The Effect of Nonlinear Springs in Jumping Mechanisms

2018 ◽  
Author(s):  
Sahand Sadeghi ◽  
Blake D. Betsill ◽  
Phanindra Tallapragada ◽  
Suyi Li
Keyword(s):  
Piecewise Linear ◽  
Equations Of Motion ◽  
Piecewise Linear Function ◽  
Displacement Curve ◽  
Spring Stiffness ◽  
Nonlinear Spring ◽  
Jumping Performance ◽  
Nonlinear Springs ◽  
Nonlinear Force ◽  
Force Displacement

This research investigates the potential effects of utilizing nonlinear springs on the performance of robotic jumping mechanisms. As a theoretical example, we study dynamic characteristics of a jumping mechanism consisting of two masses connected by a generic nonlinear spring, which is characterized by a piecewise linear function. The goal of this study is to understand how the nonlinearity in spring stiffness can impact the jumping performance. To this end, non-dimensional equations of motion of the jumping mechanism are derived and then used extensively for both analytical and numerical investigations. The nonlinear force-displacement curve of the spring is divided into two sections: compression and tension. We examine the influences of these two sections of spring stiffness on the overall performance of the jumping mechanism. It is found that compression section of the nonlinear spring can significantly increase energy storage and thus enhance the jumping capabilities dramatically. We also found that the tension section of the nonlinear force-displacement curve does not affect the jumping performance of the center of gravity, however, it has a significant impact on the internal oscillations of the mechanism. Results of this study can unfold the underlying principles of harnessing nonlinear springs in jumping mechanisms and may lead to the emergence of more efficient hopping and jumping systems and robots in the future.

Theoretical and Experimental Identification of Clearance Nonlinearities for a Continuum Structure

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Jie Liu ◽  
Bing Li
Keyword(s):  
Cantilever Beam ◽  
Piecewise Linear ◽  
Influence Factors ◽  
Piecewise Linear Function ◽  
Continuous Systems ◽  
Displacement Curve ◽  
Engineering Structures ◽  
Fitting Method ◽  
Nonlinear Force ◽  
Continuum Structure

Clearance is unavoidable in many engineering structures due to the manufacturing and installation errors. These clearances can cause intense impact and wear of the contacting pairs, which may change the dynamic response and eventually reduce the movement precision and the service life of the transmission system. Parameters identification of the clearance would provide better understanding of dynamic behaviors of the clearance and contribute significantly for the control of the induced disturbance and deviation. In this paper, based on dynamic characteristics of the clearance nonlinearity, the piecewise fitting method is first proposed to identify the clearance value of the continuum structure. During the proposed method, first, the rough scope of the clearance value extracted from the displacement response is divided into subintervals. And then, the nonlinear force is fitted by the piecewise linear function in the subintervals. Once the equivalent stiffness is obtained, the clearance value can be calculated by the sorting nonlinear force–displacement curve. The feasibility of the piecewise fitting method was verified by a cantilever beam system with clearances in simulation. Besides, some influence factors of this identification method, including the clearance value, exciting force level and measurement noise, are fully discussed to illustrate the robustness of this method. Moreover, an experiment system of a cantilever beam with adjustable clearances was designed to experimentally validate the effectiveness of the proposed method, and the results show that the piecewise fitting method can precisely identify the clearance value of continuous systems.

Design and Optimization of an Origami-Inspired Jumping Mechanism With Nonlinear Stiffness Properties

2019 ◽  
Author(s):  
Sahand Sadeghi ◽  
Blake D. Betsill ◽  
Suyi Li
Keyword(s):  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Displacement Curve ◽  
Nonlinear Stiffness ◽  
Design And Optimization ◽  
Stiffness Properties ◽  
Stiffness Characteristics ◽  
New Generation ◽  
Force Displacement

Abstract This research investigates the feasibility of utilizing origami folding techniques to create an optimized jumping mechanism. As a theoretical example, we study the dynamic characteristics of a jumping mechanism consisting of two masses connected by a Tachi-Miura Polyhedron (TMP) origami structure with nonlinear stiffness characteristics. We show how the desired “strain-softening” effects of the TMP structure can lead to design of jumping mechanisms with optimized performance. The kinematics of TMP origami structure is reviewed and a modified model of its reaction-force displacement curve is presented. We derive the equations of motion of the jumping process and use their numerical solutions extensively for design optimization. Through this process we are able to obtain optimum geometrical configurations for two different objectives: The maximum time spent in the air and the maximum clearance off the ground. Results of this study can lead to emergence of a new generation of more efficient jumping mechanisms with optimized performance in the future.

