Design of a bistable mechanism with B-spline profiledbeam for versatile switching forces

Accepted Manuscript

Title: Design of a bistable mechanism with B-spline profiled

beam for versatile switching forces

Authors: I-Ting Chi, Tien Hoang Ngo, Pei-Lun Chang, Ngoc

Dang Khoa Tran, Dung-An Wang

PII: S0924-4247(19)30560-6

DOI: https://doi.org/10.1016/j.sna.2019.05.028

Reference: SNA 11400

To appear in: Sensors and Actuators A

Received date: 1 April 2019

Revised date: 29 April 2019

Accepted date: 16 May 2019

Please cite this article as: Chi I-Ting, Ngo TH, Chang P-Lun, Tran NDK,

Wang D-An, Design of a bistable mechanism with B-spline profiled beam for

versatile switching forces, Sensors and amp; Actuators: A. Physical (2019),

https://doi.org/10.1016/j.sna.2019.05.028

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Design of a bistable mechanism with B-spline profiled

beam for versatile switching forces

I-Ting Chi1

, Tien Hoang Ngo1

, Pei-Lun Chang1

, Ngoc Dang Khoa Tran2

, Dung-An

Wang1*

1Graduate Institute of Precision Engineering, National Chung Hsing University, Taichung

40227, Taiwan, ROC

2Faculty of Mechanical Engineering, Industrial University of Ho Chi Minh City, 12

Nguyen Van Bao, Ward 4, Go Vap District, Ho Chi Minh City, Vietnam

* Corresponding author: Tel.:+886-4-22840531 ext. 365; fax:+886-4-22858362

E-mail address: [email protected] (D.-A. Wang).

Graphical Abstract

Highlights

 ‧ A bistable mechanism composed of B-spline curved beams for versatile

switching forces in the forward and backward directions is proposed.

 ‧An analytical model to solve for the nonlinear force-displacement characteristics

of the B-spline profiled beams is developed. ACCEPTED MANUSCRIPT  ‧Smoother force-displacement curve is achieved compared to existing design.

2

Abstract

A compliant bistable mechanism composed of B-spline curved beams for design of

switching forces in the forward and backward directions is developed. The parametric B￾spline curve has five control points to give a high design freedom in the output force of

the beam-type compliant mechanisms. An analytical model is developed to provide an

efficient tool to obtain the force-displacement characteristics of the B-spline profiled

bistable mechanism. B-splined profiled bistable mechanisms with various ratios of the

switching forces in the forward and backward motions are designed. The results are

confirmed by experiments. The developed bistable mechanism with high force versatility

has applications in devices where precise geometric activation and quantifiable load

bearing capacity are desired.

Keywords: compliant mechanism; B-spline curve; switching force.

1. Introduction

A compliant bistable mechanism (CBM) with desired characteristics of force and

displacement output is desired in its industrial applications. Aerospace industries need a

reliable release mechanism to launch deployable structures, such as antennae, satellites and

solar panels. CBM’s high reliability, low vibration sensibility in force response, and less

susceptibility to temperature variation have led them to space application [1]. Precise

geometric activation and quantifiable load bearing capacity of CBMs make them suitable

for emerging applications in automotive, building and biomedical industries [2]. In

automotive industry, CBMs can be employed in trunk lid design to compensate to lid

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weight during opening/closing operation [3]. Transition of a robotic end effector can be

achieved with controllable bistable positions of CBMs [4]. Precise control of the force￾displacement behavior of CBMs is a prerequisite for their successful applications in

switches [5], projection displays [6], and nonvolatile memory elements [7], etc. For

applications in nonvolatile memory devices, nearly equal switching forces in back and forth

directions of CBMs may facilitate two logical levels “1” and “0” corresponding to the two

stable states. The equal switching force of CBMs can see its use in threshold

accelerometers to achieve two sensing directions along one sensing axis [8].

Design for force/displacement output of CBMs has attracted attention in recent

years. Li and Chen [9] proposed a rational function to model the force-displacement (F-d)

characteristics of several CBMs. Their function with a cubic polynomial numerator and

quadratic polynomial denominator can capture key features of the F-d curve, where

regression analyses are required to obtain the polynomials to describe the relations between

design parameters and the F-d characteristics of the CBMs. Huang et al. [10] developed

an optimization based method for design of CBMs with specific switching forces. The

presented CBMs have cosine curved beams with multiple reinforced segments. By

modifying the length, width, thickness, element number and position of the reinforced

segments, the desired switching forces of the CBMs can be achieved. The F-d curves of

their designs with nearly equal switching forces in the forward and backward directions

might not be smooth. Smooth force spectrum may be advantageous to avoid chatter

vibration during operation. Palathingal and Ananthasuresh [11] proposed a shape

optimization approach to obtain the switching forces and the distance between equilibrium

states of CBMs numerically. For improved accuracy of their method, several mode shapes

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