A Generalized Model for Compliant Passive Bipedal Walking: Sensitivity Analysis and Implications On Bionic Leg Design

2021 ◽  
Author(s):  
Aikaterini Smyrli ◽  
Georgios Bertos ◽  
Evangelos Papadopoulos
Keyword(s):  
Early Stage ◽  
Bipedal Walking ◽  
Design Parameters ◽  
Dimensional Parameter ◽  
Passive Behavior ◽  
Gait Characteristics ◽  
Dimensional Parameters ◽  
Stable Gait ◽  
Parameter Ranges ◽  
Leg Design

Abstract The passive behavior of a compliant biped walking model, subject to variations in its design is investigated. A biped gait model is developed that allows for studying the effects of leg impedance, geometry, foot curvature and inertial properties on the stable gait performed passively. A set of non-dimensional parameters has been produced that fully defines the compass gait behavior, eliminating the dependence of our results on scale. Models emerging from parameter combinations were tested on their ability to perform stable passive walking on slope, and the characteristics of the gait performed in each case were recorded. Investigation of parameter ranges allowed us to draw relationships between various gait characteristics and specific, non-dimensional parameter selections. By mapping the changes in system behavior under simple design variations, this work facilitates the selection of design parameters at an early stage of designing bionic walking equipment, including prostheses and exoskeletons.

scholarly journals A Configurable Architecture for Two Degree-of-Freedom Variable Stiffness Actuators to Match the Compliant Behavior of Human Joints

2021 ◽  
Vol 8 ◽  
Author(s):  
Simon Lemerle ◽  
Manuel G. Catalano ◽  
Antonio Bicchi ◽  
Giorgio Grioli
Keyword(s):  
Variable Stiffness ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Dimensional Parameter ◽  
Passive Behavior ◽  
Compliant Behavior ◽  
Wide Range ◽  
Articulated Robots ◽  
Variable Stiffness Actuators ◽  
Two Degree Of Freedom

Living beings modulate the impedance of their joints to interact proficiently, robustly, and safely with the environment. These observations inspired the design of soft articulated robots with the development of Variable Impedance and Variable Stiffness Actuators. However, designing them remains a challenging task due to their mechanical complexity, encumbrance, and weight, but also due to the different specifications that the wide range of applications requires. For instance, as prostheses or parts of humanoid systems, there is currently a need for multi-degree-of-freedom joints that have abilities similar to those of human articulations. Toward this goal, we propose a new compact and configurable design for a two-degree-of-freedom variable stiffness joint that can match the passive behavior of a human wrist and ankle. Using only three motors, this joint can control its equilibrium orientation around two perpendicular axes and its overall stiffness as a one-dimensional parameter, like the co-contraction of human muscles. The kinematic architecture builds upon a state-of-the-art rigid parallel mechanism with the addition of nonlinear elastic elements to allow the control of the stiffness. The mechanical parameters of the proposed system can be optimized to match desired passive compliant behaviors and to fit various applications (e.g., prosthetic wrists or ankles, artificial wrists, etc.). After describing the joint structure, we detail the kinetostatic analysis to derive the compliant behavior as a function of the design parameters and to prove the variable stiffness ability of the system. Besides, we provide sets of design parameters to match the passive compliance of either a human wrist or ankle. Moreover, to show the versatility of the proposed joint architecture and as guidelines for the future designer, we describe the influence of the main design parameters on the system stiffness characteristic and show the potential of the design for more complex applications.

scholarly journals Solution of Q-Deformed D-Dimensional Klein-Gordon Equation Kratzer Potential using Hypergeometric Method

2019 ◽  
Vol 9 (2) ◽  
pp. 163
Author(s):  
Suparmi Suparmi ◽  
Dyah Ayu Dianawati ◽  
Cari Cari
Keyword(s):  
Gordon Equation ◽  
Energy Levels ◽  
Spin Symmetry ◽  
Relativistic Energy ◽  
Dimensional Parameter ◽  
Energy Value ◽  
Quantum Numbers ◽  
Klein Gordon ◽  
Dimensional Parameters ◽  
Klein Gordon Equation

