Stiffness Analysis of Corrugated Flexure Beam Used in Compliant Mechanisms

Conventional flexible joints generally have limited range of motion and high stress concentration. To overcome these shortcomings, corrugated flexure beam（CF beam） is designed because of its large flexibility obtained from longer overall length on the same span. The successful design of compliant mechanisms using CF beam requires manipulation of the stiffnesses as the design variables. Empirical equations of the CF beam stiffness components, except of the torsional stiffness, are obtained by curve-fitting method. The application ranges of all the parameters in each empirical equation are also discussed. The ratio of off-axis to axial stiffness is considered as a key characteristic of an effective compliant joint. And parameter study shows that the radius of semi-circular segment and the length of straight segment contribute most to the ratio. At last, CF beam is used to design translational and rotational flexible joints, which also verifies the validity of the empirical equations. CF beam with large flexibility is presented, and empirical equations of its stiffness are proposed to facilitate the design of flexible joint with large range of motion.

Enabling the transfer matrix method to model serial-parallel compliant mechanisms including curved flexure beams

Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,metamaterials,robotics,and so forth.However,serial-parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design.Here,the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial-parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods.Consequently,serial-parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure.Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach.In conclusion,the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial-parallel compliant mechanisms and beam structures,including curved flexure hinges and irregular-shaped rigid bodies.

A Large Range Flexure-Based Servo System Supporting Precision Additive Manufacturing

This paper presents the design, development, and control of a large range beam flexure-based nano servo system for the micro-stereolithography （MSL） process. As a key enabler of high accuracy in this process, a compact desktop-size beam flexure-based nanopositioner was designed with millimeter range and nanometric motion quality. This beam flexure-based motion system is highly suitable for harsh operation conditions, as no assembly or maintenance is required during the operation. From a mechanism design viewpoint, a mirror-symmetric arrangement and appropriate redundant constraints are crucial to reduce undesired parasitic motion. Detailed finite element analysis （FEA） was conducted and showed satisfactory mechanical features. With the identified dynamic models of the nanopositioner, real-time control strategies were designed and implemented into the monolithically fabricated prototype system, demonstrating the enhanced tracking capability of the MSL process. The servo system has both a millimeter operating range and a root mean square （RMS） tracking error of about 80 nm for a circular traiectorv.

Damage detection method in complicated beams with varying flexural stiffness

A damage detection method for complicated beam-like structures is proposed based on the subsection strain energy method （SSEM）, and its applicability condition is introduced. For a beam with the continuously varying fiexural stiffness and an edge crack, the SSEM is used to detect the crack location effectively by numerical modal shapes. As a complicated beam, the glass fiber-reinforced composite model of a wind turbine blade is studied based on an experimental modal analysis. The SSEM is used to calculate the damage index from the measured modal parameters and locate the damage position in the blade model successfully. The results indicate that the SSEM based on the modal shapes can be used to detect the damages in complicated beams or beam-like structures for engineering applications.

Analysis of Shear Failure in Reinforced Concrete Beams without Stirrups

This paper deals with flexural concrete members reinforced longitudinally but without transverse reinforcement. The conducted experimental investigations have shown that beams without web reinforcement may fail without attaining their full flexural capacity and then shear governs their failure. In the paper, there are presented recent results of the author＇s own experiments, which aimed at disclosing some aspects of the propagation of cracks in longitudinally reinforced concrete beams without stirrups. The experimental program has been designed especially to investigate the influence of the shear span-to-depth ratio on diagonal crack propagation and load carrying capacity of tested beams.

Distribution of Reinforcement in Tensile Flanges of Concrete T-shape Continuous Beam

In this paper the analysis of tensile stress distribution in flexural continuous T- beam has been presented. The observed damages in carrying deck of RC bridge over the Wieprz River in Baranow indicate that over pillar zones are not protected enough. The results of numerical analysis have shown that tensile stress in T- section beam appears not only in a web but in flanges as well. Thus reinforcing bars should be distributed within the whole effective width. This fact is mentioned in building codes, for example, in Eurocode 2： ＂Design of concrete structures＂, both in part 1.1 ＂General rules and rules for building＂ and in part 2 ＂Reinforced and prestressed concrete bridges＂, but there are not detailed rules how to place the bars in flanges of T-section.