scholarly journals MINLP formulations for continuous piecewise linear function fitting

2021 ◽  
Author(s):  
Noam Goldberg ◽  
Steffen Rebennack ◽  
Youngdae Kim ◽  
Vitaliy Krasko ◽  
Sven Leyffer
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Function Fitting ◽  
Computational Performance ◽  
Integer Nonlinear Programming ◽  
Minlp Model ◽  
Necessary Constraints ◽  
Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

scholarly journals Study on improvement of prefolded energy absorption device to constant resistance and its mechanical properties

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110368
Author(s):  
Dong An ◽  
Jiaqi Song ◽  
Hailiang Xu ◽  
Jingzong Zhang ◽  
Yimin Song ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Energy Absorption ◽  
Compression Test ◽  
Side Wall ◽  
Concave Side ◽  
Displacement Curve ◽  
Static Compression ◽  
Constant Resistance ◽  
The Impact ◽  
Force Displacement

When the rock burst occurs, energy absorption support is an important method to solve the impact failure. To achieve constant resistance performance of energy absorption device, as an important component of the support, the mechanical properties of one kind of prefolded tube is analyzed by quasi-static compression test. The deformation process of compression test is simulated by ABAQUS and plastic strain nephogram of the numerical model are studied. It is found that the main factors affecting the fluctuation of force-displacement curve is the stiffness of concave side wall. The original tube is improved to constant resistance by changing the side wall. The friction coefficient affects the folding order and form of the energy absorbing device. Lifting the concave side wall stiffness can improve the overall stiffness of energy absorption device and slow down the falling section of force-displacement curve. It is always squeezed by adjacent convex side wall in the process of folding, with large plastic deformation. Compared with the original one, the improved prefolded tube designed in this paper can keep the maximum bearing capacity ( Pmax), increase the total energy absorption ( E), improve the specific energy absorption (SEA), and decrease the variance ( S2) of force-displacement curve.

scholarly journals A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hamid Reza Erfanian ◽  
M. H. Noori Skandari ◽  
A. V. Kamyad
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Piecewise Linear Function ◽  
Nonsmooth Equations ◽  
Smooth Functions ◽  
Generalized Derivative ◽  
Novel Approach

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.

scholarly journals Young’s Modulus of Polycrystalline Titania Microspheres Determined by In Situ Nanoindentation and Finite Element Modeling

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Peida Hao ◽  
Yanping Liu ◽  
Yuanming Du ◽  
Yuefei Zhang
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Deformation Mechanisms ◽  
Displacement Curve ◽  
Element Simulation ◽  
Nanoindentation Experiment ◽  
Force Displacement

In situ nanoindentation was employed to probe the mechanical properties of individual polycrystalline titania (TiO2) microspheres. The force-displacement curves captured by a hybrid scanning electron microscope/scanning probe microscope (SEM/SPM) system were analyzed based on Hertz’s theory of contact mechanics. However, the deformation mechanisms of the nano/microspheres in the nanoindentation tests are not very clear. Finite element simulation was employed to investigate the deformation of spheres at the nanoscale under the pressure of an AFM tip. Then a revised method for the calculation of Young’s modulus of the microspheres was presented based on the deformation mechanisms of the spheres and Hertz’s theory. Meanwhile, a new force-displacement curve was reproduced by finite element simulation with the new calculation, and it was compared with the curve obtained by the nanoindentation experiment. The results of the comparison show that utilization of this revised model produces more accurate results. The calculated results showed that Young’s modulus of a polycrystalline TiO2microsphere was approximately 30% larger than that of the bulk counterpart.

Can indentation technique measure unique elastoplastic properties?