The Q-deformed D-dimensional Klein Gordon equation with Kratzer potential is solved by using Hypergeometric method in the case of exact spin symmetry. The linear radial momentum of D-dimensional Klein Gordon equation is disturbed by the presence of the quadratic radial posisiton. The Klein-Gordon D-dimensional equation is reduced to one-dimensional Schrodinger like equation with variable substitution. The solution of the D-dimensional Klein-Gordon equation is determined in the form of a general equation of the Hypergeometry function using the Kratzer potential variable and the quantum deformation variable. From this equation, relativistic energy and wave function are determined. In addition, the relativistic energy equation can be used to calculate numerical energy levels for diatomic particles (CO, NO, O2) using Matlab R2013a software. The results obtained show that the q-deformed quantum parameters, quantum numbers and dimensions affect the value of relativistic energy for zero-pin particles. The value of energy increases with increasing value of quantum number n, q-deformed parameters, and d-dimensional parameters. Of the three parameters, q-deformed parameter is the most dominant to give change in energy value; the increasing q-deformed parameter causes the energy value increases significantly compared to the d-dimensional parameter and quantum numbers n.

scholarly journals Introducing Value Axiom for New Design Creations

2019 ◽  
Vol 301 ◽  
pp. 00002
Author(s):  
Masayuki Nakao ◽  
Kenji Iino
Keyword(s):  
Early Stage ◽  
Design Parameters ◽  
Independence Axiom ◽  
Design Equation ◽  
Functional Requirements ◽  
Monetary Value ◽  
Perfect Set ◽  
Information Axiom ◽  
Japanese Yen

This paper proposes “Value Axiom” that states “The larger the sum of Customer Attribute values, the better the design.” A customer evaluates a design with the sum of the value produced by each Customer Attribute, expressing it with a monetary value such as Japanese yen. A designer can hardly estimate and express a perfect set of Customer Attributes at the early stage of a design. The designer writes down the design equation to visualize the entire design, and improves the sets of Design Parameters and Functional Requirements using the Independence Axiom and Information Axiom, and at the same time, it is also important to review the values of Customer Attributes using the Value Axiom.

Non-Dimensional Parameters for Comparing Conventional and Counter-Rotating Turbomachines

2019 ◽  
Author(s):  
J. J. Waldren ◽  
C. J. Clark ◽  
S. D. Grimshaw ◽  
G. Pullan
Keyword(s):  
High Efficiency ◽  
Three Dimensional ◽  
Relative Performance ◽  
Design Parameters ◽  
Blade Design ◽  
Finite Radius ◽  
Counter Rotation ◽  
Dimensional Parameters ◽  
Conventional Machine ◽  
Stage Efficiency

Abstract Counter-rotating turbomachines have the potential to be high efficiency, high power density devices. Comparisons between conventional and counter-rotating turbomachines in the literature make multiple and often contradicting conclusions about their relative performance. By adopting appropriate non-dimensional parameters, based on relative blade speed, the design space of conventional machines can be extended to include those with counter-rotation. This allows engineers familiar with conventional turbomachinery to transfer their experience to counter-rotating machines. By matching appropriate non-dimensional parameters the loss mechanisms directly affected by counter-rotation can be determined. A series of computational studies are performed to investigate the relative performance of conventional and counter-rotating turbines with the same non-dimensional design parameters. Each study targets a specific loss source, highlighting which phenomena are directly due to counter-rotation and which are solely due to blade design. The studies range from two-dimensional blade sections to three-dimensional finite radius stages. It is shown that, at hub-to-tip ratios approaching unity, with matched non-dimensional design parameters, the stage efficiency and work output are identical for both types of machine. However, a counter-rotating turbine in the study is shown to have an efficiency advantage over a conventional machine of up to 0.35 percentage points for a hub-to-tip ratio of 0.65. This is due to differences in absolute velocity producing different spanwise blade designs.

