The University of SydneySlide 1 Biomechanical Modelling of
Musculoskeletal Systems Presented by Phillip Tran AMME4981/9981
Semester 1, 2015 Lecture 5
Slide 2
The University of SydneySlide 2 The Musculoskeletal System
Slide 3
The University of SydneySlide 3 The Musculoskeletal System
Skeletal System Provides support, structure, and protection Made up
of: Bones Ligaments Cartilage Joints Muscular System Provides
movement Made up of: Muscles Tendons
Slide 4
The University of SydneySlide 4 Bones Cortical/Compact bone
Hard, dense bone Cancellous/Spongy bone Trabeculae align along
lines of stress Contains red marrow in spaces Medullary Cavity
Contains yellow marrow
Slide 5
The University of SydneySlide 5 Synovial Joints Articular
Cartilage Act as spongy cushions to absorb compressive forces Joint
Cavity Space that contains synovial fluid Articular Capsule
Synovial membrane secretes synovial fluid Fibrous layer holds the
joint together Synovial Fluid Reduces friction between cartilage
Ligaments Reinforce the entire structure
Slide 6
The University of SydneySlide 6 Tendons and Ligaments Tendons
Dense connective tissue that attach muscles to bones Made up of
collagen fibres that are aligned along the length of the tendon
Transfers pulling force of the muscle to the attached bone
Ligaments Connect one bone to another Provides stabilisation
Slide 7
The University of SydneySlide 7 Skeletal Muscles Muscle
Contraction Concentric: muscle shortens Isometric: no change in
length Eccentric: muscle extends Force of Muscle Contraction Number
of muscle fibres recruited Size of fibres Frequency of stimulation
Degree of muscle stretch
Slide 8
The University of SydneySlide 8 Anatomical Position and Planes
Anatomical Position Arms at side with palms facing forward Legs
straight and together with feet flat on the ground Movements of the
body are described in relation to this position Anatomical Planes
Coronal (front/back) Sagittal (left/right) Transverse
(top/bottom)
Slide 9
The University of SydneySlide 9 Anatomical Directions
Slide 10
The University of SydneySlide 10 Movement
Flexion/ExtensionAbduction/Adduction
Slide 11
The University of SydneySlide 11 Movement
RotationSupination/PronationDorsi/Plantarflexion
Slide 12
The University of SydneySlide 12 Biomechanical Modelling
Slide 13
The University of SydneySlide 13 Solving a Mechanical Problem
Forces are applied to a body Geometry is known Finding the internal
stresses Finding the resultant motion
Slide 14
The University of SydneySlide 14 Solving a Mechanical Problem
Known Forces F Equations of MotionDouble Integration Displacement r
Forces (known) Motion (unknown)
Slide 15
The University of SydneySlide 15 Solving a Biomechanical
Problem Internal Forces Active muscles Reactions at joints
Reactions at ligaments External Forces Inertial forces due to
acceleration of a segment Load applied directly to a body segment
External force Internal force
Slide 16
The University of SydneySlide 16 Solving a Biomechanical
Problem Known Displacement r Double DifferentiationEquations of
MotionForces F Internal Forces (unknown) Motion (known) External
Forces (known)
Slide 17
The University of SydneySlide 17 Direct/Inverse Problems Direct
Problems (Mechanical) Using known forces to determine movement
Requires accurate measurements of the geometry Requires knowledge
of external forces Inverse Problems (Biomechanical) Using known
movements to determine the internal forces: Requires full
description of the movement (displacement, velocity, acceleration)
Requires accurate measurements of anthropometry (measurement of the
human body) Requires knowledge of external forces
Slide 18
The University of SydneySlide 18 Movement: Motion Tracking
Slide 19
The University of SydneySlide 19 Movement: Motion Tracking
Slide 20
The University of SydneySlide 20 Movement: Trajectories of
Motion
Slide 21
The University of SydneySlide 21 Movement: Trajectories of
Motion
Slide 22
The University of SydneySlide 22 Measuring Movement
Slide 23
The University of SydneySlide 23 Types of Motion
Slide 24
The University of SydneySlide 24 Anthropometry Measurement of
the human body Segment length Segment mass Position of centre of
gravity Density
Slide 25
The University of SydneySlide 25 Anthropometry Body
SegmentLength (% of height) Distance of centre of mass from distal
joint (% of limb) Mass (% of body mass) Head9.450.05.7 Neck4.51.3
