Novel Universal Multistable Mechanism Based on ...

2714

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 6, JUNE 2014

Novel Universal Multistable Mechanism Based on Magnetic–Mechanical–Inertial Coupling Effects Jian Zhao, Member, IEEE, Yu Huang, Renjing Gao, Guoxi Chen, Yintang Yang, Shutian Liu, and Kefeng Fan

Abstract—Different from multistable mechanisms incorporating multiple bistable elements, a novel universal multistable mechanism possessing the capability of being triggered in all in-plane directions was first designed and fabricated by using symmetric 3-D magnetic structures, which mainly consists of one magnetic ring supported by a elastic rod and one axially magnetized pillar fixed on the aluminum case. The in-plane isotropic multistability was originated from the nonlinear interactions among the inertial force, the elastic force, and the magnetic force. According to the pseudo-rigid-body model and magnetic charge model theories, an accurate mathematical model was established for precisely analyzing the nonlinear magnetic–mechanical–inertial coupling mechanics. By considering the influence of the translational motion and the inclination angle of the magnetic ring on the magnetic field distribution and strength, the nonlinear force versus displacement relationship was obtained numerically and experimentally. The numerical results are in good accordance with those obtained by experiments, thus validating the design methodology for isotropic multistable mechanism. Index Terms—Design model, isotropic multistability, magnetic–mechanical coupling, nonlinear mechanics, universal multistable mechanism.

I. I NTRODUCTION

M

ULTISTABILITY is a nonlinear phenomenon that can maintain many stable states without any external forces. With the attractive properties such as snap-through, accurate positioning, and state holding capability, bistable and multistable mechanisms have great applications in industrial electronics, such as energy harvesting systems [1], state memories [2], valves and relays [3], [4], switches and actuators [5]–[7], and microelectromechanical systems displays [8]. In recent decades, a series of compliant bistable mechanisms with different structural configurations have been reported, Manuscript received November 7, 2012; revised March 5, 2013, May 27, 2013, and June 12, 2013; accepted June 27, 2013. Date of publication July 16, 2013; date of current version December 20, 2013. This work was supported in part by the National Natural Science Foundation of China under Grant 51105059, by the China Aviation Industry Corporation Project (cxy2011dg34), by the Doctoral Fund of Ministry of Education of China under Grant 20100041120019, and by the Fundamental Research Funds for the Central Universities. (Corresponding author: J. Zhao.) J. Zhao, Y. Huang, R. Gao, G. Chen, and S. Liu are with the State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). Y. Yang is with the School of Microelectronics, Xidian University, Xi’an 710126, China (e-mail: [email protected]). K. Fan is with the Research Center of Information Security, China Electronics Standardization Institute, Beijing 100007, China (e-mail: kefengfan@ 163.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2273475

including latch-lock mechanisms [9], [10], compliant bistable mechanisms, double slider mechanisms [11]–[13], and buckling mechanisms [14]–[18], which mainly use elastic deflections to release and absorb strain energy. By using the nonlinear stiffness, these bistable mechanisms can maintain two stable states in their range of motion. However, constrained by strict boundary conditions for achieving bistability, the moving parts of these mechanisms can only be driven in one direction or in a predefined way, hence resulting in single direction bistability, which cannot fulfill the requirement of multitriggering directions for some special applications such as universal crash recording and transport shipment monitoring systems [5], [19], [20], morphing structure controlling [21], [22], and robotic end effectors [23], [28]. To solve this problem, many researchers tried to connect a series of bistable structures together in prerequired directions to increase triggering directions, thus introducing the concept of multistable mechanisms. For example, Chen et al. [16] designed a tristable mechanism by employing orthogonally oriented compliant mechanisms. Han et al. [24] proposed a quadristable monolithic mechanism with two orthogonally connected bistable curved beams, which can arrange three stable states in two orthogonal directions. Zhao et al. [25] designed a magnetic based tristable mechanism which can transfer three stable states in two opposite directions. Pendleton and Jensen [26] designed a tristable unsymmetrical compliant mechanism with two rotary directions. Ohsaki and Nishiwaki [27] proposed a kind of pin-jointed multistable mechanism, which can be triggered in different directions. King et al. [28] proposed a quadristable mechanism consisting of a rotary compliant beam with an armature magnet attached to it and an array of stator magnets. Hafez et al. [29] proposed a robotic device with a large number of stable positions by using a series of bistable mechanisms, which can be used for tasks requiring a robot to operate in a 3-D space. Using discrete magnets arranged spatially, Petit et al. [30] proposed a novel actuator with four stable positions in two perpendicular directions. Son and Lee [31], Lee et al. [32], and Lim et al. [33] designed many spherical actuators with multimagnetic poles for omnidirectional motion. From the configurations of the multistable mechanisms mentioned earlier, it can be seen that the triggering directions are relying mainly on locations and connection styles of the corresponding bistable mechanisms. Also, the total structural complexity increases greatly with the number of bistable structures involved. Although the motion direction of the mechanism can be increased by adding stable states at the required positions, as yet, there are no specific multistable structures that can be triggered in all directions.

