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.

The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports

1969 ◽  
Vol 91 (4) ◽  
pp. 1105-1113 ◽  
Author(s):  
E. J. Gunter ◽  
P. R. Trumpler
Keyword(s):  
Internal Friction ◽  
High Speed ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Analog Computer ◽  
Three Dimensional Model ◽  
Stiffness Properties ◽  
Stiffness Characteristics ◽  
The Stability ◽  
Internal Rotor

This paper evaluates the stability of the single mass rotor with internal friction on damped, anisotropic supports. The paper shows under what conditions the rotor stability may be improved by an undamped support with anisotropic stiffness properties. A three dimensional model is presented to show the influence of rotor and support stiffness characteristics on stability. Curves are also presented on how support damping may also improve or even reduce rotor stability. An analog computer solution of the governing equations of motion is presented showing the shaft transient motion for various speed ranges, and also plots of the rotor steady state motion are given for various speeds up to and including the stability threshold. The analysis is used to explain many of the experimental observations of B. L. Newkirk concerning stability due to internal rotor friction.

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.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

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 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.

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.

scholarly journals Comparison of waveform-derived corneal stiffness and stress-strain extensometry-derived corneal stiffness using different cross-linking irradiances: an experimental study with air-puff applanation of ex vivo porcine eyes

2020 ◽  
Vol 258 (10) ◽  
pp. 2173-2184 ◽  
Author(s):  
Robert Herber ◽  
Mathew Francis ◽  
Eberhard Spoerl ◽  
Lutz E. Pillunat ◽  
Frederik Raiskup ◽  
...  
Keyword(s):  
Experimental Study ◽  
Ex Vivo ◽  
Cross Linking ◽  
Displacement Curve ◽  
Stress Strain ◽  
Strain Measurements ◽  
Deflection Amplitude ◽  
Force Displacement ◽  
Stiffening Effect ◽  
Porcine Eyes

Abstract Purpose To assess corneal stiffening of standard (S-CXL) and accelerated (A-CXL) cross-linking protocols by dynamic corneal response parameters and corneal bending stiffness (Kc[mean/linear]) derived from Corvis (CVS) Scheimpflug-based tonometry. These investigations were validated by corneal tensile stiffness (K[ts]), derived from stress-strain extensometry in ex vivo porcine eyes. Methods Seventy-two fresh-enucleated and de-epithelized porcine eyes were soaked in 0.1% riboflavin solution including 10% dextran for 10 min. The eyes were separated into four groups: controls (n = 18), S-CXL (intensity in mW/cm2*time in min; 3*30) (n = 18), A-CXL (9*10) (n = 18), and A-CXL (18*5) (n = 18), respectively. CXL was performed using CCL Vario. CVS measurements were performed on all eyes. Subsequently, corneal strips were extracted by a double-bladed scalpel and used for stress-strain measurements. K[ts] was calculated from a force-displacement curve. Mean corneal stiffness (Kc[mean]) and constant corneal stiffness (Kc[linear]) were calculated from raw CVS data. Results In CVS, biomechanical effects of cross-linking were shown to have a significantly decreased deflection amplitude as well as integrated radius, an increased IOP, and SP A1 (P < 0.05). Kc[mean]/Kc[linear] were significantly increased after CXL (P < 0.05). In the range from 2 to 6% strain, K[ts] was significantly higher in S-CXL (3*30) compared to A-CXL (9*10), A-CXL (18*5), and controls (P < 0.05). At 8% to 10% strain, all protocols induced a higher stiffness than controls (P < 0.05). Conclusion Several CVS parameters and Kc[mean] as well as Kc[linear] verify corneal stiffening effect after CXL on porcine eyes. S-CXL seems to have a higher tendency of stiffening than A-CXL protocols have, which was demonstrated by Scheimpflug-based tonometry and stress-strain extensometry.

Dynamic Characteristics of a Hydrostatic Gas Bearing Driven by Oscillating Exhaust Pressure

1984 ◽  
Vol 106 (4) ◽  
pp. 477-483 ◽  
Author(s):  
C. B. Watkins ◽  
H. D. Branch ◽  
I. E. Eronini
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Source Model ◽  
Regular Perturbation ◽  
Response Characteristics ◽  
Finite Difference Approximations ◽  
Bode Plots ◽  
Gas Bearing

Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference approximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.

scholarly journals Dynamics of nanodust particles emitted from elongated initial orbits

2018 ◽  
Vol 617 ◽  
pp. A43 ◽  
Author(s):  
A. Czechowski ◽  
I. Mann
Keyword(s):  
Solar Wind ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Dust Cloud ◽  
Theoretical Models ◽  
Ecliptic Plane ◽  
Parent Body ◽  
The Sun ◽  
Trapping Region ◽  
Eccentric Orbits

Context. Because of high charge-to-mass ratio, the nanodust dynamics near the Sun is determined by interplay between the gravity and the electromagnetic forces. Depending on the point where it was created, a nanodust particle can either be trapped in a non-Keplerian orbit, or escape away from the Sun, reaching large velocity. The main source of nanodust is collisional fragmentation of larger dust grains, moving in approximately circular orbits inside the circumsolar dust cloud. Nanodust can also be released from cometary bodies, with highly elongated orbits. Aims. We use numerical simulations and theoretical models to study the dynamics of nanodust particles released from the parent bodies moving in elongated orbits around the Sun. We attempt to find out whether these particles can contribute to the trapped nanodust population. Methods. We use two methods: the motion of nanodust is described either by numerical solutions of full equations of motion, or by a two-dimensional (heliocentric distance vs. radial velocity) model based on the guiding-center approximation. Three models of the solar wind are employed, with different velocity profiles. Poynting–Robertson and the ion drag are included. Results. We find that the nanodust emitted from highly eccentric orbits with large aphelium distance, like those of sungrazing comets, is unlikely to be trapped. Some nanodust particles emitted from the inbound branch of such orbits can approach the Sun to within much shorter distances than the perihelium of the parent body. Unless destroyed by sublimation or other processes, these particles ultimately escape away from the Sun. Nanodust from highly eccentric orbits can be trapped if the orbits are contained within the boundary of the trapping region (for orbits close to ecliptic plane, within ~0.16 AU from the Sun). Particles that avoid trapping escape to large distances, gaining velocities comparable to that of the solar wind.

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