Study on the stiffness property of a variable stiffness joint using a leaf spring

2018 ◽  
Vol 233 (3) ◽  
pp. 1021-1031 ◽  
Author(s):  
Lijin Fang ◽  
Yan Wang
Keyword(s):  
Geometric Nonlinearity ◽  
Large Deflection ◽  
Elliptic Integral ◽  
Joint Stiffness ◽  
Variable Stiffness ◽  
Leaf Spring ◽  
Stiffness Property ◽  
Force Structure ◽  
Leaf Springs ◽  
Application Requirements

Variable stiffness joints designed to ensure physical safety or adjust stiffness actively have attracted much attention in recent years. Springs are used in the internal kinematic structures of variable stiffness joints to achieve the compliance. In this paper, the stiffness property of a variable stiffness joint using a leaf spring is studied on the basis of geometric nonlinearity associated with large deflections of leaf springs. A new end structure is used in the variable stiffness joint to exert the external force on the leaf spring. Based on the elliptic integral solution to large deflection problems of cantilever beams, the effects of different end exertion force structures and geometric nonlinearity of leaf springs on the stiffness property are analyzed when the deflected angle of the joint is larger. It is found that the end exertion force structure and large deflection of leaf springs have a great impact on the changes of the joint stiffness during the joint deflection. A new variable stiffness joint using two leaf springs is proposed to meet different application requirements by changing the end exertion force structure. The experiment of the proposed joint is carried out to verify the validity of the stiffness analysis results.

scholarly journals Design and Non-Linear Analysis of a Parabolic Leaf Spring

1970 ◽  
Vol 37 ◽  
pp. 47-51 ◽  
Author(s):  
Muhammad Ashiqur Rahman ◽  
Muhammad Tareq Siddiqui ◽  
Muhammad Arefin Kowser
Keyword(s):  
Geometric Nonlinearity ◽  
Maximum Stress ◽  
Large Deflection ◽  
Linear Analysis ◽  
Leaf Spring ◽  
Cantilever Beams ◽  
Leaf Springs ◽  
Non Linear ◽  
Fixed End ◽  
Parabolic Leaf Spring

Tapered cantilever beams, traditionally termed as leaf springs, undergo much larger deflections in comparison to a beam of constant cross-section that takes their study in the domain of geometric nonlinearity. This paper studies response of a leaf spring of parabolic shape, assumed to be made of highly elastic steel. Numerical simulation was carried out using both the small and large deflection theories to calculate the stress and the deflection of the same beam. Non-linear analysis is found to have significant effect on the beam's response under a tip load. It is seen that the actual bending stress at the fixed end, calculated by nonlinear theory, is 2.30-3.39% less in comparison to a traditional leaf spring having the same volume of material. Interestingly, the maximum stress occurs at a region far away from the fixed end of the designed parabolic leaf spring. Keywords: Parabolic leaf spring, End-shortening, Geometric nonlinearity, Equilibrium Configuration Path, Varying Cross-section.doi:10.3329/jme.v37i0.819Journal of Mechanical Engineering Vol.37 June 2007, pp.47-51

scholarly journals Design and Analysis of a Novel Variable Stiffness Joint for Robot

2018 ◽  
Vol 249 ◽  
pp. 03005
Author(s):  
Xiang Zhang ◽  
Twan Capehart ◽  
Carl A. Moore
Keyword(s):  
High Frequency ◽  
Joint Stiffness ◽  
Variable Stiffness ◽  
Robotic Systems ◽  
Compliant Joint ◽  
Variable Transmission ◽  
Application Requirements ◽  
Base Application ◽  
Robotic Applications ◽  
Human Robotic Interaction

As people pay more attention to the safety of human-robotic interaction, the flexibility of machine joints is becoming more and more important. To address the needs of future robotic applications, many kinds of variable stiffness mechanisms have been designed by scientists. But most of the structures are complex. By studying and comparing many different mechanism designs of variable stiffness joint, we recognize the need to miniaturization and reduce weight of variable stiffness joints with high frequency operation. To address this, need a continuously Variable Compliant Joint (CVCJ) was designed. The core of the joint is based on the structure of the spherical continuously variable transmission (SCVT) which is the catalyst to change the stiffness continuously and smoothly. In this paper, we present a compact variable stiffness joint structure to meet the volume and weight requirements of the future robotic systems. We show the connection between the joint stiffness coefficient and the structure parameters by making mathematical analysis, modelling and simulation for the system to verify the ability to satisfy the base application requirements of the compliant joint.