0278-0046 © 2013 IEEE

IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 18, NO. 1, FEBRUARY 2013

113

A Bidirectional Acceleration Switch Incorporating Magnetic-Fields-Based Tristable Mechanism Jian Zhao, Member, IEEE, Renjing Gao, Yintang Yang, Yu Huang, and Ping Hu

Abstract—In order to fulfill the requirements of low energy consumption and two sensing directions, a novel bidirectional acceleration switch is proposed by utilizing the magnetic-fields-based tristable mechanism that can maintain the three stable states without input power and with high position accuracy and repeatability. The bidirectional acceleration switch mainly consists of an inertial mass supported by two parallel elastic beams, two metal contact points, and four permanent magnets with one imbedded in the inertial mass and the other three fixed in the case along the vertical direction. Based on the magnetic charge model, the nonlinear magnetic force is analyzed, and then, a static design model of the bidirectional switch is established by considering the elastic force, the magnetic force, the contact force, and the inertial force. To validate the feasibility of the design method, a miniature sample of the switch is fabricated. The results of the centrifugal experiment show that the threshold accelerations in two directions are 53.0 and −52.0 g, respectively, which are close to the design values of 55.0 and −50.0 g, correspondingly. In addition, the threshold values can be adjusted by changing the relative distances among the four magnets. Index Terms—Acceleration switch, bidirectional, design model, tristable mechanism.

I. INTRODUCTION WING to the ideal signal handling properties such as high isolation, low insertion loss, and excellent signal linearity, the contact-type acceleration switches [1]–[4] have been widely used in many industrial applications such as automotive safety systems, crash recorders, arming and firing systems, and so on. However, in the actual applications, the actuation and power consumption problem has been considered to be the most challenging factor affecting the switch’s reliability and service

O

Manuscript received March 30, 2011; revised June 23, 2011; accepted July 20, 2011. Date of publication September 8, 2011; date of current version September 12, 2012. Recommended by Technical Editor A. Menciassi. This work was supported in part by the National Basic Research Program of China under Grant 2011CB610304, in part by National Natural Science Foundation of China Funds (51105059), in part by the Doctoral Fund of the Ministry of Education of China under Grant 20100041120019, in part by the China Postdoctoral Science Foundation under Grant 20090461286 and Grant 201003665, and in part by the Fundamental Research Funds for the Central Universities. J. Zhao, R. Gao, and P. Hu are with the College of Automotive Engineering, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China (e-mail: [email protected]; [email protected]). Y. Yang is with the College of Microelectronics, Xidian University, Xi’an 710071, China. Y. Huang is with the State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMECH.2011.2163725

Fig. 1.

Bistable mechanism.

life [5]. For the cantilever switches, the utilization of the extra electrostatic or electromagnetic force for maintaining its close state will take a large proportion of the total power consumption. Therefore, low energy consumption mechanisms like bistable or tristable structures used in acceleration switches or relays have attracted lots of attentions from researchers [6]–[15]. Recently, aiming to reduce the power consumption, the bistable structures have been introduced as the spring elements in the acceleration switches [16]–[20] that have two well-defined stable states, as shown in Fig. 1. Besides the power saving characteristic, the bistable structures can also provide high sensitivity, large contact force, fast switching response, and better antijamming performance. The only drawback of the bistablestructure-based acceleration switch is that it only has one single sensing direction, because one of the two stable states is used as the open state, and the other as the close state to keep the contacts connected. In order to achieve the function of two sensing directions, the simplest way is to use two one-directional switches fixed in two opposite directions that induce the difficulty in the compatibility of the two switches and connecting two different switches in one triggering circuit. Liu et al. [21] designed a microelectromechanical systems impact acceleration switch with two sensitive directions by using four serpentine springs as the spring element. However, extra forces are needed to maintain the close state when the triggering threshold acceleration disappears. Therefore, the tristable structures with two different snapping threshold forces can be employed to fulfill the state maintaining capability of the bidirectional switches. Based on the nonlinear coupling characteristic between the mechanical structure and the magnetic mechanism, a novel tristable mechanism for the bidirectional acceleration switch was proposed to lower the energy consumption. By utilizing the tristability of the magnetic-field-based tristable mechanism, the acceleration switch being triggered can maintain the three stable states without input power, and meanwhile, can sense the threshold acceleration with high repeatability and positioning accuracy.

