BIOMECHANICAL MODELLING SERDAR ARITAN serdar.aritan@hacettepe.edu.tr Biomechanics Research Group www.biomech.hacettepe.edu.tr School of Sport Science&Technology www.sbt.hacettepe.edu.tr Hacettepe University, Ankara, Turkey www.hacettepe.edu.tr De Motu Animalium G.Borelli (1680) 1
WHY MODELLİNG? A model can quantify things we cannot measure: Forces and torques on the joints Individual muscle forces Joint reactions Force Forward Dynamics Inverse Dynamics Position Modelling in biomechanics works as an interface between the body and measurement settings. 2
CLASSICAL MECHANICS Whichever approach is used for modelling, first of all, the equation of motion has to be derived. The dynamics of biomechanical systems is based on classical mechanics. Newton (1643-1727) Euler (1707-1783) D Alembert (1717-1783) Lagrance (1736-1813) 3
CLASSICAL MECHANICS Lagrangian Dynamics Lagrange s equations of motion are specified in terms of the total energy of the body in the kinematic chain. Newton-Euler Dynamics In this method, the Newton-Euler equations are applied to each body in the model. All forces affecting each body must be considered, which makes this method difficult and tedious for complex systems. D Alembert s Principle Equations of motion are derived by identifying all forces on each body go through an acceleration and writing equilibrium equations. These equilibrium equations are simultaneously solved to obtain the dynamic system response. Kane s Dynamics This method is a subset of the group of methods known as Lagrange s form of D Alembert s Principle. The Newton-Euler equations are multiplied by special vectors to develop scalar representations of the forces acting on each body. 4
HOW TO CALCULATE Modelling Methods Displacement Velocity Acceleration x y z d dt v x v y vz d dt a x a y a z Equations of motions Mechanics in 3-D M I F ma Things get enormously complicated in 3-D The mass moment of inertia becomes a tensor The angles or orientation are difficult to define uniquely because many different rotation combinations can lead to the same position. 5
RIGID BODY MECHANICS Inverse Dynamics Displacement is input Force is output No muscle interaction Free-Body Diagram of Long Jumper Newton-Euler Method Alptekin, A., Arıtan, S. (2008). Biomechanical Analysis Of the Takeoff Phase in the Long Jump. IV. National Biomechanics Congress. Erzurum. 6
RIGID BODY MECHANICS Inverse Dynamics Alptekin, A., Arıtan, S. (2008). Biomechanical Analysis Of the Takeoff Phase in the Long Jump. IV. National Biomechanics Congress. Erzurum. 7
RIGID BODY MECHANICS Forward Dynamics Force is input Displacement is output No muscle interaction Symbolics Dynamics (SD/FAST) Online Dynamics (AutoLev) Mathworks (Simulink / Simmechanics) The Leg Lab. MIT Animation Lab. Georgia Tech. 8
9 2 0 0 2 0 0 0 0 2 0 0 0 0 0 0 2 1 ) ( 2 1 ) ( 2 2 0 0 0 0 t m F t v x x t t m F t t v x x dt m F dt v dx x dt dt m F v dx dt m F v dt dx x t m F v v t t m F v v dt m F dv v dt x m d dt dv m ma F t t t x x t t v v F : force m : mass a : acceleration v : velocity x : displacement t : Iteration step time Animation Lab. Georgia Tech. RIGID BODY MECHANICS Calculations of kinematics by integrating of equations of movement Euler Method [Euler 1707-1783]
RIGID BODY MECHANICS Forward Dynamics - SimMechanics Example 10
RIGID BODY MECHANICS Forward Dynamics - SimMechanics Example Biomechanics Lab. Hacettepe University 11
RIGID BODY MECHANICS Forward dynamics is often used for musculoskeletal simulation Can be used for injury simulation? Since the movement is output we are faced with the problem of finding the muscle forces that will make the model perform the desired movement.. 344 muscles were modelled. Muscle forces were calculated by using Hill s Equation (1938) F F b av 0 [ l( x )] b v 12
RIGID BODY MECHANICS Forward dynamics is often used for musculoskeletal simulation AnyBody Simulation, Denmak 13
RIGID BODY MECHANICS Forward dynamics is often used for musculoskeletal simulation OpenSim, USA 14
RIGID BODY MECHANICS Forward dynamics is often used for musculoskeletal simulation OpenSim, USA 15
RIGID BODY MECHANICS Forward dynamics is often used for musculoskeletal simulation OpenSim, USA 16
RIGID BODY MECHANICS EMG-Driven Models Basic idea. Record EMG from an experiment. Process the EMG to a muscle activation signal. Activate muscles in a computer model using the processed signal. The muscle activation signal is initially forward-simulated to produce a muscle contraction history. The muscle contractions create movement. Adjust the process parameters to get the right movement out of the model. 17
DEFORMABLE BODY MECHANICS Finite Element Modelling ELEMENT MESHES CAN BE COMPLICATED f k u f : force vector k : stifness matrix u : displacement vector 18
DEFORMABLE BODY MECHANICS Finite Element Modelling Mesh Generation from MRI Arıtan S. et al. (1997) Program for generation of three-dimensional finite element mesh from magnetic imaging scans. Med.Eng&Phys. 19
DEFORMABLE BODY MECHANICS Finite Element Modelling Mesh Generation 20
DEFORMABLE BODY MECHANICS Finite Element Modelling Simulation of what we can not measure Strees distrubition on the medial collateral ligament 21
DEFORMABLE BODY MECHANICS Finite Element Modelling with Kinematics Asai T. University of Yamagata 22
DEFORMABLE BODY MECHANICS Finite Element Modelling with Kinematics Asai T. University of Yamagata 23
DEFORMABLE BODY MECHANICS Finite Element Modelling on Layers 24
DEFORMABLE BODY MECHANICS Finite Element Modelling Whole Body FEA? The solution is only completely accurate in special cases. Finite element models are usually stiffer than the real structures Increasing the number of elements descreases the stiffness until it converges to the true value 25
DEFORMABLE BODY MECHANICS Mechanical Properties of on Layers S. Arıtan et al. A mechanical model representation of the in vivo creep behaviour of muscular bulk tissue / Journal of Biomechanics 26
INJURY When it happens? An unfortune Situation Abdüllaziz Alpak 105+ kg 185 kg Snatch 2.nd attempt 27
INJURY Being on the right place on the right time Weight -Lifting Platform were already calibrated for the movement analysis Camera 1 Camera 2 Abdüllaziz Alpak 185 kg Snatch 2.nd attempt 28
INJURY History Spondylolysis 29
INJURY History : Spondylolysis Injury : Total Rapture Medial Collateral Ligament 30
UNDERSTANDING OF MECHANISM OF SPORTS INJURIES Total 5 Video (PAL) Cameras were Used 3 Cameras captured the spinal markers 2 Cameras were used to record body markers 31
UNDERSTANDING OF MECHANISM OF SPORTS INJURIES Placement of Spinal Markers and Calibration 32
UNDERSTANDING OF MECHANISM OF SPORTS INJURIES Experimental Setup 33
UNDERSTANDING OF MECHANISM OF SPORTS INJURIES Spine and Body Movement An Inverse Dynamics Study Torque on L5, Calculated by D Alembert Principle 34
Modelling is not only science and mathematics, it is also an art. Cahit Arf, (1910-1997) 35
School of Sport Science and Technology www.sbt.hacettepe.edu.tr Hacettepe University Beytepe Campus www.hacettepe.edu.tr Thank you for your Attention 36