Exploring bundle folding in general line-symmetric Bricard mechanisms: Dimensional synthesis and performance evaluation

In this paper, a comprehensive dimensional synthesis method for general line-symmetric 6R deployable polygonal mechanisms (LS-6R-DGMs) is proposed, followed by an in-depth performance analysis of the mechanisms designed using this method. Firstly, the four types of mechanism parameters involved in constructing DGMs are reviewed. Subsequently, all seven possible layouts of revolute pair axes for LS-6R-DGMs are proposed, and a dimensional synthesis method for general LS-6R-DGMs is introduced. Using this method, all general line-symmetric Bricard mechanisms capable of achieving tight bundle folding and deployment into planar polygons can be detected. Secondly, the detailed design process is elaborated. The design results for seven types of LS-6R-DGMs are demonstrated, with prototypes developed for some of them, and the feasible domains of the corresponding design parameters identified. Finally, a comprehensive performance analysis of the LS-6R-DGMs is conducted, covering input singularity, deploying and folding performance, transmission ratio stability, and motion$/$force transmission performance. Additionally, an index for assessing the deployment performance of LS-6R-DGMs is proposed. This research broadens the diversity and quantity of DGMs, contributing to advancements in large deployable structures, metamaterials, and robotics.