Reaction Force Analysis in Generalized Machine Systems

1973 ◽  
Vol 95 (2) ◽  
pp. 617-623 ◽  
Author(s):  
D. A. Smith
Keyword(s):  
Dynamic Systems ◽  
Virtual Work ◽  
Reaction Force ◽  
Inertial Forces ◽  
Force Analysis ◽  
Lagrange’S Equation ◽  
Reaction Forces ◽  
Applied Forces ◽  
Machine Systems ◽  
Centers Of Mass

A method is developed which reduces the calculation of reaction forces for multi-degree-of-freedom, constrained, mechanical, dynamic systems to a process of accumulating a sum of terms representing inertial forces, applied forces, and Lagrange multiplier forces. This method results in an approach to reaction force calculations which is computationally more efficient than either virtual work or equilibrium when these methods are applied in conventional ways. The method is based on selecting a tree for the network being simulated in which the chords of the network correspond to revolute pairs (for two-dimensional systems). When such a tree is determined, Lagrange’s equation with constraint is used to represent the mechanical system. If the paths to the centers of mass and the paths associated with applied forces are developed from tree branches, the Lagrange multipliers are directly interpretable in terms of the total reaction forces at the chords of the network. These multipliers are obtained in the process of determining the system motion. The remaining reaction forces and torques are determined by a sequence of additions.

Repelling-Screw Based Force Analysis of Origami Mechanisms

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Chen Qiu ◽  
Ketao Zhang ◽  
Jian S. Dai
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Reaction Force ◽  
Theoretical Background ◽  
Force Analysis ◽  
Modeling Approach ◽  
Reaction Forces ◽  
Redundantly Actuated

This paper provides an approach to model the reaction force of origami mechanisms when they are deformed. In this approach, an origami structure is taken as an equivalent redundantly actuated mechanism, making it possible to apply the forward-force analysis to calculating the reaction force of the origami structure. Theoretical background is provided in the framework of screw theory, where the repelling screw is introduced to integrate the resistive torques of folded creases into the reaction-force of the whole origami mechanism. Two representative origami structures are then selected to implement the developed modeling approach, as the widely used waterbomb base and the waterbomb-based integrated parallel mechanism. With the proposed kinematic equivalent, their reaction forces are obtained and validated, presenting a ground for force analysis of origami-inspired mechanisms.

Topological Reaction Force Analysis

1979 ◽  
Vol 101 (2) ◽  
pp. 192-198 ◽  
Author(s):  
J. R. Milner ◽  
D. A. Smith
Keyword(s):  
Reaction Force ◽  
Mechanical Systems ◽  
Computational Approach ◽  
Alternative Methods ◽  
Force Analysis ◽  
Dynamic Mechanical ◽  
Reaction Forces ◽  
Linear Graphs

A method of using directed linear graphs for the determination of reaction forces in dynamic mechanical systems is developed. The method is compatible with other more classical techniques for calculating reaction forces and results in a more efficient computational approach than alternative methods. Example problems are discussed and analyzed using these topological techniques.

Ground reaction force analysis for assessing the efficacy of focused and radial shockwaves in the treatment of symptomatic plantar heel spur

2020 ◽  
pp. 1-9
Author(s):  
Piotr Król ◽  
Andrzej Franek ◽  
Tomasz Król ◽  
Arkadiusz Stanula ◽  
Paweł Dolibog ◽  
...  
Keyword(s):  
Shock Wave ◽  
Reaction Force ◽  
Extracorporeal Shock Wave Therapy ◽  
Therapeutic Effects ◽  
Force Analysis ◽  
Heel Spur ◽  
Temporal Parameters ◽  
Extracorporeal Shock Wave ◽  
Reaction Forces ◽  
Foot Function

BACKGROUND: Extracorporeal shock wave therapy is among the conservative treatments for symptomatic heel spur. OBJECTIVE: The purpose of this trial is to evaluate and compare the therapeutic effects of radial shock wave (RSWT) and focused shock wave (FSWT) applied in the treatment of symptomatic heel spur. METHODS: Fifty-five participants were randomly divided into two comparative groups that were administered FSWT and RSWT, respectively. The severity of dysfunction (Foot Function Index, FFI), ground reaction forces (GRF) and walking temporal parameters were measured in all patients at baseline and at weeks 1, 3, 6, 12 and 24 after treatment. RESULTS: In both groups, a gradual decrease in the FFI values occurred after treatment. The percentage reduction in the FFI was comparable for both groups. Statistically significant changes were only noted between some measurements of GRF and walking temporal parameters. The percentage changes in the values of the force and temporal parameters were similar between the groups. CONCLUSIONS: Both FSWT and RSWT are efficacious in the treatment of symptomatic heel spur and their therapeutic effects are comparable. Objective data registered by force platforms during walking are not useful for tracing the progress of treatment applied to patients with symptomatic heel spur between consecutive procedures.

