Matrix Solution of Digitized Planar Human Body Dynamics for Biomechanics Laboratory Instruction

1992 ◽  
Author(s):  
David G. Alciatore ◽  
Lawrence D. Abraham ◽  
Ronald E. Barr
Keyword(s):  
Human Body ◽  
Body Position ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Iterative Solution ◽  
The Body ◽  
Body Motion ◽  
Laboratory Instruction ◽  
Matrix Formulation ◽  
Body Dynamics

Abstract The dynamics of planar human body motion, solved with a non-iterative matrix formulation, is presented. The approach is based on applying Newton-Euler equations of motion to an assumed 15 body segment model resulting in a system of 48 equations. The system of equations was carefully ordered to result in a banded system (bandwidth = 10) which is solved efficiently. The method is more favorable than a traditional iterative solution because it is more easily coded, reaction forces are more easily dealt with, and multiple solutions for a given body position can be readily obtained. The results described are limited to planar body motion but the method is easily extendible to general three-dimensional motion. A computer program was developed to process digitized body point coordinate data and calculate resultant joint forces and moments for each frame of data. This method of human body dynamics analysis was developed to support laboratory instruction for an Engineering Biomechanics course. Athletic activities are captured with a three-dimensional video digitizing system and the data is processed resulting in time histories of force and moment distributions throughout the body during the captured event. Computer software performs the analyses and provides real-time graphical illustrations of the kinematics and dynamics results. The dynamics results for the leg of a runner are presented here as an example of the application of the method.

scholarly journals Improving Inverse Dynamics Accuracy in a Planar Walking Model Based on Stable Reference Point

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Alaa Abdulrahman ◽  
Kamran Iqbal ◽  
Gannon White
Keyword(s):  
Human Body ◽  
Reference Point ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
The Body ◽  
Sensor Position ◽  
Reaction Forces ◽  
The Cost

Physiologically and biomechanically, the human body represents a complicated system with an abundance of degrees of freedom (DOF). When developing mathematical representations of the body, a researcher has to decide on how many of those DOF to include in the model. Though accuracy can be enhanced at the cost of complexity by including more DOF, their necessity must be rigorously examined. In this study a planar seven-segment human body walking model with single DOF joints was developed. A reference point was added to the model to track the body’s global position while moving. Due to the kinematic instability of the pelvis, the top of the head was selected as the reference point, which also assimilates the vestibular sensor position. Inverse dynamics methods were used to formulate and solve the equations of motion based on Newton-Euler formulae. The torques and ground reaction forces generated by the planar model during a regular gait cycle were compared with similar results from a more complex three-dimensional OpenSim model with muscles, which resulted in correlation errors in the range of 0.9–0.98. The close comparison between the two torque outputs supports the use of planar models in gait studies.

scholarly journals A faster escape does not enhance survival in zebrafish larvae

2017 ◽  
Vol 284 (1852) ◽  
pp. 20170359 ◽  
Author(s):  
Arjun Nair ◽  
Christy Nguyen ◽  
Matthew J. McHenry
Keyword(s):  
High Speed ◽  
Larval Fish ◽  
Body Position ◽  
Three Dimensional ◽  
Limited Range ◽  
The Body ◽  
Model Parameters ◽  
Fish Prey ◽  
Zebrafish Larvae ◽  
Fish Predators

An escape response is a rapid manoeuvre used by prey to evade predators. Performing this manoeuvre at greater speed, in a favourable direction, or from a longer distance have been hypothesized to enhance the survival of prey, but these ideas are difficult to test experimentally. We examined how prey survival depends on escape kinematics through a novel combination of experimentation and mathematical modelling. This approach focused on zebrafish ( Danio rerio ) larvae under predation by adults and juveniles of the same species. High-speed three-dimensional kinematics were used to track the body position of prey and predator and to determine the probability of behavioural actions by both fish. These measurements provided the basis for an agent-based probabilistic model that simulated the trajectories of the animals. Predictions of survivorship by this model were found by Monte Carlo simulations to agree with our observations and we examined how these predictions varied by changing individual model parameters. Contrary to expectation, we found that survival may not be improved by increasing the speed or altering the direction of the escape. Rather, zebrafish larvae operate with sufficiently high locomotor performance due to the relatively slow approach and limited range of suction feeding by fish predators. We did find that survival was enhanced when prey responded from a greater distance. This is an ability that depends on the capacity of the visual and lateral line systems to detect a looming threat. Therefore, performance in sensing, and not locomotion, is decisive for improving the survival of larval fish prey. These results offer a framework for understanding the evolution of predator–prey strategy that may inform prey survival in a broad diversity of animals.

