Experimental Validation of a Walking Model for Planar Bipeds With Curved Feet

2011 ◽  
Author(s):  
Anne E. Martin ◽  
James P. Schmiedeler
Keyword(s):  
Mathematical Model ◽  
Humanoid Robot ◽  
Experimental Validation ◽  
Equations Of Motion ◽  
Experimental Results ◽  
Bipedal Walking ◽  
Human Gait ◽  
Bipedal Robots ◽  
Simplifying Assumptions ◽  
The Mathematical Model

Bipeds with curved feet typically require less energy for walking than do point- or flat-footed bipeds, and they tend to mimic human gait more closely. Thus, understanding the effects of curved feet on bipedal walking gaits has the potential to improve both humanoid robot efficiency and human rehabilitation. This paper derives the equations of motion for planar bipeds with curved feet under the assumption, among others, of instantaneous transfer of support between the legs. The paper then verifies the mathematical model by comparing the results of simulation to previous experimental results for two very different bipedal robots — McGeer’s two-link, passive dynamic walker traversing a decline and the five-link, actuated biped ERNIE walking on a treadmill with a supporting boom. In both cases, the results from simulation match the experimental results very well despite the simplifying assumptions, indicating that the mathematical model captures the dominate dynamics of bipedal robots with curved feet.

A Study on Exhaust Muffler Using Counter-Phase Counteract

2014 ◽  
Vol 986-987 ◽  
pp. 810-813
Author(s):  
Ying Li Shao
Keyword(s):  
Mathematical Model ◽  
Experimental Validation ◽  
Noise Source ◽  
Low Frequency ◽  
Frequency Noise ◽  
Expansion Chamber ◽  
Band Noise ◽  
Exhaust Noise ◽  
Perforated Pipe ◽  
The Mathematical Model

The exhaust noise, which falls into low-frequency noise, is the dominant noise source of a diesel engines and tractors. The traditional exhaust silencers, which are normally constructed by combination of expansion chamber, and perforated pipe or perforated board, are with high exhaust resistance, but poor noise reduction especially for the low-frequency band noise. For this reason, a new theory of exhaust muffler of diesel engine based on counter-phase counteracts has been proposed. The mathematical model and the corresponding experimental validation for the new exhaust muffler based on this theory were performed.

Mathematical Modeling of Electrochemical Deburring

2010 ◽  
Vol 126-128 ◽  
pp. 545-550 ◽  
Author(s):  
Wen Ji Xu ◽  
W. Wang ◽  
Xu Yue Wang ◽  
Gui Bing Pang
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Influencing Factors ◽  
Applied Voltage ◽  
Experimental Results ◽  
Electrode Gap ◽  
Workpiece Material ◽  
Burr Height ◽  
Object A ◽  
The Mathematical Model

The drilling burr is taken as the research object. A mathematical model of electrochemical deburring (ECD) is established and the effects of main influencing factors, such as inter-electrode gap, applied voltage and deburring time, on burr height have been analyzed. The results show that the deburring time increases with the increase of initial burr height, inter-electrode gap, with the decrease of volume of electrochemical equivalent of the workpiece material, conductivity of electrolyte and applied voltage. The deburring time for various burr heights can be predicted by the mathematical model. The calculated results obtained from the mathematical model are approximately consistent with the experimental results. The results show that initial burr height h0=0.722mm is removed, and the fillet radius R=0.211mm is obtained.

Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

2001 ◽  
Author(s):  
Jia Xiaohong ◽  
Ji Linhong ◽  
Jin Dewen ◽  
Zhang Jichuan
Keyword(s):  
Mathematical Model ◽  
Equations Of Motion ◽  
Experimental Studies ◽  
Active System ◽  
New Concepts ◽  
Sliding Joint ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model ◽  
Kane Method

Abstract Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

Experimental Validation of a Dynamic Model for Flexible Link Mechanisms

2001 ◽  
Author(s):  
R. Caracciolo ◽  
A. Gasparetto ◽  
A. Trevisani
Keyword(s):  
Mathematical Model ◽  
Experimental Validation ◽  
Numerical Results ◽  
Test Case ◽  
Planar Mechanisms ◽  
Transient Period ◽  
Element Approach ◽  
Multi Body ◽  
The Mathematical Model ◽  
Good Agreement

Abstract This paper presents an experimental validation of a finite element approach for the dynamic analysis of flexible multi-body planar mechanisms. The mathematical model employed accounts for mechanism geometric and inertial non-linearities and considers coupling effects among rigid-body and elastic motion. A flexible five-bar linkage actuated by two electric motors is employed as a test case. Experimentally determined link absolute deformations are compared with the numerical results obtained simulating the system dynamic behavior through the mathematical model. The experimental and numerical results are in good agreement especially after the very first transient period.