Design and Analysis of a Cross Trapezoid Spatial Compliant Device With Variable Stiffness

2018 ◽  
Author(s):  
Zhuang Zhang ◽  
Genliang Chen ◽  
Lingyu Kong ◽  
Hao Wang
Keyword(s):  
Large Deflection ◽  
Variable Stiffness ◽  
Rigid Bodies ◽  
Main Concept ◽  
Compliance Matrix ◽  
Leaf Springs ◽  
Principal Axes ◽  
Great Force ◽  
Structural Compliance ◽  
Novel Design

This paper presents a novel design of spatial compliant device with variable stiffness. The main concept of the device is to have two elastic trapezoid four-bar linkages arranging in orthogonal. The tool side of the device can switch between totally stiff and compliant by changing the arrangement of leaf springs and passive joints. Based on the principal axes decomposition of structural compliance matrix, the leaf springs are approximated by hyper-redundant linkages with rigid bodies connected by passive elastic joints. Hence, the nonlinear large deflection problems of the leaf springs can be solved efficiently in a mechanism way. In order to demonstrate the compliance of the proposed device, a numerical simulation is provided using the proposed approach. The result shows that the leaf springs in the compliant device are easy to be deformed and can not generate great force. Due to these characteristics, as an end-of-arm tool, the device has the ability to prevent hard collisions under the compliant status and finish precise positioning under the stiff status.

scholarly journals Efficient Method for Calculating the Composite Stiffness of Parabolic Leaf Springs with Variable Stiffness for Vehicle Rear Suspension

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Wen-ku Shi ◽  
Cheng Liu ◽  
Zhi-yong Chen ◽  
Wei He ◽  
Qing-hua Zu
Keyword(s):  
Efficient Method ◽  
Calculation Method ◽  
Variable Stiffness ◽  
Simplified Model ◽  
Leaf Spring ◽  
Leaf Springs ◽  
Computer Aided ◽  
Basic Parameters ◽  
Composite Stiffness ◽  
Fea Analysis

The composite stiffness of parabolic leaf springs with variable stiffness is difficult to calculate using traditional integral equations. Numerical integration or FEA may be used but will require computer-aided software and long calculation times. An efficient method for calculating the composite stiffness of parabolic leaf springs with variable stiffness is developed and evaluated to reduce the complexity of calculation and shorten the calculation time. A simplified model for double-leaf springs with variable stiffness is built, and a composite stiffness calculation method for the model is derived using displacement superposition and material deformation continuity. The proposed method can be applied on triple-leaf and multileaf springs. The accuracy of the calculation method is verified by the rig test and FEA analysis. Finally, several parameters that should be considered during the design process of springs are discussed. The rig test and FEA analytical results indicate that the calculated results are acceptable. The proposed method can provide guidance for the design and production of parabolic leaf springs with variable stiffness. The composite stiffness of the leaf spring can be calculated quickly and accurately when the basic parameters of the leaf spring are known.

Controllable Compliance Joint For Human Oriented Robots

2013 ◽  
Vol 43 (1) ◽  
pp. 47-60
Author(s):  
Mihail Tsveov ◽  
Dimitar Chakarov
Keyword(s):  
Numerical Experiments ◽  
Position Control ◽  
Joint Stiffness ◽  
Joint Motion ◽  
Compliance Control ◽  
Leaf Springs ◽  
Antagonistic Actuation

Abstract In the paper, different approaches for compliance control for human oriented robots are revealed. The approaches based on the non- antagonistic and antagonistic actuation are compared. In addition, an approach is investigated in this work for the compliance and the position control in the joint by means of antagonistic actuation. It is based on the capability of the joint with torsion leaf springs to adjust its stiffness. Models of joint stiffness are presented in this paper with antagonistic and non-antagonistic influence of the spring forces on the joint motion. The stiffness and the position control possibilities are investigated and the opportunity for their decoupling as well. Some results of numerical experiments are presented in the paper too.

scholarly journals Development of an Exoskeleton-Type Assist Suit Utilizing Variable Stiffness Control Devices Based on Human Joint Characteristics

Actuators ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 17
Author(s):  
Seigo Kimura ◽  
Ryuji Suzuki ◽  
Katsuki Machida ◽  
Masashi Kashima ◽  
Manabu Okui ◽  
...  
Keyword(s):  
Joint Stiffness ◽  
Knee Extensor ◽  
Artificial Muscle ◽  
Variable Stiffness ◽  
Lower Limbs ◽  
Joint Characteristics ◽  
Standing Up ◽  
Maximum Decrease ◽  
Control Devices ◽  
The Relationship

In this paper, the prototype of the assistive suit for lower limbs was developed. The prototype was based on an assist method with joint stiffness and antagonized angle control. The assist method comprises a system consisting of a pneumatic artificial muscle and a pull spring, which changes the joint stiffness and the antagonized angle to correspond to the movement phase and aims at coordinated motion assistance with the wearer. First, the characteristics of the developed prototype were tested. It was confirmed that the measured value of the prototype followed the target value in the relationship between torque and angle. In addition, there was hysteresis in the measured value, but it did not affect the assist. Next, the evaluation of standing-up and gait assist by measuring electromyography (EMG) of the knee extensor muscle was conducted using the prototype. In all subjects, a decrease in EMG due to the assist was confirmed. In one subject, the maximum decrease rate at the peak of the EMG was about 50% for standing-up motion and about 75% for gait motion. From the results of these assist evaluations, the effectiveness of the assist method based on the joint stiffness and antagonistic angle control using the prototype was confirmed.