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

Modeling of Human Reactions to Whole-Body Vibration

1987 ◽  
Vol 109 (3) ◽  
pp. 210-217 ◽  
Author(s):  
Farid M. L. Amirouche
Keyword(s):  
Human Body ◽  
Equations Of Motion ◽  
Vertical Direction ◽  
The Body ◽  
Whole Body ◽  
Connective Tissues ◽  
Finite Segment ◽  
Body Vibration ◽  
Forcing Function ◽  
Impulse Function

A computer-automated approach for studying the human body vibration is presented. This includes vertical, horizontal, and torsional vibration. The procedure used is based on Finite Segment Modeling (FSM) of the human body, thus treating it as a mechanical structure. Kane’s equations as developed by Huston et al. are used to formulate the governing equations of motion. The connective tissues are modeled by springs and dampers. In addition, the paper presents the transient response of different parts of the body due to a sinusoidal forcing function as well as an impulse function applied to the lower torso in the vertical direction.

Anguilliform body dynamics: modelling the interaction between muscle activation and body curvature

1991 ◽  
Vol 334 (1271) ◽  
pp. 385-390 ◽  
Keyword(s):  
Muscle Activation ◽  
Equations Of Motion ◽  
Relative Displacement ◽  
Travelling Wave ◽  
The Body ◽  
Linear Functions ◽  
Careful Examination ◽  
Body Tissues ◽  
Body Dynamics ◽  
Dynamics Modelling

A simple two-dimensional rod and pivot model is proposed for the mechanical structure of the lamprey, each pivot being controlled by a muscle segment attached via perpendicular extensions to the two rods. The elastic and viscous properties of the body tissues (including muscle) are described as linear functions of the relative displacement and angular velocity of the rods at each pivot. The contractile properties of the muscle are introduced as time-dependent forcing torques at the pivots, which are generated by a travelling wave of activation. The angles between the rods at each pivot are used as adapted coordinates, and the equations of motion are linearized by assuming low curvature dynamics, corresponding to slow swimming speeds. Investigation of these equations with varying viscous and elastic parameters leads to a reconstruction of a lamprey viewed in motion on a smooth flat surface out of water. The most striking feature is of an apparently standing wave motion, which is indeed observed in the real animal but which on careful examination in the model corresponds to a travelling wave of varying amplitude.

ENVELOPING SURFACES AND ADMISSIBLE VELOCITIES OF HEAVY RIGID BODIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2525-2553 ◽  
Author(s):  
IGOR N. GASHENENKO ◽  
PETER H. RICHTER
Keyword(s):  
Three Dimensional ◽  
Rigid Bodies ◽  
First Integrals ◽  
The Body ◽  
Heegaard Splitting ◽  
Body Motion ◽  
Invariant Sets ◽  
Poisson Problem ◽  
Integral Manifolds ◽  
Angular Velocities

The general Euler-Poisson problem of rigid body motion is investigated. We study the three-dimensional algebraic level surfaces of the first integrals, and their topological bifurcations. The main result of this article is an analytical and qualitatively complete description of the projections of these integral manifolds to the body-fixed space of angular velocities. We classify the possible types of these invariant sets and analyze the dependence of their topology on the parameters of the body and the constants of the first integrals. Particular emphasis is given to the enveloping surfaces of the sets of admissible angular velocities. Their pre-images in the reduced phase space induce a Heegaard splitting which lends itself for a general choice of complete Poincaré surfaces of section, irrespective of whether or not the system is integrable.

Temperature profiles with respect to inhomogeneity and geometry of the human body

1988 ◽  
Vol 65 (3) ◽  
pp. 1110-1118 ◽  
Author(s):  
J. Werner ◽  
M. Buse
Keyword(s):  
Human Body ◽  
Three Dimensional ◽  
The Body ◽  
Physiological Data ◽  
Physical Parameters ◽  
Temperature Profiles ◽  
Metabolic Heat ◽  
Spatially Distributed ◽  
Adequate Representation ◽  
Neutral Conditions

Temperature profiles within the human body are highly dependent on the geometry and inhomogeneity of the body. Physical parameters such as density and heat conductivity of the various tissues and variables such as blood flow and metabolic heat production of different organs are spatially distributed and thereby influence the temperature profiles within the human body. Actual physiological knowledge allows one to take into account up to 54 different spatially distributed values for each parameter. An adequate representation of the anatomy of the body requires a spatial three-dimensional grid of at least 0.5-1.0 cm. This is achieved by photogrammetric treatment of three-dimensional anatomic models of the human body. As a first essential result, the simulation system has produced a realistic picture of the topography of temperatures under neutral conditions. Compatibility of reality and simulation was achieved solely on the basis of physical considerations and physiological data base. Therefore the simulation is suited to the extrapolation of temperature profiles that cannot be obtained experimentally.

