A geometric and analytic technique for studying single-DOF planar mechanisms' dynamics. (February 2022)

• Record Type: Journal Article
• Authors: Di Gregorio, Raffaele
• Is Part Of: Mechanism and machine theory. Volume 168(2022)
• Publication Date: 2022-02
• Subjects: Multibody system dynamics -- Virtual work -- Planar mechanism -- Instant center -- Higher education; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2021.104609
• Languages: English
• ISSNs: 0094-114X

Abstract

Highlights: A novel dynamics-analysis method for single-DOF planar mechanisms is presented. The presented method is applicable to any single-DOF planar mechanism. The proposed method fully discloses instant centers' role in dynamics analyses. A geometric interpretation of the deduced dynamic model is provided. The proposed method is simple enough to present it in graduate courses. Abstract: Relating geometric interpretations to analytic procedures for solving mechanical problems improves their comprehension and gives a deeper insight on how to eliminate unwanted behaviors of the studied machine. This aspect is well stated in Newton-Euler formulation of mechanism dynamics. Unfortunately, many approaches of analytical mechanics build dynamic models of mechanisms that are difficult to put in relation with clear geometric constructions. D'Alembert principle, which is based on the virtual work principle, is one of these approaches. Here, a systematic way for modeling single-degree-of-freedom (single-DOF) planar mechanisms through the D'Alembert principle and the instant centers' (ICs') positions is presented which is related to geometric interpretations of the terms appearing in it. The proposed geometric interpretation is so effective that, formally, the model could be written starting from it without any analytic consideration as same as the equilibrium equations can be written from free-body diagrams in the Newton-Euler formulation. The resulting dynamic model is novel and general. The proposed model and the associated solution algorithms of the dynamic problems are also illustrated through a case study. The obtained results are of interest in mechanism analysis and design and, due to their simple theoretical bases, can be presented in courses for undergraduate or graduate students.