Experimental Validation of the Mathematical Model of the Dimethyl Phthalate Degradation by Ozone in the Solid Phase

2020 ◽  
Vol 59 (37) ◽  
pp. 16136-16145
Author(s):  
Jaime Dueñas Moreno ◽  
Tatyana Poznyak ◽  
Julia Liliana Rodríguez ◽  
Isaac Chairez ◽  
Hector J. Dorantes-Rosales
Keyword(s):  
Mathematical Model ◽  
Experimental Validation ◽  
Solid Phase ◽  
Dimethyl Phthalate ◽  
The Mathematical Model

scholarly journals Parametric Method For Evaluating Optimal Ship Deadweight

2014 ◽  
Vol 21 (2) ◽  
pp. 3-8
Author(s):  
Jan P. Michalski
Keyword(s):  
Mathematical Model ◽  
Closed Form ◽  
Parametric Method ◽  
Freight Rate ◽  
Ship Design ◽  
Design Parameters ◽  
Optimal Value ◽  
Simplifying Assumptions ◽  
The Mathematical Model ◽  
Economic Measure

Abstract The paper presents a method of choosing the optimal value of the cargo ships deadweight. The method may be useful at the stage of establishing the main owners requirements concerning the ship design parameters as well as for choosing a proper ship for a given transportation task. The deadweight is determined on the basis of a selected economic measure of the transport effectiveness of ship - the Required Freight Rate (RFR). The mathematical model of the problem is of a deterministic character and the simplifying assumptions are justified for ships operating in the liner trade. The assumptions are so selected that solution of the problem is obtained in analytical closed form. The presented method can be useful for application in the pre-investment ships designing parameters simulation or transportation task studies.

Shaping Law and Motion Design in NC-ECM under Effect of Twiste Angle

2011 ◽  
Vol 128-129 ◽  
pp. 1010-1014
Author(s):  
Rui Wu ◽  
Dan Wen Zhang ◽  
Juan Sun
Keyword(s):  
Mathematical Model ◽  
Electrochemical Machining ◽  
Experimental Results ◽  
Working Face ◽  
Relationship Of ◽  
The Mathematical Model ◽  
The Relationship ◽  
Motion Design

The twiste angle has a great effect on shaping law and stability of Numerical Controlled Electrochemical Machining (NC-ECM) process. In order to avoid the disadvantages caused by twiste angle, a methode of study shaping law by dispersing cathode working face in NC-ECM was proposed, and a mathematical model of the shaping law with the effects of twiste angle has been established in this paper. The mathematical model disclosed the relationship of twiste angle β, feeding velocity vf and thickness of removal material h in NC-ECM. Theoretical and experimental results show the the mathematical model of shaping law described in this paper can be considered as a useful reference and is helpful for the analysis of the NC-ECM and general ECM process.

Hydropneumatic Suspension Design

2003 ◽  
Author(s):  
Mauri´cio Baldi ◽  
Pable Siqueira Meirelles
Keyword(s):  
Mathematical Model ◽  
Hydraulic System ◽  
Experimental Validation ◽  
Crop Protection ◽  
Load Factor ◽  
Height Control ◽  
Suspension Parameters ◽  
High Dynamic ◽  
The Mathematical Model ◽  
Dynamic Load Factor

This study proposes a robust and cheap hydropneumatic suspension system for agricultural trailers used to spread crop protection. This kind of vehicle has a high dynamic load factor that increases the axles loads when it is in use and require a height control to assure the same spraying efficiency keeping constant the distance between the spray nozzles and the crop. As the tractor has its own hydraulic system, the hydropneumatic suspension conception take in account that height control will be done by the hydraulic fluid, being the mass of gas kept constant. A mathematical model of the hydropneumatic spring stiffness behavior was developed, as well as a methodology to define the suspension parameters. Experimental validation of the mathematical model was carried out through the use of a real agricultural trailer, equipped with a hydropneumatic suspension projected using the procedure presented, and tested in a hydropuls® road simulator.

scholarly journals Mathematical Model of Spatial Motion of the Controlled Parachute-Tether System of the Wind Kite Type

2021 ◽  
Vol 24 (4) ◽  
pp. 17-24
Author(s):  
V.M. Churkin ◽  
T.Yu. Churkina ◽  
A.M. Girin
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Solid Body ◽  
Equations Of Motion ◽  
Vertical Plane ◽  
Spatial Motion ◽  
Mathematical Task ◽  
Spatial Movement ◽  
Elastic Thread ◽  
The Mathematical Model

Mathematical modeling is created for the mathematical task of spatial motion of the controlled parachute-tether system of the “wind kite” type. The mathematical model parachute-tether system consists of a model of the main parachute and a model of the braking parachute. The parachutes are connected by the tether. The model of the main parachute is supposed to be the solid body. This solid body has two planes of symmetry. The braking parachute is the solid body with axial symmetry. The tether model is an absolutely flexible elastic thread. The tether is connected by ideal hinges with the main parachute and braking parachute. The control of the main parachute is carried out by changing the length of the control slings. Changing the length causes deformation of the dome. This is the reason for the change in its aerodynamics. Maneuvering of the main parachute occurs in the vertical plane, when the length of the control slings changes simultaneously. Maneuvering of the main parachute in space is carried out when the length of the control slings changes, when the slings are given a travel difference. The system of dynamic and kinematic equations is designed for calculating the controlled spatial movement of the main parachute, braking parachute and tether. The option exists when the mass of the tether and the forces applied to the tether cannot be neglected. The motion of the tether is represented by the equations of motion of an absolutely flexible elastic thread in projections on the axis of a natural trihedron. The mathematical model is represented by a system of ordinary differential equations and partial differential equations. The problem is solved using various numerical methods. The solution is possible with the help of an integrated numerical and analytical approach as well.

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