Abstract
A metamorphic linkage is capable of changing its motion branches and can be used as mechanisms for reconfigurable robots for various tasks. This paper presents two novel metamorphic linkages as the spherical-planar 6R metamorphic linkage and the Bennett-spherical 6R metamorphic linkage both of which have three various distinguished motion branches. Having established the close-loop equation of the spherical-planar 6R metamorphic linkage, the paper reveals the conditions of various motion branches and a set of transformations for switching motion branches. The paper further uses to reveal the inherent properties of this over-constrained metamorphic 6R linkage that is able to perform both spherical and planar motion with mobility one. Because of geometrical constraints at bifurcation points, the linkage is able to reconfigure to the deployed spherical motion branch, the planar motion branch and the folded spherical motion branch. The two spherical motion branches could be seen on both a large sphere that presents the deployed spherical motion and a small sphere that presents the folded spherical motion. This leads to the revelation of the novel Bennett-spherical 6R metamorphic linkage that has the transition from one deployed Bennett configuration branch to a spherical configuration branch and then to another folded Bennett configuration branch. Given the geometric parameters of both metamorphic linkages, it reveals that these linkages are special cases of Bricard line-symmetric 6R linkage.
Highlights
Over-constrained linkages are a kind of special linkages that mobility does not satisfy the Grübler–Kutzbach [1] formula. 6R close-loop linkages with mobility one are typical over-constrained linkages
This paper presented two novel 6R metamorphic linkages as the spherical-planar metamorphic linkage and the Bennettspherical metamorphic linkage with each of them having three motion branches
The Spherical-planar 6R metamorphic linkage was originated from a kirigami and has two deployed and folded spherical motion branches and one planar motion branch
Summary
Over-constrained linkages are a kind of special linkages that mobility does not satisfy the Grübler–Kutzbach [1] formula. 6R close-loop linkages with mobility one are typical over-constrained linkages. There were two kinds of reconfigurable linkages as kinemetatropic linkages presented by Wohlhart [17] and metamorphic linkages proposed by Dai and Rees Jones [18] They are reconfigurable when they run to bifurcation or multifurcation points. The former is extracted from a kirigami fold while the latter is reveled from the study of the transition index The paper analyzes these 6R metamorphic linkages and provides the transition index to describe the reconfiguration between motion branches. The transition index is used to describe the reconfiguration of the linkage and to design a new 6R metamorphic linkage The three motion branches and the close-loop transformation are given
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