Sylvester's dialytic elimination in analysis of a metamorphic mechanism derived from ladybird wings. (January 2023)

• Record Type: Journal Article
• Authors: Chen, Zhuo; Chen, Qiuhao; Jia, Guanglu; Dai, Jian S.
• Is Part Of: Mechanism and machine theory. Volume 179(2023)
• Publication Date: 2023-01
• Subjects: Ladybird beetles -- Origami -- Screw theory -- Metamorphic mechanism -- Sylvester's dialytic elimination; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2022.105102
• Languages: English
• ISSNs: 0094-114X

Abstract

Abstract: This paper investigates the metamorphic mechanism derived from the hindwing in ladybird beetles, which creates its mathematical models and analyzes kinematics based on screw theory using mathematical software. The hindwing in ladybird beetles is an origami-like structure. Considering the concept of equivalent mechanisms, any origami pattern can be seen as being composed of several spherical multi-bar linkages connecting to each other. Hence, this paper proposes an algebra method to reveal the relations between different joint angles in the spherical multi-bar linkage, using the loop equations and Sylvester's dialytic elimination method. The results can be used to find the location and the motion trajectory of any desired point in this ladybird wing metamorphic mechanism. The way of analysis of the spherical multi-bar mechanism used in this paper can be widely applied in design and practical applications. Highlights: Mathematical modelling of the ladybird wing equivalent mechanism is established. A method for analysing tandem spherical linkage based on screw theory is proposed. Sylvester's elimination method is used to obtain the joint angles relationship. The forward kinematics analysis of the mechanism is complete.