1083-4435/$26.00 © 2011 IEEE

1612

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 3, MARCH 2014

A New Sensitivity-Improving Method for Piezoelectric Resonance Mass Sensors Through Cantilever Cross-Section Modification Jian Zhao, Member, IEEE, Renjing Gao, Shutian Liu, and Yu Huang

Abstract—Resonant cantilever sensors have been extensively used in mass detection applications. In this paper, a new sensitivity-improving method was proposed by modifying the cross-section shape of the cantilever. With the same dimension, the proposed sensor can offer two to eight times greater sensitivity than traditional rectangular section cantilever sensors. To eliminate the size effect, a dimensionless mathematical model was established for examining the sensitivity improvement brought by adding axial grooves to elastic structures. By utilizing wirecutting technology, a novel grooved-section cantilever sensor was designed and fabricated, which is comprised of one lead zirconate titanate layer bonding to the grooved cantilever for self-exciting and self-sensing. Experimental results show that the sensitivity of the grooved-cantilever sensor is 37.5 kHz/g with the theoretical sensitivity of 38.1 kHz/g, which is about 120% greater than that of the rectangular section sensor of 17.9 kHz/g with the theoretical sensitivity of 18.2 kHz/g. Thus, the comparison validated the effectiveness of the sensitivity-improving method within the same geometric dimension. Furthermore, by optimizing both the crosssection shape and the geometrical ratios of the elastic extension to the piezoelectric layer simultaneously, the overall sensitivity can be increased by 8.15 times greater than that of the rectangular section cantilever sensor, which has great potential applications in high-resolution mass sensors. Index Terms—Cantilever, cross-section modification, piezoelectric layer, resonance mass sensor, sensitivity improvement.

I. I NTRODUCTION

A

RESONANT cantilever mass sensor can quantitatively detect unknown analytes by measuring the frequency shift, which mainly consists of one piezoelectric or piezoresistive layer, one elastic supporting layer, and one functional layer for absorbing analyte on the cantilever surface. With the elegance of not requiring analyte labeling, such cantilevers with different functional layers have been very popular mass-sensing structures, which also have been successfully applied in various

Manuscript received July 18, 2012; revised October 31, 2012 and February 4, 2013; accepted March 30, 2013. Date of publication April 16, 2013; date of current version August 23, 2013. This work was supported in part by the National Natural Science Foundation of China under Grant 51105059 and 11172052, by the Doctoral Fund of the Ministry of Education of China under Grant 20090041110023 and 20100041120019, by the National Basic Research Program of China under Grant 2011CB610304, and by the Fundamental Research Funds for the Central Universities. (Corresponding author: S Liu) The authors are with the State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2013.2258298