scholarly journals A Black-Box method for parametric model order reduction based on matrix interpolation with application to simulation and control

2016 ◽  
Vol 64 (9) ◽  
Author(s):  
Matthias Geuß
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Black Box ◽  
Design Parameters ◽  
Dimensional Parameter ◽  
Model Order ◽  
Parametric Model Order Reduction ◽  
Box Method ◽  
Matrix Interpolation ◽  
And Control

AbstractThis thesis deals with model order reduction of parameter-dependent systems based on interpolation of locally reduced system matrices. A Black-Box method is proposed that automatically determines the optimal design parameters and delivers a reduced system with desired accuracy. In addition, the method is extended to stability preservation and interpolation for high-dimensional parameter spaces.

Numerical Modeling and Parametric Analysis of Multiplanar CHS KT-Joints with K-Plane Overlap and Out-of-Plane Gap

2011 ◽  
Vol 94-96 ◽  
pp. 575-582
Author(s):  
Jian Dong Sun ◽  
Jun Li Lv ◽  
Tao Du ◽  
Yang Xian Li
Keyword(s):  
Numerical Modeling ◽  
Parametric Analysis ◽  
Element Model ◽  
Ultimate Capacity ◽  
Dimensional Parameter ◽  
International Convention ◽  
Out Of Plane ◽  
Dimensional Parameters ◽  
Test Result ◽  
Good Agreement

A finite element model simulating the experiment on multiplanar unstiffened CHS KT joints with K-plane overlapped and out-of-plane not (KT-IPOv joints), with the background of Suzhou International Convention & Exhibition Center, was advanced and validated by comparing failure mode and the ultimate capacity with experimental results, which is shown to be in good agreement with the test result. Using this model, the effect of non-dimensional parameters on ultimate capacity of KT-IPOv joints were studied, and resistance comparison between multiplanar KT-IPOv joints and uniplanar overlapped K-joints was carried out. The results of FE parametric Analysis conclude that multiplanar parameter ζ t, τT and βT have not significant influence on the ultimate strength; the effect of non-dimensional parameter βK, τK, γ, Ov on the resistance of multiplanar KT-IPOv joints has the same as that of uniplanar overlapped K-joints; the strength of multiplanar KT-IPOv joints have been not significantly influenced by the configuration with the brace inside T-plane which it is not subjected to force; it is suitable and feasiable that ultimate capacities of KT-IPOv joints predicted by formula of uniplanar K-joints.

Effect of Trunk Swinging Behaviors on Planar Bipedal Walking with an Upper Body on Gentle Slope

2019 ◽  
Vol 31 (5) ◽  
pp. 686-696
Author(s):  
Toyoyuki Honjo ◽  
◽  
Hidehisa Yoshida
Keyword(s):  
Angular Momentum ◽  
Step Length ◽  
Bipedal Walking ◽  
Knee Joints ◽  
Upper Body ◽  
Lower Body ◽  
Gentle Slope ◽  
Gait Characteristics ◽  
Bipedal Gait ◽  
Walking Locomotion

Bipedal walking locomotion is one of the characteristics of human behavior. Both the lower body and the upper body (trunk) behaviors affect walking characteristics. To achieve a suitable gait, it is important to understand the effect of the trunk behavior. Therefore, in this paper, the effects of three types of trunk swinging behavior on planar bipedal gait in a model with an upper body – forward swinging, backward swinging, and no swinging – were evaluated using numerical simulations. To reduce control inputs and reflect the effect of upper body behavior, an underactuated bipedal walker without knee joints was adopted. This walker walked down a gentle slope using only hip actuation between the stance leg and the trunk. As a result, unique gait characteristics that depended on the direction of the trunk swinging behavior were found, including a longer step length and a lower-frequency gait with forward trunk swinging behavior and a shorter step length and higher-frequency gait with smaller angular momentum with backward trunk swinging behavior.

