Analysis on the Performance of the SLIP Runner with Nonlinear Spring Leg

The spring-loaded inverted pendulum(SLIP) has been widely studied in both animals and robots.Generally,the majority of the relevant theoretical studies deal with elastic leg,the linear leg length-force relationship of which is obviously conflict with the biological observations.A planar spring-mass model with a nonlinear spring leg is presented to explore the intrinsic mechanism of legged locomotion with elastic component.The leg model is formulated via decoupling the stiffness coefficient and exponent of the leg compression in order that the unified stiffness can be scaled as convex,concave as well as linear profile.The apex return map of the SLIP runner is established to investigate dynamical behavior of the fixed point.The basin of attraction and Floquet Multiplier are introduced to evaluate the self-stability and initial state sensitivity of the SLIP model with different stiffness profiles.The numerical results show that larger stiffness exponent can increase top speed of stable running and also can enlarge the size of attraction domain of the fixed point.In addition,the parameter variation is conducted to detect the effect of parameter dependency,and demonstrates that on the fixed energy level and stiffness profile,the faster running speed with larger convergence rate of the stable fixed point under small local perturbation can be achieved via decreasing the angle of attack and increasing the stiffness coefficient.The perturbation recovery test is implemented to judge the ability of the model resisting large external disturbance.The result shows that the convex stiffness performs best in enhancing the robustness of SLIP runner negotiating irregular terrain.This research sheds light on the running performance of the SLIP runner with nonlinear leg spring from a theoretical perspective,and also guides the design and control of the bio-inspired legged robot.

Macro Model Study for Nonlinear Spring of Tense Torsion Bar in Gap-Closing Type Electrostatic Micromirror

Nonlinear spring characteristics of the tense torsion bar in the gap-closing type electrostatic micromirror are examined. The macro model is introduced for the experimental study. The tension applied in the torsion bar is well controlled using the electromagnetic attraction. This controllability is suited for clearing the nonlinear nature. The tension is confirmed to have the effect to widen the controllable angle range of the mirror suppressing the pull-in. The pull-in angle is observed to increases to about 74% of the mechanical limit angle at the tension of 0,96 N. This is significantly larger than 44% of the case with the linear spring. The larger resonant frequency is maintained. The hardening of the spring can keep the balance with the electrostatic force over the limit of the linear spring. The observed features are explained reasonably with the combination of twisting and bending displacements of the torsion bar.

Fatigue Characteristic Analysis of Deepwater Steel Catenary Risers at the Touchdown Point

This paper presents fatigue characteristic analysis of a deepwater steel catenary riser （SCR） under ambient excitations. The SCR involves complex nonlinear dynamic behaviors, especially at the touchdown point （TDP） where the riser first touches the seafloor. Owing to the significant interaction with soil, the touchdown zone is difficnlt to be modeled. Based on Lumped-Mass method and P-y curve, nonlinear springs are used to simulate the SCR-seabed coupled interaction. In case studies, an SCR＇s dynamic features have been obtained by transient analysis and the structure fatigue assessment has been carried out by S-N approach. The comparative analysis shows that the TDP is the key location where soil-riser interaction rises steeply and minimum fatigue life occurs. Parameters such as ocean environment loads, vessel motions, riser material and geometric parameters are discussed. The results indicate that the vessel motion is the principal factor for the structure fatigue life distribution.

Improved concept models for straight thin-walled columns with box cross section

This paper focuses on developing improved concept models for straight thin-walled box sectional columns which can better predict the peak crushing force that occurs during crashworthiness analyses. We develop a nonlinear translational spring based on previous research and apply such a spring element to build the enhanced concept models. The work presented in this article is developed on the basis of the publication of the author (Liu and Day, 2006b) and has been applied in a crashworthiness design issue, which is presented by the author in another paper (Liu, 2008).

New nonlinear stiffness actuator with predefined torque‒deflection profile

A nonlinear stiffness actuator(NSA)could achieve high torque/force resolution in low stiffness range and high bandwidth in high stiffness range,both of which are beneficial for physical interaction between a robot and the environment.Currently,most of NSAs are complex and hardly used for engineering.In this paper,oriented to engineering applications,a new simple NSA was proposed,mainly including leaf springs and especially designed cams,which could perform a predefined relationship between torque and deflection.The new NSA has a compact structure,and it is lightweight,both of which are also beneficial for its practical application.An analytical methodology that maps the predefined relationship between torque and deflection to the profile of the cam was developed.The optimal parameters of the structure were given by analyzing the weight of the NSA and the mechanic characteristic of the leaf spring.Though sliding friction force is inevitable because no rollers were used in the cam-based mechanism,the sliding displacement between the cam and the leaf spring is very small,and consumption of sliding friction force is very low.Simulations of different torque‒deflection profiles were carried out to verify the accuracy and applicability of performing predefined torque‒deflection profiles.Three kinds of prototype experiments,including verification experiment of the predefined torque‒deflection profile,torque tracking experiment,and position tracking experiment under different loads,were conducted.The results prove the accuracy of performing the predefined torque‒deflection profile,the tracking performance,and the interactive performance of the new NSA.

Pull-through capacity of bolted thin steel plate

The loading capacity in the axial direction of a bolted thin steel plate was investigated.A refined numerical model of bolt was first constructed and then validated using existing experiment results.Parametrical analysis was performed to reveal the influences of geometric parameters,including the effective depth of the cap nut,the yield strength of the steel plate,the preload of the bolt,and shear force,on the ultimate loading capacity.Then,an analytical method was proposed to predict the ultimate load of the bolted thin steel plate.Results derived using the numerical and analytical methods were compared and the results indicated that the analytical method can accurately predict the pull-through capacity of bolted thin steel plates.The work reported in this paper can provide a simplified calculation method for the loading capacity in the axial direction of a bolt.

Nanometer-Order Contouring Control in a Feed Drive System Using Linear Ball Guides by Applying a Combination of Modified Disturbance Observer and Repetitive Control

This paper proposes a quadrant glitch compensation method to achieve nanometer-level accuracy of contouring control for a feed drive system using linear ball guides.The proposed method is a combination of a modified disturbance observer(“disturbance suppressor”)and an improved repetitive control scheme.Sinusoidal motion tests with 1 mm amplitude and 0.1 Hz driving frequency were conducted using a single-axis feed drive system to verify the quadrant glitch compensation ability of this method.First,the repeatability of the quadrant glitches in the experimental system was verified,which is the most important characteristic required for compensation via repetitive control.Then,by applying the combination of disturbance suppressor and conventional repetitive control,the amplitudes of the quadrant glitches were decreased to less than 1 nm;in other words,the ratio of the magnitude of the quadrant glitch to the amplitude of the position reference was less than 1/1,000,000.However,for both compensation schemes mentioned before,vibrations were generated when the feed speed increased.Moreover,the amplitudes increased with the number of repetitions.The reason for the vibrations was identified as the repetitive control mechanism.To suppress these vibrations,the repetitive control was applied only to narrowed regimes near the quadrant glitches.Thus,the maximum contouring error was decreased to 2 nm.In addition,the nonlinear spring behavior of the linear ball guides was confirmed to affect the stability of the control systems.