Intramolecular Proton Transfer in the Isomerization of Hydroxyacetone: A Detailed Characterization Based on Reaction Force Analysis and the Bond Fragility Spectrum

2020 ◽  
Author(s):  
Wallace Derricotte ◽  
Huiet Joseph
Keyword(s):  
Chemical Potential ◽  
Reaction Force ◽  
Intramolecular Proton Transfer ◽  
Intermediate Energy ◽  
Force Analysis ◽  
Activation Energy Barrier ◽  
Detailed Characterization ◽  
Proton Transfers ◽  
Reaction Force Constant

The mechanism of isomerization of hydroxyacetone to 2-hydroxypropanal is studied within the framework of reaction force analysis at the M06-2X/6-311++G(d,p) level of theory. Three unique pathways are considered: (i) a step-wise mechanism that proceeds through formation of the Z-isomer of their shared enediol intermediate, (ii) a step-wise mechanism that forms the E-isomer of the enediol, and (iii) a concerted pathway that bypasses the enediol intermediate. Energy calculations show that the concerted pathway has the lowest activation energy barrier at 45.7 kcal mol<sup>-1</sup>. The reaction force, chemical potential, and reaction electronic flux are calculated for each reaction to characterize electronic changes throughout the mechanism. The reaction force constant is calculated in order to investigate the synchronous/asynchronous nature of the concerted intramolecular proton transfers involved. Additional characterization of synchronicity is provided by calculating the bond fragility spectrum for each mechanism.

scholarly journals Running ground reaction forces across footwear conditions are predicted from the motion of two body mass components

2019 ◽  
Vol 126 (5) ◽  
pp. 1315-1325 ◽  
Author(s):  
Andrew B. Udofa ◽  
Kenneth P. Clark ◽  
Laurence J. Ryan ◽  
Peter G. Weyand
Keyword(s):  
Ground Reaction Force ◽  
Lower Limb ◽  
Reaction Force ◽  
Ground Reaction Forces ◽  
Vertical Ground Reaction Force ◽  
Time Patterns ◽  
Foot Strike ◽  
Reaction Forces ◽  
Vertical Ground ◽  
Force Time

Although running shoes alter foot-ground reaction forces, particularly during impact, how they do so is incompletely understood. Here, we hypothesized that footwear effects on running ground reaction force-time patterns can be accurately predicted from the motion of two components of the body’s mass (mb): the contacting lower-limb (m1 = 0.08mb) and the remainder (m2 = 0.92mb). Simultaneous motion and vertical ground reaction force-time data were acquired at 1,000 Hz from eight uninstructed subjects running on a force-instrumented treadmill at 4.0 and 7.0 m/s under four footwear conditions: barefoot, minimal sole, thin sole, and thick sole. Vertical ground reaction force-time patterns were generated from the two-mass model using body mass and footfall-specific measures of contact time, aerial time, and lower-limb impact deceleration. Model force-time patterns generated using the empirical inputs acquired for each footfall matched the measured patterns closely across the four footwear conditions at both protocol speeds ( r2 = 0.96 ± 0.004; root mean squared error  = 0.17 ± 0.01 body-weight units; n = 275 total footfalls). Foot landing angles (θF) were inversely related to footwear thickness; more positive or plantar-flexed landing angles coincided with longer-impact durations and force-time patterns lacking distinct rising-edge force peaks. Our results support three conclusions: 1) running ground reaction force-time patterns across footwear conditions can be accurately predicted using our two-mass, two-impulse model, 2) impact forces, regardless of foot strike mechanics, can be accurately quantified from lower-limb motion and a fixed anatomical mass (0.08mb), and 3) runners maintain similar loading rates (ΔFvertical/Δtime) across footwear conditions by altering foot strike angle to regulate the duration of impact. NEW & NOTEWORTHY Here, we validate a two-mass, two-impulse model of running vertical ground reaction forces across four footwear thickness conditions (barefoot, minimal, thin, thick). Our model allows the impact portion of the impulse to be extracted from measured total ground reaction force-time patterns using motion data from the ankle. The gait adjustments observed across footwear conditions revealed that runners maintained similar loading rates across footwear conditions by altering foot strike angles to regulate the duration of impact.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

scholarly journals Ground Reaction Forces and Kinematics of Ski Jump Landing Using Wearable Sensors

Sensors ◽  
2019 ◽  
Vol 19 (9) ◽  
pp. 2011 ◽  
Author(s):  
Bessone ◽  
Petrat ◽  
Schwirtz
Keyword(s):  
Wearable Sensors ◽  
Reaction Force ◽  
Ground Reaction Forces ◽  
Inertial Motion ◽  
Jump Landing ◽  
The Past ◽  
Landing Biomechanics ◽  
Reaction Forces ◽  
The Hill ◽  
Kinematics And Kinetics

In the past, technological issues limited research focused on ski jump landing. Today, thanks to the development of wearable sensors, it is possible to analyze the biomechanics of athletes without interfering with their movements. The aims of this study were twofold. Firstly, the quantification of the kinetic magnitude during landing is performed using wireless force insoles while 22 athletes jumped during summer training on the hill. In the second part, the insoles were combined with inertial motion units (IMUs) to determine the possible correlation between kinematics and kinetics during landing. The maximal normal ground reaction force (GRFmax) ranged between 1.1 and 5.3 body weight per foot independently when landing using the telemark or parallel leg technique. The GRFmax and impulse were correlated with flying time (p < 0.001). The hip flexions/extensions and the knee and hip rotations of the telemark front leg correlated with GRFmax (r = 0.689, p = 0.040; r = −0.670, p = 0.048; r = 0.820, p = 0.007; respectively). The force insoles and their combination with IMUs resulted in promising setups to analyze landing biomechanics and to provide in-field feedback to the athletes, being quick to place and light, without limiting movement.

