BBS1004 Brain, behavior and movement summary of all lectures

1. Basic biomechanics
Units
Base units
 kg (mass)
 m (length)
 s (time)
 A (electric current)
 Derived units
 N (force or weight; kg.m.s-2)
 J (energy or work; N.m or kg.m2.s-2)
 W (power; J/s or kg.m2.s-3)
 Hz (frequency; s-1)
 Radian (angle; - or m.m-1) NB 1 rad=57.3o
 V (voltage; kg.m2.s-3.A-1)

Translation
Position, velocity and acceleration  vector
Origin  x=0 , y=0
Direction (angle) and magnitude  (a, √(x2+y2))
We assume only 2 dimensions, even though we know that there are 3.
SOS-CAS-TOA (SOH-CAH-TOA) is used to determine side or angle of triangle
 Sine = Opposite ÷ Hypotenuse (=schuine)
 Cosine = Adjacent ÷ Hypotenuse(=schuine)
 Tangent = Opposite ÷ Adjacent
Fy = Fperpendicular sin (a)




Velocity = Δ position / time
Speeds is only a number  speed ≠ velocity  speed = |velocity|
Acceleration = Δvelocity / Δtime

Newton's Laws
2nd: ΣF=m.a F=m.a
3rd: Faction= -Freaction




* e.g. 100m sprint : velocity is low at the end, acceleration is low at the end as well  deceleration

,Rotation
– Angle, angular velocity, angular acceleration
– Torque (Moment)  most important in joint movement

Joint angle  dependent on convention
Angular velocity = Δjoint angle / Δtime joint angle / Δjoint angle / Δtime time
Angular acceleration = Δjoint angle / Δtime angular velocity / Δjoint angle / Δtime time

Torque (=Moment)
e.g. force on the door
 Force times distance to the axis
M = Fm x d [N.m]
Moment arm (=lever arm)

Sign :
– counterclockwise is positive (elbow flexion)
– clockwise is negative (elbow extension)

Axis of rotation
In 3D there are 3 axes of rotation  3 torques
 Flexion, extension and hyperextension
 Abduction and adduction
 External rotation and internal rotation
 body movement are caused by joint rotation
E.g. Hand movement by shoulder, elbow, and wrist rotation

Static torque  does not produce an angular acceleration
Dynamic torque  does produce an angular acceleration
Angle of peak torque = the joint angle where we are the strongest.




Energy

,  Etotal = Ep + Ek
 Potential energy : Ep = m.g.h  height
 Kinetic energy : Ek = ½.m.v2  velocity
 Elastic energy
Ek is highest when the amplitude is zero  in equilibrium position
Ep is highest when the amplitude is maximal

Work, “muscle force times change in length”
W=∫Fds ≈ FxΔjoint angle / Δtime s=F.s.cos(α))
 Work = force x displacement
Positive work: direction of movement is same as the direction of exerted force (isotonic concentric)
 Positive work results in an increase in kinetic or potential energy or both.
Negative work: direction of movement is in opposite direction of exerted force (isotonic eccentric)

Muscle can be used as motor AND as brake
Motor
 Performing (positive) work increases the energy in the system (body)
 e.g. increase in velocity (kinetic energy) or height (potential energy)
Brake
 Performing negative work decreases the energy in the system (body)
 e.g. decrease in velocity (kinetic energy) or height (potential energy)

Power
Power equals work per unit time  P = W / Δjoint angle / Δtime t




• Muscle length sinusoidally variated
• Muscle activated electrically
• Muscle force is measured
• Red is work between start and max force
• Green + blue area = work generated during shortening
• Blue area = work dissipated during lengthening
 negative
• Green area = net work generated
 Muscle work equals Muscle force times Muscle change in length
(work loop) = work done




Translation (muscle) and rotation (joint)  Mechanical work in muscles during contraction.

, Isometric contraction
 No net length change of muscle
 Velocity is zero
Concentric contraction
 Bicep muscle shortens, elbow flexes
 Positive velocity / power
Eccentric conctraction
 Biceps muscle lengthens, elbow extends
 Negative velocity / power

Isometric contraction: no mechanical work, muscle length remains unchanged.
Isokinetic: muscle length remains unchanged, produce movements with constant speed