application fields such as proteomics [1]–[3], genomics [4], gas sensing [5], food contamination [6], cancer detection [7], and chemical or fluidic detection [8]–[10]. In the recent years, much attention has been paid to improving the detection sensitivity and on simplifying the measurement procedure. According to the operating principle of resonant sensors, the mass detection sensitivity Δf /Δm (resonance frequency shift per unit mass change) is directly bound with the cantilever geometry and configuration and with the properties of the materials composing it. Using this principle, the existing methods are categorized into three main topics: geometrical dimension reduction [5], [11]–[20], regulation of high-order vibration [21]–[23], and configuration optimization [24]–[41]. Jang and Hassibi [16] have examined the compatibility of CMOS process in integrated affinity-based biosensor systems. Admittedly, reducing geometry dimensions by MEMS or NEMS technology is an effective way to improve sensitivity and spatial resolution of resonance mass sensors. However, practical size limits of mass sensors have been reached by using present NEMS technology, and the detection sensitivity is improved at the expense of complex supplementary equipment for accurate detection and low antijamming ability to environmental factors such as air dust, humidity, and acoustic noise. Hence, geometry minimization sometimes is not an all-purpose way to improve mass detection sensitivity. Practically, cantilever shape modification is another effective way to improve mass detection sensitivity by adjusting the mass distribution and the sensitive area location on the cantilever surface. Recently, there have been some efforts devoted to improving the resolution by modifying the cantilever configurations without largely changing the structure dimensions. Yang and Chang [24] designed a modified microcantilever sensor to eliminate the biaxial effect of the surface stress and the thermal effect. Ansari and Cho [25] investigated the sensor performance with different microcantilevers including rectangular, triangular, and step profile. Also, the authors [26] presented a novel design of microcantilever with a rectangular hole on the surface of the fixed end, which was proven to have 75% more sensitivity than the conventional design. Wang et al. [27] reported a sandwich structured piezoresistive microcantilever with the piezoresistive layer in the middle. Besides the piezoresistive sensing principle in [24]–[27], piezoelectric cantilevers integrating both selfactuating and self-sensing functions have also been used in resonance mass sensors by offering many competitive advantages such as relatively simple structure, low driving voltage, portability for outdoor application, and in situ biodetection and

0278-0046 © 2013 IEEE

Mechanism and Machine Theory 83 (2015) 56–68

Contents lists available at ScienceDirect

Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmt

Nonlinear coupling mechanical model for large stroke magneticbased multistable mechanisms Jian Zhao a,⁎, Renjing Gao a,⁎, Guoxi Chen a, Shutian Liu a, Qikai Cao b, Tao Qiu b a b

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, PR China Shenyang Aircraft Design and Research Institute, Shenyang 110035, PR China

a r t i c l e

i n f o

Article history: Received 9 July 2013 Received in revised form 16 August 2014 Accepted 4 September 2014 Available online 21 September 2014 Keywords: Tristability Multistable mechanism Magnetic–mechanical coupling Large deformation Constant-force generation

a b s t r a c t In the previous model for small deformation multistable mechanisms, the axial displacement induced by structural vertical deflection is very small and has not been considered. However, for large deformation magnetic based multistable mechanisms, such axial displacement can directly result in the great deviation in predicting the nonlinear magnetic coupling mechanics. To enlarge the multistability design space, an accurate mathematical model was established for analyzing the nonlinear magnetic–mechanical coupling mechanics. To demonstrate the multistability analyzing procedure, a rotation constrained tristable mechanism was introduced which is also called mechanical memory element that can remember three different mechanical states including structural configurations, stable positions, and threshold triggering forces. By theoretically analyzing the influence of the large deformation induced position variation of multiple magnets on the magnetic field distribution and strength, the nonlinear force-displacement characteristic was obtained numerically, which was in good agreement with experimental results, thus validating the feasibility and practicability of the proposed nonlinear coupling mechanical model. Additionally, the multistable features such as stable positions, threshold forces and motion modes can be adjusted in a wide range for switching applications by just adjusting the magnets' arrangement. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Multistable mechanisms have many stable force-balanced positions within their range of motion, in which the mechanism can maintain stability with high repeatability and positioning accuracy. Since no actuation voltage has to be provided for maintaining stable states, the tristable mechanisms have great potential applications in ultra-low power consumption systems such as satellitebased communication modules [1], the switching of capacitor banks in filters or impedance matching networks, and the switching of resistors in variable gain amplifiers [2,3]. Traditionally, multistable mechanisms are mainly originated from pure mechanical mechanisms which use the elastic deflection of compliant segments to release and absorb strain energy [4–13]. Hence, the multistable properties including the stable positions, threshold forces and motion modes are always determined by the styles of the component bistable structures such as rotary links, deflection beams, pre-stressed beams, locking hooks and so on [14–23]. For achieving multistablility, great attentions have been paid on the connecting styles of bistable cell structures. Han [4] designed a quadristable monolithic mechanism with two bistable curved beams connected orthogonally. Chen [5,6] proposed a double tensural tristable micromechanism by mechanically connecting upper and lower bistable structures together. Oberhammer [7] designed a mechanically tristable switch by locking two fixed hooks at the ends of two cantilevers. Jensen [8] designed a tristable unsymmetrical compliant mechanism by arranging rotary links in ⁎ Corresponding authors.

http://dx.doi.org/10.1016/j.mechmachtheory.2014.09.004 0094-114X/© 2014 Elsevier Ltd. All rights reserved.

