2) Elements of biomechanics Flashcards
Biomechanics
Studies the medical properties of living tosses and organs
The mechanical phenomena talking place in the body as a whole and in the organs
Degree of freedom
The sets of independent displacements or rotations that specify the displaced position and orientation of the system
The number of degrees of freedom of the body is equal to the number of independent displacement and rotations of the body.
Dof example 1
Unobstructed ridged body has 6 dof
3 transitional = along each axis
3 rotational = rotations around each axis
DRAWING
DOF example 2
An unobstructed material point has 3 translational dof
Eg: atom of mono atomic gas
DRAWINGS
DOF example 3
A rigid body that can only rotate around one axis and has one rotational DOF
DRAWING
DOF example 4
2 material points with ridges connection between them have 5 DOF
3 transitional and 2 rotational
Joints of the human musculoskeletal system
The elements of a mechanism are connected to each other at the joint, this can be fixed or kinematic
Bones of the human skeleton are connected to other bones at fixed or kinematic joints
Single axis, 2 linked system
When A is fixed B has one rotation DOF
Elbow joint and knee joint
DRAWING
Single axis, three linked system
When A is fixed, B had one rotation dof and C has 2 DOF
Joints of the hand- phalanges
Double axis, two linked system
Double axis joints allow links to rotate around two perpendicular axis.
Link B has 2 rotation DOF relative to A
Atlanto occipital joint
Provides rotation of the head from left to right and front to back
Triple axis, two linked system
Allows the links to rotate around 3 perpendicular axes.
Link B has 3 rotational degrees of freedom
An example of this is the ball and socket shoulder joint and hip joint
Leavers in the human body
The human musculoskeletal system consists of bones connect to each other at joints and muscles attached to bones by tendons
Biomechanics studies musculoskeletal system as a set of linked levers and forces applied to these levers
Levers
Lever is a rigid body that can roatate around a fixed axis (fulcrum) by forces being applied to it
Lever has one rotation DOF
W=load
F= effort
DRAWING
Equilibrium condition
The torques is the load M_w and of the effort M_f rotate the lever in opposite directions.
Equilibrium:
Sigma M_w= sigma M_f
If torque is positive
Sigma M_i= 0
If load and effort have different signs
First, second and third class lever
Equilibrium condition:
F1_f =W1_w
DRAWING X3
Work accomplished by levers
Input:
A_f= F1_f 🌑
Output:
A_w = W1_w 🌑
Mechanical advantage:
M= w/f = 1_f/1_w
DRAWING
First class lever example
The skull:
The fulcrum is at the Atlanto occipital joint
The load, the weight of the front portion of the head, is applied in front of the joint
The effort of the muscle is applied behind the joint at the back of the skull
Second class lever example
Bones of the middle ear
The fulcrum is the joint between the malleus and incus
The load is applied at the oval window and stapes
The effort is applied at the tympanum and malleus.
3rd class lever example
The jaw
The fulcrum is at the tenpormandibular joint.
The load is applied at the teeth
The effort of the muscles is applied on both sides of the jaw
3rd class lever example ||
The forearm when used for lifting
The fulcrum is at the elbow joint
The load is applied at the hand
The effort is applied at the radius
Action of the muscle effort
The vector of the force F developed by the muscle can be resolved by 2 components- along the bone F1 and normal to the bone Fn.
The longitudinal component F1 =F cos(alpha) the points at the joints press the bones without causing rotation.
The normal component Fn=Fsin(alpha) generates rotation of bone around fulcrum.
Action of muscle effort 2
Useful work for moving the load is performed only by the normal
Fn= Fsin(alpah)
The muscle performs more work when Fn is larger
Movement of the body
Muscles are the active parts of the musculoskeletal system.
Muscles contract and apply effort to skeletal bones causing them to move
This results in movement of parts of the body
Types of muscle contractions
Isotonic
The length of the muscle changes and the tension remains constant
LOAD MOVES
Isometric
The length of the muscle remains constant and then tension changes
LOAD DOES NOT MOVE
Work and power
Work A
The energy spent for displacing a body S by a constant force F
A=Fs
Power P
The amount of work performed per unit of time
P= da/dt = Fv
Dynamic work of muscles 1
Equation
The work performed at an isotonic contraction of the muscle is
Applied muscular force x change of the length of the muscle
Dynamic work of the muscles
The maximum force exerted by the muscle is proportional to the cross section of the muscle
The maximum work performed by one contraction of the muscle is proportional to the volume of the muscle.
Dynamic power
When walking the human body performs work for
- repeated lifting of the body
- acceleration and deceleration of limbs
Mass of body is 75kg
- speed 5Kmh = 60w power
- speed 7kmh = 200w power
Dynamic power 2
When jumping (brief effort)
- body mass 70kh
- centre of mass lifted by 1m
- thrust time is 0.2s
The power is 3.5kw
Statics( postural) work
When the body supports a weight the muscle get tired
The load doesn’t move and no useful work is performed
Tiredness means that muscles perform work- static work
Static work 2
The muscles perform small contractions followed by relaxations (isometric contractions)
This results in dynamic work being performed against gravity
Static work is essentially dynamic work
Equilibrium of the body
The center of mass of the body is above the ball and socket fulcrum (hip joint) unstable equilibrium
The body doesn’t fall because the supporting muscles perform work to sustain the posture of the body