Experimental and Numerical Investigation on the Tensile Fracture of Compacted Clay

This paper performed flexural test and numerical simulation of clay-beams with different water contents to study the tensile fracture of clay soil and the relevant mechanisms.The crack initiation and propagation process and the accompanied strain localization behaviors were all clearly observed and analyzed.The exponential cohesive zone model was proposed to simulate the crack interface behavior of the cohesive-frictional materials.The experimental results show that the bending capacity of clay-beams decrease with the water content,while those of the crack mouth opening displacement,crack-tip strain and the strain localization range increase.The numerical predictions successfully reproduce the evolving tensile cracks and the strain localization phenomenon of the clay beams with different fracture ductility,which demonstrates the validity of the proposed cohesive zone model in modelling clay fractures.

Higher mode effects in hinged wall with BRBsin base-frame structures using distributed parameter models

To investigate the effect of higher modes on the displacement and inner forces in HWBB(hinged wall with buckling-restrained braces in base)-frame structure,distributed parameter models for both the HWBB-hinged frame structure and the HWBB-MRF(moment resisting frame)structure are built.The hinged wall is simplified as a flexural beam.BRBs(bucking-restrained braces)are simplified to a rotational spring.MRF is simplified to a shear beam.Vibration equations of distributed parameter models are derived.Natural periods,natural modes of vibration,inner forces and displacements of the distributed parameter models are derived based on the vibration equations using numerical methods.The effect of the relative stiffness ratio and the rotational stiffness ratio on the higher mode effects is investigated.For elastic structures,the global displacement and shear in MRF are predominantly controlled by the first mode,while the shear and bending moment in the wall are significantly affected by higher mode effects.The effect of the yielding of BRB on the inner forces distribution in the HWBB-hinged frame is investigated.The results indicate that the first mode will no longer contribute to the inner forces and the contribution from higher modes to inner forces increases after the BRBs yield.Displacement is not sensitive to higher mode effects and it is controlled by the first mode after the BRBs yield.Parameter analysis demonstrates that the displacement amplitudes are reduced with the increase in the flexural stiffness of the wall before the flexural stiffness reaches a certain value.The first three periods decrease with the increase in the rotational stiffness.With the increase in the rotational stiffness ratio,the contribution from the first mode decreases while contributions from both the second mode and third mode increase.

A closed-form nonlinear model for spatial Timoshenko beam flexure hinge with circular cross-section

Beam flexure hinges can achieve accurate motion and force control through the elastic deformation. This paper presents a nonlinear model for uniform and circular cross-section spatial beam flexure hinges which are commonly employed in compliant parallel mechanisms. The proposed beam model takes shear deformations into consideration and hence is applicable to both slender and thick beam flexure hinges. Starting from the first principles, the nonlinear strain measure is derived using beam kinematics and expressed in terms of translational displacements and rotational angles. Second-order approximation is employed in order to make the nonlinear strain within acceptable accuracy. The natural boundary conditions and nonlinear governing equations are derived in terms of rotational Euler angles and subsequently solved for combined end loads. The resulting end load-displacement model, which is compact and closed-form, is proved to be accurate for both slender and thick beam flexure using nonlinear finite element analysis. This beam model can provide designers with more design insight of the spatial beam flexure and thus will benefit the structural design and optimization of compliant manipulators.

Effects of Adhesive Characteristic on the Test Results of Damping Material's DMP

In the measurement of damping material's dynamic mechanical performance(DMP) using flexural resonating cantilever beam method,the specimen's adhesive characteristic influences the test precision and accuracy. Taking its effect into account,the improved measurement equations based on the resonance method are presented. The simulated results show that,for the sake of weakening the adhesive's influence on the measured results,the adhesive should be spreaded as thin as possible when specimen is prepared,the adhesive's density and loss factor should be selected as small as possible also,and its Young's modulus should be selected according to the damping material being measured;the same adhesion condition effects differently on the test results of different damping materials,i.e. the error due to the adhesive is more inconspicuous if the damping layer has bigger thickness,modulus,loss factor and a certain density according to the damping material being measured. These conclusions provide theoretical basis for selecting adhesive,improving adhesion technology,and designing specimen.

Research on the relaxor ferroelectric single crystal flexural beam vector hydrophone

A two-dimensional vector hydrophone was developed utilizing the PMN-PT relaxor ferroelectric single crystal,which is composed of a dual-axis piezoelectric composite flexural beam accelerometer and PZT-5 piezoelectric ceramic rings.Based on the principle of elastic mechanics and underwater particle velocity measurement,the receiving voltage sensitivity of the flexural beam vector hydrophone is derived.The influence of stress distribution in the flexural beam on the performance of hydrophones is analyzed,and the match between PMNPT single crystal cells and the structure of flexural beam is studied.The tested results indicate that the PMN-PT hydrophone presents an 11 dB increase in sensitivity and a 3 dB decrease in self-noise than the PZT-5 one.