2009 ◽  
Vol 24 (3) ◽  
pp. 784-800 ◽  
Author(s):  
Ling Liu ◽  
Nagahisa Ogasawara ◽  
Norimasa Chiba ◽  
Xi Chen
Keyword(s):  
Critical Strain ◽  
Indentation Test ◽  
Strain Curve ◽  
Spherical Indentation ◽  
Plastic Behavior ◽  
Displacement Curve ◽  
Application Range ◽  
Indentation Technique ◽  
Elastoplastic Properties ◽  
Force Displacement

Indentation is widely used to extract material elastoplastic properties from measured force-displacement curves. Many previous studies argued or implied that such a measurement is unique and the whole material stress-strain curve can be measured. Here we show that first, for a given indenter geometry, the indentation test cannot effectively probe material plastic behavior beyond a critical strain, and thus the solution of the reverse analysis of the indentation force-displacement curve is nonunique beyond such a critical strain. Secondly, even within the critical strain, pairs of mystical materials can exist that have essentially identical indentation responses (with differences below the resolution of published indentation techniques) even when the indenter angle is varied over a large range. Thus, fundamental elastoplastic behaviors, such as the yield stress and work hardening properties (functions), cannot be uniquely determined from the force-displacement curves of indentation analyses (including both plural sharp indentation and deep spherical indentation). Explicit algorithms of deriving the mystical materials are established, and we qualitatively correlate the sharp and spherical indentation analyses through the use of critical strain. The theoretical study in this paper addresses important questions of the application range, limitations, and uniqueness of the indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material constitutive properties.

scholarly journals DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

Crack Propagation Experiments on Flip Chip Solder Joints

1998 ◽  
Vol 515 ◽  
Author(s):  
S. Wiese ◽  
F. Feustel ◽  
S. Rzepka ◽  
E. Meusel
Keyword(s):  
Crack Propagation ◽  
Flip Chip ◽  
Solder Joints ◽  
Shear Loading ◽  
Displacement Curve ◽  
In Situ Experiments ◽  
Propagation Experiment ◽  
Crack Propagation Experiment ◽  
Number Of Cycles ◽  
Force Displacement

ABSTRACTThe paper presents crack propagation experiments on real flip chip specimens applied to reversible shear loading. Two specially designed micro testers will be introduced. The first tester provides very precise measurements of the force displacement hysteresis. The achieved resolutions have been I mN for force and 20 nm for displacement. The second micro tester works similar to the first one, but is designed for in-situ experiments inside the SEM. Since it needs to be very small in size it reaches only resolutions of 10 mN and 100nm, which is sufficient to achieve equivalence to the first tester. A cyclic triangular strain wave is used as load profile for the crack propagation experiment. The experiment was done with both machines applying equivalent specimens and load. The force displacement curve was recorded using the first micro mechanical tester. From those hysteresis, the force amplitude has been determined for every cycle. All force amplitudes are plotted versus the number of cycles in order to quantify the crack length. With the second tester, images were taken at every 10th … 100th cycle in order to locate the crack propagation. Finally both results have been linked together for a combined quatitive and spatial description of the crack propagation in flip chip solder joints.

High transparency flexible sensor for pressure and proximity sensing

2018 ◽  
Vol 32 (32) ◽  
pp. 1850394 ◽  
Author(s):  
Dan Bu ◽  
Si Qi Li ◽  
Yun Ming Sang ◽  
Cheng Jun Qiu
Keyword(s):  
Indium Tin Oxide ◽  
Pressure Range ◽  
Piecewise Linear ◽  
High Sensitivity ◽  
Maximum Error ◽  
Piecewise Linear Function ◽  
Good Repeatability ◽  
Flexible Pressure Sensor ◽  
Human Finger ◽  
Proximity Sensing

A high-sensitivity and high-transmittance flexible pressure sensor is presented in this paper. Using polydimethylsiloxane (PDMS) sensing film to cover indium tin oxide (ITO) electrodes interdigitated on the polyethylene terephthalate (PET) substrate, an interdigital capacitance (IDC) structure is constructed. The pressure and proximity sensing characteristics of the fabricated IDC sensor are investigated. The experiment results show that the IDC sensor has the piecewise linear function in different pressure range, especially sensitive to the low-pressure range with the pressure sensitivity of 6.64 kPa[Formula: see text]. Moreover, it has a good repeatability with the maximum error rate of 2.73% and a high transmittance over 90% in the wavelength range from 400 nm to 800 nm. As a human finger approaches or leaves, the proximity sensing characteristic emerges, with a maximum sensing distance of about 20 cm.

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