Lecture 2 - Degrees of Freedom Flashcards

(70 cards)

1
Q

Define: DOF

A

variable has N degrees of freedom of we need N numbers to distinguish all its possible values

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2
Q

DOF is a measure of ____

A

a system’s complexity

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3
Q

another word for DOF =

A

N-dimensional

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4
Q

define: point particle

A

object with a location but no magnitude (size is negligible)

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5
Q

Point particle has ___ DOF

A

3

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6
Q

define: constraint

A

condition which a system satisfied (DOF may be reduced by satisfying this condition)

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7
Q

What is the highest DOF a rigid system can have?

A

6

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8
Q

define: rigid body

A

A set of 3 or more non-collinear points, where the distances between all points are fixed

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9
Q

list 3 biological examples of rigid bodies (under normal circumstances)

A
  1. Eyes
  2. Skull
  3. Bones
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10
Q

The position of any rigid body can be described with ___ numbers.

  • How many used to describe ___?
  • How many used to describe ___?
A
  1. 6
  2. 3 used to describe location
  3. 3 used to describe orientation
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11
Q

Position of a rigid body has ___ components. What are they?

A
  1. 2
  2. location & orientation
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12
Q

Location has ___ DOF. Orientation has ___ DOF.

A

3, 3

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13
Q

Define: linkage

A

chain of rigid bodies

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14
Q

Linkages are made up of… (define each)

A
  1. Links: rigid bodies making up the linkages
  2. Joints: connections between the links
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15
Q

Human skeleton has ___ kind of joints. What kind of joints are they?

A
  1. 6
  2. Rotary
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16
Q

What are the 6 types of rotary joints in the body? List their DOF.

A
  1. Plane joints (0)
  2. Hinge joints (1)
  3. Pivot joints (1)
  4. Saddle joints (2)
  5. Ellipsoidal joints (2)
  6. Ball and socket joints (3 DOF)
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17
Q

Plane joints

A
  • Have very little motion
  • Adjacent links meet along flat surfaces
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18
Q

Examples of plane joints

A
  • palm of hand
  • palm of foot
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19
Q

Hinge joints

A
  • 1 DOF
  • swing about single axis relative to one another
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20
Q

example of hinge joints

A
  • humero-ulnar joint of elbow
  • 2 distal joints in each finger
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21
Q

Pivot joints

A
  • 1 DOF
  • link rotates about its own long axis
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22
Q

example of pivot joint

A
  • radio-ulnar joint of the elbow
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23
Q

what happens at the radio-ulnar joint?

A

radius turns in a tissue ring attached to the ulna

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24
Q

where is the radius?

A

forearm bone on thumb side

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25
Saddle joints
* Allow for extension/flexion & adduction/abduction * Concave & convex directions match up * 2 DOF
26
Example of saddle joint
joint between wrist and thumb (on the bottom, closer to wrist)
27
Ellipsoidal joints
* 2 DOF * Articular surfaces are ellipsoids (different from ball and socket because not spherical) * 1 concaves in, one concaves out
28
Example of ellipsoidal joints
* wrist * metacarpophalangeal joints (base of each finger)
29
Ball and socket joints
* 3 DOF * up-down movement = pitch * side-side movement = yaw * turning movement = roll
30
Examples of ball and socket joints
* shoulder * hip * eyeball in socket
31
How to calculate DOF of a linkage?
Σ DOF of it's joints
32
When is a system redundant?
when it has more DOF than it needs for its job
33
What is the purpose of redundancy?
lets you do things in more than 1 way * obstacle avoidance * keep joints near center of range * provide alternative ways to do things
34
How many DOF is is vision (gaze)?
2 (we see things in a sphere kind of way)
35
How many DOF does VOR need?
3
36
Why is the macula only 5 degrees across?
* If it covered the entire retina, visual input increases by 100x * visual imput is 1/5 of all sensory input * 20x increase in sensory input * overwhelm brain * optic nerve needs to be huge to send info to brain * huge blind spot
37
How do we compensate for small macula?
move our eyes very quickly
38
Define: saccades
* rapid eye movement that shift the gaze point * direct fovea at objects * quickest eye movements
39
weakness of saccades
we can't see well during saccades
40
macula is ___ degrees across? Fovea is ___ degrees across?
5, 2
41
define: fovea
small, central, high-acuity region of the retina
42
Speed of saccades? Duration?
500 degrees/second; 20 ms
43
What kind of axis can be picked for determining eye movement between two points?
any axis that lines in the plane bisecting the angle between the initial and final gaze directions
44
Size of eye rotation depends on...
axis picked for eye movement
45
Which axis gives the smallest eye rotation?
axis that is orthogonal (right angles) to both initial and final gaze directions
46
Shortest path strategy
* Make smallest saccade that brings gaze to target * Orthogonal axis * eyeball rotation small as possible
47
Rationale for shortest-path strategy
save energy & time
48
What law do we follow to pick axis for gaze direction?
Donders' Law
49
Donders' Law
for any 1 gaze direction, the brain always chooses the same eye position
50
Rationale for Donders' law
for any 1 gaze direction there is presumably 1 eye position that is in some sense best, and we should therefore only use that position
51
Can we use both Donders' law and the shortest-path strategy?
No, imcompatible
52
When does Donders' law hold? When does it not hold?
Holds when: * fixations * saccades with head fixed (not moving) Not holds when: * head moves * sleep
53
Besides eye movement, what else obeys Donders' law?
Head & arm control (hand adopts same 3D orientation for any 1 direction when straight arm pointing)
54
Difference between Donders' law in gaze control and other areas?
In the arms & head, Donders' law can be broken voluntarily
55
Define: synergy
laws that steers a system so that its behaviour is lower dimentsional than the max its plant would permit (e.g. Donders' law)
56
Donders' law ____ redundant dimension. What does it do exactly?
* eliminates * 3D -\> 2D
57
Why do we want synergies?
it simplifies things, so there is less for the brain to worry about
58
Donders' law does not specify...
which positions are used, just that the SAME position is used
59
Which law specifies which position is used when looking at a particular direction (sub of Donders' Law)
Listing's law
60
Listing's Law
* there is a special eye position called primary position * there is head-fixed plane called Listing's plane * plane is orthoganol to gaze direction in primary position * eye will only rotate in positions that can be reacked from primary position by some axis on the Listing's plane
61
What DOESN'T Listing's law say?
It doesn't say that you ALWAYS move tho these positions by a single fixed-axis rotation from primary, but you COULD
62
When is Listing's Law broken?
* head moves * sleep
63
When does Listing's law hold?
* fixation * saccades with head fixed
64
What area of the brain causes saccades that obey Listing's law?
stimulating the superior colliculus (at the midbrain)
65
What area of the brain causes saccades that doesn't obey Listing's law?
stimulating short-lead burst neurons in the brainstem
66
Where isthe control system for Listing's law?
between the midbrain (superior colliculus) and brainstem (short-lead burst neurons)
67
What is 1 example where you obey Donders' law but not Listing's?
Fick Pattern: * pan horizontally by pivoting arbout vertical axis * pan veritcally about horizontal axis
68
motions intermediate between Fick and Listings are seen in...
* straight arm pointing * head motion during spontaneous eye-head gaze shifts
69
Purpose of Listing's law
1. simplify visual processing (movement vs. still) (orientation of image on retina will always be the same because image will fall on same set of retinal receptors) 2. motor efficiency (saccades move along shortest path from primary position)
70
Proof that Listing's law is important
animals use it (e.g. chameleons)