Response of Composite Leaf Springs to Low Velocity Impact Loading

2014 ◽  
Vol 591 ◽  
pp. 47-50 ◽  
Author(s):  
S. Rajesh ◽  
G.B. Bhaskar
Keyword(s):  
Impact Test ◽  
Low Velocity Impact ◽  
Leaf Spring ◽  
Fiber Reinforced ◽  
Test Rig ◽  
Low Velocity ◽  
Velocity Impact ◽  
Fiber Reinforced Plastic ◽  
Leaf Springs ◽  
Reinforced Plastic

Leaf springs are the traditional suspension elements, occupying a vital position in the automobile industry. This paper deals us the replacement of existing steel leaf spring by composite leaf spring. The dimensions of existing middle steel leaf spring of commercial vehicle (Tata ace mini truck) were taken and fabricated using a specially designed die. Single leaf of the suspension springs, each made up composite with bidirectional carbon fiber reinforced plastic (CFRP), bidirectional glass fiber reinforced plastic (GFRP) and hybrid glass-carbon fiber reinforced plastic (G-CFRP), was fabricated by hand layup process. It is to be mentioned here that the cross sectional area of the composite spring same as the metallic spring. A low velocity impact test rig was fabricated in the laboratory with loading set up. The composite leaf springs were tested with the low velocity impact test rig. By using the low velocity impact test rig, the deflection due to various drop height were measured.

Effect of End Rubber Gasket on the Performance of Parabolic Leaf Spring

2020 ◽  
Author(s):  
Junhong Zhang ◽  
Feiqi Long ◽  
Hongjie Jia ◽  
Jiewei Lin
Keyword(s):  
Ride Comfort ◽  
Orthogonal Experiment ◽  
Element Model ◽  
Considerable Effect ◽  
Leaf Spring ◽  
Static Stiffness ◽  
Rubber Gasket ◽  
Maximum Deformation ◽  
Leaf Springs ◽  
Parabolic Leaf Spring

Abstract Leaf springs play an important role in the handling stability and ride comfort of vehicle. End rubber gaskets are widely used to reduce the friction between leaves, but they also have considerable effect on the stiffness of the suspension assembly. The ride comfort may deteriorate with the stiffness of leaf spring changes. In this paper the influence of the end rubber gasket on the static stiffness performance of a parabolic leaf spring is studied. A finite element model of the leaf spring is developed and verified against the static stiffness test. Effects of the end rubber gasket parameters on the static stiffness of the leaf spring are analyzed based on an orthogonal experiment. The sensitivities of the five parameters are identified including the width, the length, the end thickness, the tail thickness and the distance to the end of the middle leaf. It is found that the contributions can be ranked in descending order as the tail thickness, the end thickness, the distance from end rubber gasket to the end of Leaf 2, and the width and length. The first two factors are considered of significant effects on the leaf spring stiffness. According to single-factor analysis, it is found that under the same load, as the tail thickness and the end thickness increase, the maximum deformation of the rubber gasket decreases, the stiffness of the rubber gasket increases, and the stiffness of the leaf spring increases, which provides a reference for the forward design of the end rubber gasket and the stiffness matching of leaf springs.

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

1995 ◽  
Vol 117 (1) ◽  
pp. 156-165 ◽  
Author(s):  
L. L. Howell ◽  
A. Midha
Keyword(s):  
Closed Form ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Cantilever Beams ◽  
Simple Method ◽  
Body Angle ◽  
Analysis And Design ◽  
Integral Solutions

Geometric nonlinearities often complicate the analysis of systems containing large-deflection members. The time and resources required to develop closed-form or numerical solutions have inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter called the pseudo-rigid-body angle. The approximations are accurate to within 0.5 percent of the closed-form elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms.

scholarly journals A Stiffness Variable Passive Compliance Device with Reconfigurable Elastic Inner Skeleton and Origami Shell

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Zhuang Zhang ◽  
Genliang Chen ◽  
Weicheng Fan ◽  
Wei Yan ◽  
Lingyu Kong ◽  
...  
Keyword(s):  
Variable Stiffness ◽  
Rehabilitation Robotics ◽  
Human Robot Interaction ◽  
Main Concept ◽  
Robot Interaction ◽  
Switching Speed ◽  
Leaf Springs ◽  
Stiffness Variation ◽  
Low Stiffness ◽  
Large Deflection Problem

Abstract Devices with variable stiffness are drawing more and more attention with the growing interests of human-robot interaction, wearable robotics, rehabilitation robotics, etc. In this paper, the authors report on the design, analysis and experiments of a stiffness variable passive compliant device whose structure is a combination of a reconfigurable elastic inner skeleton and an origami shell. The main concept of the reconfigurable skeleton is to have two elastic trapezoid four-bar linkages arranged in orthogonal. The stiffness variation generates from the passive deflection of the elastic limbs and is realized by actively switching the arrangement of the leaf springs and the passive joints in a fast, simple and straightforward manner. The kinetostatics and the compliance of the device are analyzed based on an efficient approach to the large deflection problem of the elastic links. A prototype is fabricated to conduct experiments for the assessment of the proposed concept. The results show that the prototype possesses relatively low stiffness under the compliant status and high stiffness under the stiff status with a status switching speed around 80 ms.

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