On the comprehensive static characteristic analysis of a translational bistable mechanism. (December 2016)

• Record Type: Journal Article
• Authors: Hao, Guangbo; Mullins, John
• Is Part Of: Proceedings of the Institution of Mechanical Engineers. Volume 230:Number 20(2016)
• Page Start: 3803
• Page End: 3817
• Publication Date: 2016-12
• Subjects: Characteristic analysis -- compliant mechanisms -- bistable mechanisms -- negative stiffness equation -- off-axis stiffness -- finite element analysis; Mechanical engineering -- Periodicals; 621.05
• DOI: 10.1177/0954406215616418
• Languages: English
• ISSNs: 0954-4062

Abstract

Bistable mechanisms have two stable positions and their characteristic analysis is much harder than the traditional spring system due to their postbuckling behaviour. As the strong nonlinearity induced by the postbuckling, it is difficult to establish a correct model to reveal the comprehensive nonlinear characteristics. This paper deals with the in-plane comprehensive static analysis of a translational bistable mechanism using nonlinear finite element analysis. The bistable mechanism consists of a pair of fixed-clamped inclined beams in symmetrical arrangement, which is a monolithic design and works within the elastic deformation domain. The displacement-controlled finite element analysis method using Strand7 is first discussed. Then the force–displacement relation of the bistable mechanism along the primary motion direction is described followed by the detailed primary translational analysis for different parameters. A simple analytical (empirical) equation for estimating the negative stiffness is obtained, and experimental testing is performed for a case study. It is concluded that (a) the negative stiffness magnitude has no influence from the inclined angle, but is proportional to the product of the Young's modulus, beam depth, and cubic ratio for in-plane thickness to the beam length; (b) the unstable position is proportional to the product of the beam length and the Sine function of the inclined angle, and is not affected by the in-plane thickness and the material (or the out-of-plane thickness). The in-plane off-axis (translational and rotational) stiffness is further analysed to show the stiffness changes over the primary motion and the off-axis motion, and a negative rotational stiffness domain has been obtained.