Simulink Model of
Human’s Elbow Neuromuscular System
Tian Bo
Simulink Model of Human’s Elbow Neuromuscular System
What is Elbow Neuromuscular System?
The joint torque which sets human elbow
into motion is generated by a separate group
of muscles provided for the joint. As the
activation of each muscle is determined by a
neural input, a neuromuscular system
controlling all muscles has to be considered
in order to understand human movements.
So we should firstly understand the
Mechanism of the elbow movement.
Simulink Model of Human’s Elbow Neuromuscular System
The goal and assumed data
GOAL
The goal is to investigate the effects of muscle
strength on the relative contributions of four
muscles to dynamic elbow motion.
ASSUMED DATA
In order to sample the model, we make some
assumed data:
1. Elbow moves in a 2-D path.
2. There are two muscle in arm, each one’s
origin of force is in the middle of arm.
3. Acceleration of gravity G is 9.8067 .
4. The drag torque is only happened in
elbow.
Simulink Model of Human’s Elbow Neuromuscular System
What is Elbow Neuromuscular System?
Recommend three books in this area:
<< Introduction to Sports Biomechanics >>
---By Roger Bartlett, E & FN Spon in 1997
<<Sports Biomechanics Reducing Injury and Improving
Performance >>
---By Roger Bartlett, E & FN Spon in 1999
<<Sports Biomechanics The Basics: Optimising Human
Performance>>
--- By Anthony Blazevich, A&C Black in 2007
Simulink Model of Human’s Elbow Neuromuscular System
Mechanism of the elbow movement
Basic theory
Kinematical
equation
second-order
linear time
invariant
differential
equation
methods
Newton's
laws of
motion
Dynamical
equation
Newton's
laws of
motion
Simulink Model of Human’s Elbow Neuromuscular System
Nomenclature
:Vector from origin to wrist
: Shoulder joint acceleration vector
:Vector from origin to elbow
: Elbow joint acceleration vector
:Vector from elbow to wrist
: C1 Centrobaric acceleration vector in X
:Shoulder joint angle
: C1 Centrobaric acceleration vector in Y
:Elbow joint angle
: C2 Centrobaric acceleration vector in X
:Lengh from origin to elbow
: C2 Centrobaric acceleration vector in Y
:Lengh from elbow to wrist
:Shoulder joint velocity vector
:Elbow joint velocity vector
Simulink Model of Human’s Elbow Neuromuscular System
Kinematical equation model
Simulink Model of Human’s Elbow Neuromuscular System
Kinematical equation
scalar equation
corresponding to X and Y
derivation operation
derivation operation
Simulink Model of Human’s Elbow Neuromuscular System
Kinematical equation
Suppose if the center of gravity is in the middle of forearm, then obtained
following equation
Simulink Model of Human’s Elbow Neuromuscular System
Dynamical equation
Simulink Model of Human’s Elbow Neuromuscular System
Dynamical equation
Forearm &1
Simulink Model of Human’s Elbow Neuromuscular System
Dynamical equation
Forearm &2
Simulink Model of Human’s Elbow Neuromuscular System
Dynamical equation
Actual load
Simulink Model of Human’s Elbow Neuromuscular System
Simultaneous
matrix from the 6 dynamical equations and 8 kinematical equations
Simulink Model of Human’s Elbow Neuromuscular System
What is Simulink?
Simulink® is an environment for multidomain
simulation and Model-Based Design for dynamic
and embedded systems. It provides an
interactive
graphical
environment
and
a
customizable set of block libraries that let you
design, simulate, implement, and test a variety of
time-varying
systems,
including
communications, controls, signal processing,
video processing, and image processing.
--- www.mathworks.com
Simulink Model of Human’s Elbow Neuromuscular System
Solving matrix equation by calling matlab
Code in function mdlOutputs
% Rectangular array declarations
% A rectangular array
Simulink Model of Human’s Elbow Neuromuscular System
Solving matrix equation by calling matlab
Code in function mdlOutputs
% B rectangular array
Simulink Model of Human’s Elbow Neuromuscular System
Solving matrix equation by calling matlab
Code in function mdlOutputs
% solve the equations
fff=inv(a)*b;
%output the result
outfff(1)=fff(1);
outfff(2)=fff(2);
outfff(3)=fff(7);
outfff(4)=fff(8);
outfff(5)=error;
sys=outfff;
Add this function to a s-function model (sfuntmp1. m ).
Simulink Model of Human’s Elbow Neuromuscular System
Simulink model: s-function
mdlInitializeSizes：Specify the number of inputs, outputs, states, parameters,
and other characteristics of the S-function;
mdlDerivatives： Compute the S-function's derivatives ;
mdlUpdate： Update a block's states ;
mdlOutputs： Compute the signals that this block emits;
mdlGetTimeOfNextVarHit： Initialize the state vectors of this S-function ;
mdlTerminate： Perform any actions required at termination of the
simulation;
Simulink Model of Human’s Elbow Neuromuscular System
Simulink model
Simulink Model of Human’s Elbow Neuromuscular System
Output
Simulink Model of Human’s Elbow Neuromuscular System
Next step
1. This system is just a sample of elbow system, it’s far away from the truly world.
And need to rebuild the model and add more parameter into the system.
2. Need to limit the elbow moving angle in next step.
3. Actually do the real model neuromuscular system.
Simulink Model of Human’s Elbow Neuromuscular System
References
[1] Timotej Kodek, Marko Munih, An analysis of static and dynamic joint torques
in elbow flexion-extension movements, Simulation Modelling Practice and Theory 11
(2003) 297–311
[2] Tadashi Kashima, Yoshihisa Isurugi, Masasuke Shima, An optimal control model of
a neuromuscular system in human arm movements and its control characteristics, Artif
Life Robotics (2002) 6:205-209
[3] AME Project #1 test, A university’s class project
[4] Vague, 单关节平面机器人动力学仿真
[5] Sybert Stroeve, Neuromuscular control model of the arm including feedback
and feedforward components, Acta Psychologica 100 (1998) 117±131
[6] Tsukasa Kanchiku, James V. Lynskey, Neuromuscular electrical stimulation induced
forelimb movement in a rodent model, Journal of Neuroscience Methods 167 (2008)
317–326
[7] N. Lan and T. Murakata, A REALISTIC HUMAN ELBOW MODEL FOR
DYNAMIC SIMULATION, Dept. of Biomedical Engineering, University of Southern
California
Simulink Model of Human’s Elbow Neuromuscular System
References
[8] Roger Bartlett, Introduction to Sports Biomechanics, E & FN Spon in 1997
[9] 姚俊,马松辉 , Simulink 建模与仿真 ,西安电子科技大学出版社 2004
[10] Patrick J. Schimoler, DESIGN OF A CONTROL SYSTEM FOR AN ELBOW
JOINT MOTION SIMULATOR , University of Pittsburgh, 2005
[11] 李良标, 运动生物力学, 北京体育学院出版社 1991