A Loop-Based Approach for the Detection of Rigid Substructures in Spatial Nucleation-Free Spherical-Spherical Bar Mechanisms

F. Simroth ； H. Ding ； A. Kecskeméthy

《Proceedings of the 14th IFToMM World Congress》 14th-1 (2015/10) Pp. 382-391

https://doi.org/10.6567/IFToMM.14TH.WC.OS2.034

並列摘要

Detection of rigid substructures in mechanisms has challenged researchers for many years and is of importance in a variety of fields ranging from synthesis of mechanisms up to molecular flexibility. While for the planar case effective algorithms based on Laman's theorem already exist, spatial mechanisms are still an open challenge. Hereby, a special class of counter-examples termed nucleation-free mechanisms has been introduced in 2009 by Cheng, Sitharam and Streinu, where originally mobile ＂cells＂ become partially rigid and rotate about ＂implied edges＂ when embedded into the whole mechanism. To the knowledge of the authors, no method currently exists for structurally detecting the rigid cells and the remaining degrees of freedom (DOF) for such mechanisms. This paper presents a novel solution approach to tackle this problem. The approach is based on regarding the mechanism not as a system of joint-coupled bodies, but as a system of interconnected kinematical loops. This allows one to follow much better the transmission of relative DOF, and to easily mix spherical, planar or spatial subsystems. In addition, a new methodology of tracking so-called isolated DOF is proposed. By discerning between fully isolated, transmitted isolated, and structurally isolated DOF, the automatic detection of implied edges is possible. While the approach has already been recently presented for the ＂Double Banana＂ problem, which implies proper rigid substructures, this paper describes for the first time the detection of rigid cells in nucleation-free mechanisms. The paper suggests that by using the loop interconnection graph and by tracking the isolated DOF, a novel, systematic and universally applicable alternative method emanates which may be used for the structural mobility analysis of general mechanisms.

並列關鍵字

rigidity detection ； nucleation-free ； 7-roof ； kinematical network ； multiple spherical-spherical joints