Modification of the contact area of a standard force platform and runway for small breed dogs

2014 ◽  
Vol 27 (04) ◽  
pp. 257-262 ◽  
Author(s):  
J. Y. W. Kim ◽  
T. C. Garcia-Nolan ◽  
S. Y. Kim ◽  
K. Hayashi ◽  
P. L. Hitchens ◽  
...  
Keyword(s):  
Reaction Force ◽  
Force Plate ◽  
Force Platform ◽  
Standard Size ◽  
Plate Size ◽  
Propulsion Force ◽  
In Series ◽  
Reaction Forces ◽  
Wood Frame ◽  
Clinically Significant

SummaryObjectives: To develop a platform that used standard size force plates for large breed dogs to capture ground reaction force data from any size dog.Methods: A walkway platform was constructed to accommodate two force plates (60 cm x 40 cm) positioned in series to a variety of smaller sizes. It was constructed from a custom wood frame with thick aluminium sheet force plate covers that prevented transfer of load to the force plate, except for rectangular windows of three different dimensions. A friction study was performed to ensure plates did not translate relative to one another during gait trials. A prospective, observational, single crossover study design was used to compare the effect of force platform configuration (full plate size [original plate], half plate size [modified plate]) on ground reaction forces using eight adult healthy Labrador Retriever dogs.Results: Slippage of the steel plate on the force plate did not occur. Peak propulsion force was the only kinetic variable statistically different between the full size and half sized platforms. There were no clinically significant differences between the full and half force platforms for the variables and dogs studied.Discussion and conclusion: The modified force platform allows the original 60 x 40 cm force plate to be adjusted effectively to a 30 x 40 cm, 20 x 40 cm and 15 x 40 cm sized plate with no clinically significant change in kinetic variables. This modification that worked for large breed dogs will potentially allow kinetic analysis of a large variety of dogs with different stride lengths.

Optimal Design of Bi- and Multi-Stable Compliant Cellular Structures

2018 ◽  
Author(s):  
Quantian Luo ◽  
Liyong Tong
Keyword(s):  
Optimal Design ◽  
Virtual Work ◽  
Reaction Force ◽  
Nonlinear Finite Element ◽  
Cellular Structures ◽  
Stress And Strain ◽  
Principle Of Virtual Work ◽  
Stable States ◽  
Threshold Method ◽  
Element Analysis

This paper presents optimal design for nonlinear compliant cellular structures with bi- and multi-stable states via topology optimization. Based on the principle of virtual work, formulations for displacements and forces are derived and expressed in terms of stress and strain in all load steps in nonlinear finite element analysis. Optimization for compliant structures with bi-stable states is then formulated as: 1) to maximize the displacement under specified force larger than its critical one; and 2) to minimize the reaction force for the prescribed displacement larger than its critical one. Algorithms are developed using the present formulations and the moving iso-surface threshold method. Optimal design for a unit cell with bi-stable states is studied first, and then designs of multi-stable compliant cellular structures are discussed.

Dynamic Simulation of Piping System Around Safety Valve for Closed Discharge System

2011 ◽  
Author(s):  
Yoshiaki Sakamoto ◽  
Hisao Izuchi ◽  
Naoko Suzuki
Keyword(s):  
Dynamic Simulation ◽  
Safety Valve ◽  
Flow Direction ◽  
Reaction Force ◽  
Time History ◽  
Piping System ◽  
Discharge System ◽  
Fluid Transient ◽  
Short Period ◽  
Reaction Forces

Reaction force of safety valves acting to the piping system is one of key factors for the piping system design around the safety valves. In case of open discharge system, it is well known that a large reaction force acts to the piping corresponding to the fluid momentum force at the atmospheric discharge. On the other hand, reaction forces for closed discharge system may be relatively small since the forces acting to the adjacent two points with flow direction change such as elbows and tees are balanced within very short period. However, large reaction forces may act as a result of unsteady flow just after the initial activation of the safety valve. API RP520 mentioned that a complex time history analysis of the piping system around the safety valves may be required to obtain the transient forces. This paper explains a method of a comprehensive dynamic simulation of piping system around safety valves taking interaction among the valve disc motion, the fluid transient for compressible flow and the piping structural dynamics into account. The simulation results have good agreement with the experimental data. The effectiveness of this method is confirmed throughout an application to actual piping system around safety valves.

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