Penalty Formulations for the Dynamic Analysis of Elastic Mechanisms

1989 ◽  
Vol 111 (3) ◽  
pp. 321-327 ◽  
Author(s):  
E. Bayo ◽  
M. A. Serna
Keyword(s):  
Finite Element Method ◽  
Dynamic Analysis ◽  
Simulation Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Numerical Algorithms ◽  
Body Motion ◽  
The Finite Element Method ◽  
Floating Frame ◽  
Flexible Mechanisms

A series of penalty methods are presented for the dynamic analysis of flexible mechanisms. The proposed methods formulate the equations of motion with respect to a floating frame that follows the rigid body motion of the links. The constraint conditions are not appended to the Lagrange’s equations in the form of algebraic or differential constraints, but inserted in them by means of a penalty formulation, and therefore the number of equations of the system does not increase. Furthermore, the discretization of the equations using the finite element method leads to a system of ordinary differential equations that can be solved using standard numerical algorithms. The proposed methods are valid for three dimensional analysis and can be very easily implemented in existing codes. Furthermore, they can be used to model any type of constraint conditions, either holonomic or nonholonomic, and with any degree of redundancy. A series of mechanisms composed of elastic members are analyzed. The results demonstrate the capabilities of the proposed methods for simulation analysis.

scholarly journals A Specific Algorithm Based on Motion Direction Prediction

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhesen Chu ◽  
Min Li
Keyword(s):  
Human Body ◽  
Body Position ◽  
Motion Vector ◽  
Human Motion ◽  
Generative Model ◽  
Experimental Results ◽  
Body Motion ◽  
Motion Vectors ◽  
Motion Direction ◽  
Current Frame

In this paper, we study the estimation of motion direction prediction for fast motion and propose a threshold-based human target detection algorithm using motion vectors and other data as human target feature information. The motion vectors are partitioned into regions by normalization to form a motion vector field, which is then preprocessed, and then the human body target is detected through its motion vector region block-temporal correlation to detect the human body motion target. The experimental results show that the algorithm is effective in detecting human motion targets in videos with the camera relatively stationary. The algorithm predicts the human body position in the reference frame of the current frame in the video by forward mapping the motion vector of the current frame, then uses the motion vector direction angle histogram as a matching feature, and combines it with a region matching strategy to track the human body target in the predicted region, thus realizing the human body target tracking effect. The algorithm is experimentally proven to effectively track human motion targets in videos with relatively static backgrounds. To address the problem of sample diversity and lack of quantity in a multitarget tracking environment, a generative model based on the conditional variational self-encoder conditional generation of adversarial networks is proposed, and the performance of the generative model is verified using pedestrian reidentification and other datasets, and the experimental results show that the method can take advantage of the advantages of both models to improve the quality of the generated results.

scholarly journals Distinct Representations of Body and Head motion are Dynamically Encoded by Purkinje cell Populations in the Macaque Cerebellum

2021 ◽  
Author(s):  
Omid A Zobeiri ◽  
Kathleen E Cullen
Keyword(s):  
Postural Control ◽  
Purkinje Cells ◽  
Body Position ◽  
The Body ◽  
Body Motion ◽  
Whole Body ◽  
Head Motion ◽  
Response Dynamics ◽  
Dynamic Representation ◽  
Self Motion

The ability to accurately control our posture and perceive spatial orientation during self-motion requires knowledge of the motion of both the head and body. However, whereas the vestibular sensors and nuclei directly encode head motion, no sensors directly encode body motion. Instead, the integration of vestibular and neck proprioceptive inputs is necessary to transform vestibular information into the body-centric reference frame required for postural control. The anterior vermis of the cerebellum is thought to play a key role in this transformation, yet how its Purkinje cells integrate these inputs or what information they dynamically encode during self-motion remains unknown. Here we recorded the activity of individual anterior vermis Purkinje cells in alert monkeys during passively applied whole-body, body-under-head, and head-on-body rotations. Most neurons dynamically encoded an intermediate representation of self-motion between head and body motion. Notably, these neurons responded to both vestibular and neck proprioceptive stimulation and showed considerable heterogeneity in their response dynamics. Furthermore, their vestibular responses demonstrated tuning in response to changes in head-on-body position. In contrast, a small remaining percentage of neurons sensitive only to vestibular stimulation unambiguously encoded head-in-space motion across conditions. Using a simple population model, we establish that combining responses from 40 Purkinje cells can explain the responses of their target neurons in deep cerebellar nuclei across all self-motion conditions. We propose that the observed heterogeneity in Purkinje cells underlies the cerebellum's capacity to compute the dynamic representation of body motion required to ensure accurate postural control and perceptual stability in our daily lives.

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