 presents a method for the model fabrication. Then in Section 3 we describe in detail the construction of mobile assemblies and analyse their geometric characteristics. First, in Section 2 we introduce a Myard’s first five-bar linkage constructed by combining two Bennett linkages and its closure equations. Here we present a new method to construct a family of mobile assemblies of Myard linkage unlimitedly using tilings and patterns. In a previous study it has been found that the Myard linkages can be used as deployable units for the construction of an umbrella-shaped deployable structure. Unlike the original Myard linkage, the angle of twists in the Bennett linkages is not necessary to be π / 2.
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Chen and You have presented the extended Myard linkage, in which they reported the possibility of constructing an extended 5 R Myard linkage by combining two complementary Bennett linkages. Baker pointed out that the Myard linkage can also be considered as a degeneracy of a plane-symmetric 6 R linkage. So the Myard 5 R linkage can be treated as special case of the Goldberg 5 R linkage. Baker gave the geometric condition and closure equations of the Myard linkage through the analysis of the Goldberg 5 R linkage. The original Myard linkage is plane-symmetric for which the two ‘rectangular’ Bennett chains, with one pair of twists being π / 2, are symmetrically disposed before combining them. In this paper, our attention is paid to the Myard’s first five-bar linkage, an overconstrained 5 R linkage. A most detailed study of the overconstrained mechanisms was done by Baker, , etc. A number of 3D overconstrained linkages are the combinations of two or more Bennett linkages, e.g., two five-bar and two six-bar Myard linkages, the Goldberg 5 R and 6 R linkages, the Bennett-joint 6 R linkage, the Dietmaier 6 R linkage and the Wohlhart double-Goldberg linkages and most recently some 6 R linkages proposed by Baker and Chen and You.
![cardminder mobile linkage cardminder mobile linkage](https://img.alicdn.com/imgextra/i3/6000000000243/O1CN01U14QI51DfKjRx78R4_!!6000000000243-0-tbvideo.jpg)
Among them, the Bennett linkage, is the most interesting one, with only four links connected by four revolute joints whose axes are not parallel or concurrent to each other. Since then, other overconstrained mechanisms have been discovered. The first overconstrained mechanism which appeared in the literature was Sarrus linkage in 1853. These linkages have always drawn much research interest from kinematicians. All of the spatial 4 R, 5 R and 6 R close-loop linkages are regarded as overconstrained simply because their mobility is due to special geometrical arrangements. For close-loop linkage consisting of only links and revolute joints, generally seven links are needed to form a mobile loop according to the Kutzbach criterion.