Prediction of the Pressure Distribution for Radial Inflow Between Co-Rotating Discs

1988 ◽  
Author(s):  
John W. Chew ◽  
Robert J. Snell
Keyword(s):  
Pressure Drop ◽  
Pressure Coefficient ◽  
Integral Solution ◽  
Solution Technique ◽  
Quick Method ◽  
Dimensional Parameter ◽  
Rotating Discs ◽  
Wide Range ◽  
Dimensional Parameters ◽  
Good Agreement

The problem of radial inflow between two plane co-rotating discs with the angular velocity of the fluid at inlet equal to that of the discs is considered. An integral solution technique for turbulent flow, based on that of von Karman (1921), is described. Solutions are shown to be in good agreement with most of the available experimental data. For incompressible flow the pressure drop coefficient is a function of just two non-dimensional parameters; the radius ratio for the cavity and a throughflow parameter. For air flows compressibility can be important and an additional non-dimensional parameter is needed. Results for a wide range of conditions are presented graphically. These show the sensitivity of the pressure coefficient to the governing parameters and provide a quick method for estimating the pressure drop.

Theoretical Analysis of Externally Pressurized Air Journal Bearing

1970 ◽  
Vol 12 (2) ◽  
pp. 123-129 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Experimental Data ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Design Parameters ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Dimensional Parameters ◽  
Bearing Design

A theoretical investigation is made to predict the performance of an externally pressurized air journal bearing having several pressure sources. The pressure distribution, which leads to the determination of load-carrying capacity and flow requirement, is obtained by solving Reynolds equation numerically. The load and flow, expressed in non-dimensional parameters, are presented for different bearing design parameters (dimensionless). The results predicted by this method are compared with others' experimental data.

scholarly journals Sensory modulation of gait characteristics in human locomotion: a neuromusculoskeletal modeling study

2020 ◽  
Author(s):  
Andrea Di Russo ◽  
Dimitar Stanev ◽  
Stéphane Armand ◽  
Auke Ijspeert
Keyword(s):  
Central Pattern Generators ◽  
Step Length ◽  
Human Locomotion ◽  
The Other ◽  
Human Gait ◽  
Dimensional Parameter ◽  
Fast Walking ◽  
Gait Characteristics ◽  
Other Hand ◽  
Step Duration

AbstractThe central nervous system of humans and animals is able to modulate the activity in the spinal cord to achieve several locomotion behaviors. Previous neuromechanical models investigated the modulation of human gait changing selected parameters belonging to the CPGs (Central Pattern Generators) feedforward oscillatory structures or to the feedback reflex circuits. CPG-based models could replicate slow and fast walking by changing only the oscillation’s properties. On the other hand, reflex-based models could achieve different behaviors mainly through optimizations of a large dimensional parameter space, but could not identify effectively individual key reflex parameters responsible for the modulation of gait characteristics. This study, investigates which reflex parameters modulate the gait characteristics through neuromechanical simulations. A recently developed reflex-based model is used to perform optimizations with different target behaviors on speed, step length and step duration in order to analyse the correlation between reflex parameters and their influence on these gait characteristics. We identified 9 key parameters that influence the target speed ranging from slow to fast walking (0.48 and 1.71 m/s) as well as a large range of step lengths (0.43 and 0.88 m) and step duration (0.51, 0.98 s). The findings show that specific reflexes during stance have a major effect on step length regulation mainly given by the contribution of positive force feedback on the ankle plantarflexors’ group. On the other hand, stretch reflexes active during swing of iliopsoas and gluteus maximus regulate all the gait characteristics under analysis. Additionally, the results show that the stretch reflex of the hamstring’s group during landing phase is responsible for modulating the step length and step duration. Additional validation studies in simulations demonstrated that the identified reflexes are sufficient to modulate gait in human locomotion. Thus, this study provides an overview of the possible reflexes to control the gait characteristics.Author summary

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