3152

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 12, DECEMBER 2014

A Wireless MEMS Inertial Switch for Measuring Both Threshold Triggering Acceleration and Response Time Jian Zhao, Member, IEEE, Pengbo Liu, Zhenan Tang, Member, IEEE, Kefeng Fan, Xiaosong Ma, Renjing Gao, and Jiading Bao

Abstract— Response time is one of the core attributes for threshold acceleration switches for determining the impact severity. Different from single function inertial switches for only converting circuit states, a wireless inertial microswitch incorporating the bistable flexible mechanism was designed and fabricated using multilayered microelectroforming technology, which can be used for remote detection of both the threshold acceleration and the corresponding response time in severe environments. The threshold snap-through characteristic of the nonlinear bistable mechanism has been introduced to achieve the threshold acceleration sensing capability. The switch mainly consists of one wireless module, one proof mass supported by two pairs of ultralong V-shaped slender beams with the dimension of 28.0 µm × 25.0 µm × 5150.0 µm, and two contact points for recording triggering times through the high speed sending and receiving wireless module. Then, an accurate design model for analyzing the threshold acceleration and the dynamic response time was established. The 20 repeated experimental results are in good agreement under the same triggering threshold acceleration of 32.38 g, in which, the response time with the traveling distance of 530.0 µm is 179.80 ± 0.20 ms. Index Terms— Bistability, inertial microswitch, microelectromechanical systems (MEMS), response time recording, threshold acceleration, wireless remote measurement.

I. I NTRODUCTION

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ITHOUT complex signal processing circuits in traditional accelerometers [1]–[3], inertial switches can be used to detect threshold acceleration and then trigger a Manuscript received March 10, 2014; revised April 24, 2014; accepted April 25, 2014. Date of publication May 27, 2014; date of current version November 6, 2014. This work was supported in part by the National Natural Science Foundation of China under Grant 51105059, Grant 11372063, and Grant 11332004, in part by the National Basic Research Program of China under Grant 2011CB610304, in part by the China Aviation Industry Corporation Project under Grant cxy2011dg34, in part by the Open Project of Guangxi Key Laboratory of Manufacturing System and Advanced Manufacturing Technology, and in part by the Fundamental Research Funds for the Central Universities. The Associate Editor coordinating the review process was Dr. Salvatore Baglio. (Corresponding authors: J. Zhao and R. Gao.) J. Zhao and R. Gao are with the State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China (e-mail: [email protected]; [email protected]). P. Liu and Z. Tang are with the School of Electronic Science and Technology, Dalian University of Technology, Dalian 116023, China. K. Fan is with the School of Computer Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, China. X. Ma and J. Bao are with the Guangxi Key Laboratory of Manufacturing System and Advanced Manufacturing Technology, Guilin University of Electronic Technology, Guilin 541004, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2014.2327483

safety mechanism to prevent major damage from a sudden impact. With the distinguished advantage of fast response, microelectromechanical systems (MEMS) inertial switches have great potentials for industrial and military applications, such as crash sensing systems, fuse system, and drop detection systems. Accurately speaking, the two switching characteristics of threshold acceleration sensing capability and the response time are of great importance for threshold accelerometers. In this regard, researchers have paid great attention to improve the switch performances by means of geometry design and advanced machining technologies [4]–[11]. In practice, the reduction of geometric dimensions through MEMS can significantly improve the response speed of inertial switches [4]–[10]. To further improve the static and dynamic performance, special elastic structures for supporting the inertial masses have been introduced in inertial switches, including linear elastic cantilever structures [4]–[9] and nonlinear bistable mechanisms [10]–[15] whose threshold snap-through characteristic and stable state maintaining capability play an important role in improving the sensing accuracy and contact reliability. With the snap-through characteristic, the bistable mechanism can quickly snap from the original stable state to the other stable state when the applied force exceeds the threshold value. In addition, the two stable states can be used as the open and close status avoiding supplementary means to prolong the contact time [4]. In recent years, some works on improving the contact reliability have been reported [16]–[20]. Ongkodjojo and Tay [16] proposed a micromachined G-switch without contact points to lower the actuation voltage and energy consumption. Cai et al. [17] developed a MEMS inertial switch with compliant electrode to prolong the contact time. Guo et al. [18] and Currano et al. [19] designed an inertial switch with self-locking function to ensure the contact stability of the close state. Yoo et al. [20] presented a special MEMS switch with liquid droplet to reduce the contact resistance. According to the dynamic analysis of inertial switches [15], the response time under the triggering acceleration is related to the switch stiffness, the damping coefficient, the acceleration magnitude, and the self-inertia of the system. For a certain inertial switch, the response time for switching the two states decreases with the increasing magnitude of the applied acceleration, which may be useful for analyzing the crash severity in