Thorax+Abdomen25.030.3 Upper Arm18.043.62.6 Forearm26.043.01.9
Hand50.60.7 Pelvis9.414.0 Thigh31.543.312.8 Shank23.043.35.1
Foot16.050.01.3
Slide 26
The University of SydneySlide 26 Anthropometry Body
SegmentDensity (g/cm 3 )Mass moment at centre of mass per segment
length (kmm 2 /m) Head 1.11 Neck 1.11 Thorax+Abdomen Upper Arm
1.070.322 Forearm 1.130.303 Hand 1.160.297 Pelvis Thigh 1.050.323
Shank 1.090.302 Foot 1.100.475
Slide 27
The University of SydneySlide 27 External Forces Gravitational
Forces Acting downward through the centre of mass of each segment
Ground Reaction Forces Distributed over an area Assumed to be
acting as a single force at the centre of pressure Externally
Applied Forces Restraining or accelerating force that acts outside
the body Mass being lifted
Slide 28
The University of SydneySlide 28 Biomechanical Modelling: Body
Segments Body segments can be modelled as rigid bodies Free body
diagrams can be drawn for each segment Forces and moments acting at
joint centres Gravitational forces acting at the centres of mass
Accurate measurements are needed of: Segment masses (m) Location of
centres of mass Location of joint centres Mass moment of inertia
(I)
Slide 29
The University of SydneySlide 29 Biomechanical Modelling:
Assumptions Rigid body motion (deformation is small relative to
overall motion) Body segments interconnected at joints Length of
each body segment remains constant Each body segment has a fixed
mass located at its centre of mass The location of each body
segments centre of mass is fixed Joints are considered to be hinge
(2D) or ball and socket (3D) The moment of inertia of each body
segment about any point is constant during any movement
Slide 30
The University of SydneySlide 30 Examples
Slide 31
The University of SydneySlide 31 Arm Analysis: Part 1 A flexed
arm is holding a ball of W b =20 N with a distance of 35 cm to the
elbow centre. What is the force required in the biceps (B) if the
forearm weighs W a =15 N and the centre of mass for the forearm is
15 cm from the elbow centre of rotation? Also find the reaction
force at the elbow joint. Assume the forearm is in the horizontal
position and the angle between the forearm and upper arm at the
elbow is 100 degrees. The biceps tendon is inserted 3 cm from the
elbow centre of the forearm, and at the proximal end of the upper
arm, which is 30 cm in length.
Slide 32
The University of SydneySlide 32 Arm Analysis: Part 1 Free Body
Diagram Using trig formulae: = 74.5
Slide 33
The University of SydneySlide 33 Arm Analysis: Part 1
Slide 34
The University of SydneySlide 34 Arm Analysis: Part 2 The ball
is lifted from the horizontal forearm position with an angular
acceleration of =2rad/s 2. Determine the additional force required
by the bicep to provide this movement. The radius of the forearm is
4cm. Assume that the upper arm remains stationary.
Slide 35
The University of SydneySlide 35 Arm Analysis: Part 2
Slide 36
The University of SydneySlide 36 Summary The skeletal and
muscular systems work together to provide movement for the human
body The body can be modelled biomechanically Inverse method to
derive the internal muscle forces and joint reactions Movement
Anthropometry External forces
Slide 37
The University of SydneySlide 37 Joint Reaction Analysis A
person stands statically on one foot. The ground reaction force R
acts 4cm anterior to the ankle centre of rotation. The body mass is
60kg and the foot mass is 0.9kg. The centre of mass of the foot is
6cm from the centre of rotation. Determine the forces and moment in
the ankle. Rotation Centre Mass Centre RyRy RxRx mg AxAx AyAy
MAMA
Slide 38
The University of SydneySlide 38 Joint Reaction Analysis
Slide 39
The University of SydneySlide 39 Joint Reaction Analysis A
person exercises his left shoulder rotators. Calculate the forces
and moments exerted on his shoulder. F = 200 N a = 25 cm b = 30 cm
y x z RjRj MjMj F A a b B C a b
Slide 40
The University of SydneySlide 40 Joint Reaction Analysis
Slide 41
The University of SydneySlide 41 Muscle Analysis A weight
lifter raises a barbell to his chest. Determine the torque
developed by the back and the hip extensor muscles (M j ) when the
barbell is about knee height. Weight of barbell, W b = 1003N Mass
of upper body, m u = 53.5kg a = 38cm, b = 32cm, d = 64cm I G = 7.43
kgm 2, = 8.7 rad/s 2 a Gx = 0.2 m/s 2, a Gy = -0.1 m/s 2 MjMj FjFj
O y x 60 WbWb a mugmug b G d
