1. Simulink Model of Human’s Elbow Neuromuscular System Tian Bo

2. Simulink Model of Human’s 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. What is Elbow Neuromuscular System?

3. 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.

4. What is Elbow Neuromuscular System? Recommend three books in this area: > ---By Roger Bartlett, E & FN Spon in 1997 > ---By Roger Bartlett, E & FN Spon in 1999 > --- By Anthony Blazevich, A&C Black in 2007 Simulink Model of Human’s Elbow Neuromuscular System

5. 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

6. Nomenclature Simulink Model of Human’s Elbow Neuromuscular System :Vector from origin to wrist :Vector from origin to elbow :Vector from elbow to wrist :Shoulder joint angle :Elbow joint angle :Lengh from origin to elbow :Lengh from elbow to wrist : Shoulder joint velocity vector : Elbow joint velocity vector : Shoulder joint acceleration vector : Elbow joint acceleration vector : C1 Centrobaric acceleration vector in X : C1 Centrobaric acceleration vector in Y : C2 Centrobaric acceleration vector in X : C2 Centrobaric acceleration vector in Y

7. Simulink Model of Human’s Elbow Neuromuscular System Kinematical equation model

8. Simulink Model of Human’s Elbow Neuromuscular System scalar equation derivation operation corresponding to X and Y derivation operation Kinematical equation

9. Simulink Model of Human’s Elbow Neuromuscular System Suppose if the center of gravity is in the middle of forearm, then obtained following equation Kinematical equation

10. Simulink Model of Human’s Elbow Neuromuscular System Dynamical equation

11. Simulink Model of Human’s Elbow Neuromuscular System Dynamical equation Forearm &1

12. Simulink Model of Human’s Elbow Neuromuscular System Dynamical equation Forearm & 2

13. Simulink Model of Human’s Elbow Neuromuscular System Dynamical equation Actual load

14. Simulink Model of Human’s Elbow Neuromuscular System Simultaneous matrix from the 6 dynamical equations and 8 kinematical equations

15. 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 What is Simulink? Simulink Model of Human’s Elbow Neuromuscular System

16. Solving matrix equation by calling matlab Simulink Model of Human’s Elbow Neuromuscular System Code in function mdlOutputs % Rectangular array declarations % A rectangular array

17. Solving matrix equation by calling matlab Simulink Model of Human’s Elbow Neuromuscular System Code in function mdlOutputs % B rectangular array

18. Solving matrix equation by calling matlab Simulink Model of Human’s Elbow Neuromuscular System 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 ).

19. Simulink model: s-function Simulink Model of Human’s Elbow Neuromuscular System 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;

20. Simulink model Simulink Model of Human’s Elbow Neuromuscular System

21. Output Simulink Model of Human’s Elbow Neuromuscular System

22. Next step Simulink Model of Human’s Elbow Neuromuscular System 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.

23. References Simulink Model of Human’s Elbow Neuromuscular System [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

24. References Simulink Model of Human’s Elbow Neuromuscular System [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