0018-9456 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Jian Zhao1 State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China e-mail: [email protected]

Yongcun Zhang State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China e-mail: [email protected]

Yu Huang State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China e-mail: [email protected]

Mechanical-Magnetic Coupling Analysis of a Novel Large Stroke Penta-Stable Mechanism Possessing Multistability Transforming Capability

Shutian Liu State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China e-mail: [email protected]

Guoxi Chen State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

Renjing Gao State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

Considering the nonlinear mechanical-magnetic coupling effects, an accurate mathematical model was established for analyzing large stroke penta-stable mechanism possessing multistability transforming capability, with which the mechanism can be switched from pentastability to quadristability. The multistability with any number of stable states can be achieved by integrating spatially arranged magnets and large deformation beams as the fundamental energy storage elements to maintain stable states. By theoretically analyzing the influence of the large mechanical deformation on the magnetic field distribution and system energy, the nonlinear force–displacement characteristics of the multistable mechanism were obtained numerically, which were in good agreement with those obtained by experiments and finite element simulation. Then, an energy-based design criterion for magnetic-mechanical multistable mechanisms was proposed according to the stability theory and energy variation principle. In addition, the multistable transformability was theoretically analyzed, which can transform the proposed mechanism from penta-stability to quadristability by only changing the magnetization direction of moving magnets without varying the structure parameters. [DOI: 10.1115/1.4026630]

Yintang Yang School of Microelectronics, Xidian University, Xi’an, Shaanxi 710071, China e-mail: [email protected]

1

Introduction

Multistable mechanism has many different force-balanced positions within its range of motion, in which the mechanism can maintain stability with high repeatability, high positioning accuracy and low energy consumption [1–5]. With the characteristic of prescribing different desirable shapes or positions, multistable mechanisms have great applications in optical switches, intelligent deployable devices in satellite-antennas, capacitor banks in filters or impedance matching networks, valves, relays, and reconfigurable robots [6–8]. Also, the multistable mechanism possesses many different stable natural frequencies due to the variable stiffness at different stable states. As it is known, less power is needed 1 Corresponding author. Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 13, 2013; final manuscript received December 30, 2013; published online April 3, 2014. Assoc. Editor: Anupam Saxena.

Journal of Mechanisms and Robotics

to create a large output by adjusting the actuation system to work at its natural frequency. Therefore, multistable mechanism can also be incorporated in high efficient actuators with variable resonant frequencies. Traditionally, multistability was mainly originated from the geometric combination of multiple compliant bistable mechanisms including latch-lock mechanisms [9], compliant bistable mechanisms [10–15], and residual compressive-stress buckledbeams [16–18], which process excellent bistable properties such as snap-through, accurate positioning, and state holding capability without power consumption. Due to the inherently nonlinearity of the bistable cell structures or energy storage elements used to maintain different stable positions, it is difficult to obtain a general design methodology for multistable mechanisms. One most commonly used method was to connect multiple bistable structures together according to their geometric configurations [19–21]. For example, Pham and Wang [22] embedded two bistable structures in a surrounding frame structure to obtain a

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[33] Mutlu, R., and Alici, G., 2010, “A Multistable Linear Actuation Mechanism Based on Artificial Muscles,” ASME J. Mech. Des., 132(11) p. 111001. [34] King, C., Beaman, J. J., Sreenivasan, S. V., and Campbell, M., 2004, “Multistable Equilibrium System Design Methodology and Demonstration,” ASME J. Mech. Des., 26(6), pp. 1036–1046. [35] Zhao, J., Gao, R., Yang, Y., Huang, Y., and Hu, P., 2013, “A Bidirectional Acceleration Switch Incorporating Magnetic-Fields-Based Tristable Mechanism,” IEEE/ASME Trans. Mechatronics, 18(1), pp. 113–120. [36] Gerson, Y., Krylov, S., Ilic, B., and Schreiber, D., 2012, “Design Considerations of a Large-Displacement Multistable Micro Actuator With Serially Connected Bistable Elements,” Finite Elem. Anal. Des., 49(1), pp. 58–69.

