Lecture 5 - Biomechanics Flashcards
How do motor systems create motion? What laws apply?
exert force; Newton’s and Euler’s laws of motion
Motor control depends on…
viscous and elastic properties of the body
What is mechanics?
the study of force and motion
Relate force with motion (what type of motion is it?)
F = ma (Newton’s 2nd Law) (translational motion)
Unit for force
Newtons
define 1 newton
1 newton = 1 kg m/s2
A force of 1 newton imparts to an object of mass 1 kg an acceleration of 1 m/s2
Newton’s 3rd Law describes…
How force propagate through linkages
Newton’s 3rd Law
Objects will exert equal and opposite forces on each other
Newton’s 3rd Law in terms of linkages
If bone A exerts a force F on bone B in the linkage, then bone B exerts a force -F on bone A
Law for rotational motion is discovered by…
Euler
Euler’s law is expressed in terms of…
Torque (~force) & inertia (~mass)
Define: inertia
resistance to rotary acceleration
The same object has different inertias depending on…
the point used on the object
In real life, inertia is a ___ and varies with ______
matrix;
the orientation of the rigid body
Euler’s Law
T = Ia
(torque = inertia x rotary acceleration)
What is rotary acceleration (α)?
rate of change of ω
How to find the direction of α vector?
Right hand rule: point thumb in direction of α and the direction of the vector is where the fingers curl
Formula for torque
T = M x F (moment arm cross product force)
Torque depends on…
forces’ application points and directions
How to find net torque?
For each Fi acting around the joint, find it’s moment arm Mi and compute Ti = Mi X Fi
Sum all the torque vectors (ΣTi)
Direct mechanics
computing motion from force
i.e., after finding net T, find rotary acceleration using α = T/I
Plant is subject to ____ and ___ forces
intrinsic, driving
driving forces
muscle forces ordered by the brain;
force from controller
intrinsic forces
viscous and elastic forces of the tendons and other tissues
Why do we need to know about intrinsic forces?
Newton’s Law tells us about total force influences (intrinsic + driving), but we are interested in only observing driving force
examples of viscous forces
friction, air resistance
viscous forces increase with…
velocity
what is terminal velocity for skydiver in spread position? In straight position?
spread = 200 km/h
straight = 300 km/h
A constant driving force acting against a viscous force yields…
a transient (lasting a short time) acceleration followed by a constant velocity
elastic forces depend on ____ rather than its ____
position of an object rather than its velocity
define: stiffness
ratio of change in force to change in length
example of elastic force
springs
A constant driving force acting on an elastic system brings it to…
an equilibrium position where the elastic force exactly balances the driving force
For an elastic system, the driving force determines…
(steady-state) position
Define: resonance
things have natural frequencies, and stimulating at that natural frequency produces a very strong response
