Analytical and numerical analysis of mobility and kinematic bifurcation of planar linkages. (October 2022)

• Record Type: Journal Article
• Authors: Wang, Yutao; Zhang, Qian; Zhang, Xiaohui; Cai, Jianguo; Jiang, Chao; Xu, Yixiang; Feng, Jian
• Is Part Of: International journal of non-linear mechanics. Volume 145(2022)
• Publication Date: 2022-10
• Subjects: Mobility -- Kinematic bifurcation -- Analytical and numerical analysis -- Planar linkages; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2022.104110
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: Mobility analysis of linkage systems remains a topic of extensive research. Some criteria were proposed to determine whether a system is a moveable mechanism, such as the Maxwell criterion. However, the most frequently used criteria at a given configuration are not sufficient and necessary conditions for a finite mechanism. For the kinematic analysis, many researchers proposed numerical methods rather than using analytical approaches. In this paper, the mobility and kinematic bifurcation of mechanisms can be determined by analytical and numerical analysis of system constraint equations. If the solution of system constraint equations exists and the system constraint equations are continuous, the system is moveable. The kinematic bifurcation and the limit point in the kinematic path of mechanisms are also discussed. Finally, all the motion paths can be obtained by this method considering bifurcation and limit point in the kinematic paths at any configurations. Highlights: Sufficient and necessary conditions for mobility of planar linkages are proposed. Motion path is obtained according to analytical or numerical analysis of mechanism. Kinematic bifurcation exists if system constraint equations have multiple solutions. Limit point in the kinematic path is determined by observing the iteration error.