Journal of Mechanisms and Robotics

[37] Hafez, M., Lichter, M. D., and Dubowsky, S., 2003, “Optimized Binary Modular Reconfigurable Robotic Devices,” IEEE/ASME Trans. Mechatronics, 8(1), pp. 18–25. [38] Zhao, J., Yang, Y., and Wang, H., 2010, “A Novel Magnetic Actuated Bistable Acceleration Switch With Low Contact Resistance,” IEEE Sens. J., 10(4), pp. 869–876. [39] Yonnet, J. P., and Hemmerlin, S., 1993, “Analytical Calculation of Permanent Magnet Couplings,” IEEE Trans. Magn., 29, pp. 2932–2934. [40] Akoun, G., and Yonnet, J., 1984, “3D Analytical Calculation of the Forces Exerted Between Two Cuboidal Magnets,” IEEE Trans. Magn., 20, pp. 1962–1964.

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Considering the compensation of the mass gravity and axial contraction of the parallel beams, the nonlinear force–displacement characteristic obtained by numerical simulation technology is consistent with that by experiments, as shown in Fig. 13. In Fig. 13, it can be found that the analytical model proposed in this paper is much more accurate than the linear model in Ref. [31] when the mechanism performs large deformation. According to the stability theory, five of the nine force-balanced positions can maintain the stable states without external forces. And the good agreement between the simulation and experimental results validate the feasibility and correctness of the theoretical design model for magnetic-mechanical coupled multistable mechanism with multistability transforming capability.

5

Conclusion

In this paper, a novel large stroke penta-stable mechanism is proposed by using the nonlinear magnetic-mechanical coupling effects. The multistability with any number of stable states can be achieved by integrating spatially arranged magnets and large deformation beams as the fundamental energy storage elements to maintain stable states. Different from the purely mechanical multistable mechanisms incorporating fully bistable compliant structures, the magnetic-mechanical based multistability can be transformed from penta-stability to quadristability. Moreover, the multistable properties such as stable positions, threshold snapping forces, and traveling stroke can be adjusted freely by changing the parameters such as the magnets arrangements, relative distances, and polarization of the magnets. With the nonlinear magnetic interactions, at least three interacting magnets were introduced to sustain each stable state, and the corresponding threshold forces for state transformation can also be adjusted to be the same or different. According to the magnetic charge model and pseudo-rigidbody model, an accurate mathematic model for precisely calculating the large deformation penta-stable mechanics was established. Considering the influence of the relative distance variation induced by large deformation compliant beams on the magnetic forces, the nonlinear snap-through mechanics of the penta-stable mechanism was obtained numerically, which were in good accordance with the results by experiments and FEM simulation. Most importantly, the traveling range of the proposed mechanism can be adjusted for different applications, which does not depend on the traveling distances of bistable cell structures. Finally, the methodology feasibility of introducing multiple permanent magnets in designing multistable mechanisms is validated by experiments. Especially, the concept of using multiple magnets to sustain stable states arranged in a limited range of motion are useful in simplifying the configuration of traditionally multistable mechanisms with multiconnected bistable cell structures, which have great potential applications in deployable satellite-antennas, switches, valves, relays, positioners, sensors, and reconfigurable robots.

Acknowledgment This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 51105059, 11372063, 11332004), the China Aviation Industry Corporation Project (cxy2011dg34), Doctoral Fund of Ministry of Education of China (No.20100041120019), the National Basic Research Program of China (No. 2011CB610304), the open project of Guangxi Key Laboratory of Manufacturing System & Advanced Manufacturing Technology, and the Fundamental Research Funds for the Central Universities.

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Transactions of the ASME


A novel alignment mechanism employing orthogonal connected multilayered flexible hinges for both leveling and centering Jian Zhao, Hongxi Wang, Renjing Gao, Ping Hu, and Yintang Yang Citation: Rev. Sci. Instrum. 83, 065102 (2012); doi: 10.1063/1.4722946 View online: http://dx.doi.org/10.1063/1.4722946 View Table of Contents: http://rsi.aip.org/resource/1/RSINAK/v83/i6 Published by the American Institute of Physics.

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065102-6

Zhao et al.

Rev. Sci. Instrum. 83, 065102 (2012)

TABLE III. The leveling resolution measured by the displacement sensor.

VI. CONCLUSION

Testing order

Fully utilizing the advantages of flexible hinges such as no back lash, no friction and no noise, a new alignment mechanism integrating the functions of both leveling and centering is designed and fabricated in this paper. Four groups of orthogonal connected hinges were introduced in the align mechanism to eliminate the coupling problems in the traditional leveling mechanisms with three supporting points. The centering function is achieved by regulating the parallelogram flexible hinges, and the leveling function by adjusting the single circumferential notch hinges. Furthermore, the four groups of hinges are manufactured in one part, which can simplify the structural complexity and improve the measuring precision. The aligning mechanism has been equipped in the gear measuring machine with the centering difference of 1.0 μm within the range of ±1 mm, and the leveling precision of 1 in. within the range of ±1◦ . Finally, the feasibility of the design methodology for the leveling and centering mechanism is validated by the experimental results.

Displacement of the sensor (μm) Relative displacement (μm) Leveling resolution (in.)

Initial value

1

2

3

4

1.1

2.0 0.9 0.93

3.0 1.0 1.03

4.1 1.1 1.13

5.1 1.0 1.03

anism is 3.2 × 105 N/m according to Eqs. (13) and (15). The resolution of the centering and leveling mechanism mainly depends on the structure parameters of the adjusting screws. Figure 8 shows the adjusting mechanism of the leveling screw. The lead of the nonstandard screw M6 is 0.5 mm. And the length of the handle is 150 mm, which can control the rotating angle. In the experiments, the leveling and centering mechanism is installed on the working surface of the C40 type gear measuring machine made by Gongda Ltd, which is shown in Fig. 9. An additional adjusting lever with the length of 150.0 mm is employed to meet the required resolution. Figure 10 shows the arrangement of the gear sample and the adjusting mechanisms. To meet the requirement of the mechanism resolution, displacement of the lever end should be calculated first. When the leveling resolution is 1in., the vertical displacement of the leveling screw should be 0.96 μm. And then the rotation angle of the leveling screw with the lead is obtained as 0.69o . Finally, the step displacement of the lever should be 1.8 mm to realize the designed resolution. In the experiments, the one-dimensional displacement sensor (Tesa GT31) with the resolution of 0.1 μm was utilized to measure the displacement of the alignment mechanism. By rotating the end point of the lever step by step, the corresponding displacements were recorded and displayed on the output screen. The experimental results for measuring the leveling resolution are obtained in Table III.The results show that the measured resolution is nearly consistent with the design value of 1in. Similarly, the displacement of the lever end was calculated to fulfill the centering resolution of 1 μm. With the theoretical analysis, the displacement of the lever end can be obtained as 1.90 mm for each step of centering adjustment. Then, the relative displacement of the centering mechanism was measured by the displacement sensor. Table IV shows the experimental results of the centering mechanism. Therefore, the average centering resolution can be calculated as 1.05 μm, which was basically consistent to that of 1.0 μm obtained theoretically. Finally, the feasibility of the alignment mechanism combining both the leveling and centering functions is validated by the good agreement between the numerical simulation and experiments. TABLE IV. Experimental results of the centering part. Testing order Displacement of the sensor (μm) Centering resolution (μm)

Initial value

1

2

3

4

31.0

31.9 0.9

33.1 1.2

34.2 1.1

35.2 1.0

ACKNOWLEDGMENTS

This work was supported in part by the National Natural Science Foundation of China Funds (Grant No. 51105059), in part by National Natural Science Foundation of China (Grant No. 10932003), “973”National Basic Research Project of China (Grant No. 2010CB832700) and “04” Great Project of Ministry of Industrialization and Information of China (Grant No. 2011ZX04001-21), in part by the Doctoral Fund of the Ministry of Education of China (Grant No. 20100041120019), the China Postdoctoral Science Foundation (Grant Nos. 20090461286 and 201003665), and in part by the Fundamental Research Funds for the Central Universities. 1 G.

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