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PSL304 > Lecture 2 - Degrees of Freedom > Flashcards

Lecture 2 - Degrees of Freedom Flashcards

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
Q

Saddle joints

A
  • Allow for extension/flexion & adduction/abduction
  • Concave & convex directions match up
  • 2 DOF
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26
Q

Example of saddle joint

A

joint between wrist and thumb (on the bottom, closer to wrist)

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27
Q

Ellipsoidal joints

A
  • 2 DOF
  • Articular surfaces are ellipsoids (different from ball and socket because not spherical)
  • 1 concaves in, one concaves out
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28
Q

Example of ellipsoidal joints

A
  • wrist
  • metacarpophalangeal joints (base of each finger)
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29
Q

Ball and socket joints

A
  • 3 DOF
  • up-down movement = pitch
  • side-side movement = yaw
  • turning movement = roll
30
Q

Examples of ball and socket joints

A
  • shoulder
  • hip
  • eyeball in socket
31
Q

How to calculate DOF of a linkage?

A

Σ DOF of it’s joints

32
Q

When is a system redundant?

A

when it has more DOF than it needs for its job

33
Q

What is the purpose of redundancy?

A

lets you do things in more than 1 way

  • obstacle avoidance
  • keep joints near center of range
  • provide alternative ways to do things
34
Q

How many DOF is is vision (gaze)?

A

2 (we see things in a sphere kind of way)

35
Q

How many DOF does VOR need?

A

3

36
Q

Why is the macula only 5 degrees across?

A
  • 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
Q

How do we compensate for small macula?

A

move our eyes very quickly

38
Q

Define: saccades

A
  • rapid eye movement that shift the gaze point
  • direct fovea at objects
  • quickest eye movements
39
Q

weakness of saccades

A

we can’t see well during saccades

40
Q

macula is ___ degrees across? Fovea is ___ degrees across?

A

5, 2

41
Q

define: fovea

A

small, central, high-acuity region of the retina

42
Q

Speed of saccades? Duration?

A

500 degrees/second; 20 ms

43
Q

What kind of axis can be picked for determining eye movement between two points?

A

any axis that lines in the plane bisecting the angle between the initial and final gaze directions

44
Q

Size of eye rotation depends on…

A

axis picked for eye movement

45
Q

Which axis gives the smallest eye rotation?

A

axis that is orthogonal (right angles) to both initial and final gaze directions

46
Q

Shortest path strategy

A
  • Make smallest saccade that brings gaze to target
  • Orthogonal axis
  • eyeball rotation small as possible
47
Q

Rationale for shortest-path strategy

A

save energy & time

48
Q

What law do we follow to pick axis for gaze direction?

A

Donders’ Law

49
Q

Donders’ Law

A

for any 1 gaze direction, the brain always chooses the same eye position

50
Q

Rationale for Donders’ law

A

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
Q

Can we use both Donders’ law and the shortest-path strategy?

A

No, imcompatible

52
Q

When does Donders’ law hold? When does it not hold?

A

Holds when:

  • fixations
  • saccades with head fixed (not moving)

Not holds when:

  • head moves
  • sleep
53
Q

Besides eye movement, what else obeys Donders’ law?

A

Head & arm control (hand adopts same 3D orientation for any 1 direction when straight arm pointing)

54
Q

Difference between Donders’ law in gaze control and other areas?

A

In the arms & head, Donders’ law can be broken voluntarily

55
Q

Define: synergy

A

laws that steers a system so that its behaviour is lower dimentsional than the max its plant would permit (e.g. Donders’ law)

56
Q

Donders’ law ____ redundant dimension. What does it do exactly?

A
  • eliminates
  • 3D -> 2D
57
Q

Why do we want synergies?

A

it simplifies things, so there is less for the brain to worry about

58
Q

Donders’ law does not specify…

A

which positions are used, just that the SAME position is used

59
Q

Which law specifies which position is used when looking at a particular direction (sub of Donders’ Law)

A

Listing’s law

60
Q

Listing’s Law

A
  • 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
Q

What DOESN’T Listing’s law say?

A

It doesn’t say that you ALWAYS move tho these positions by a single fixed-axis rotation from primary, but you COULD

62
Q

When is Listing’s Law broken?

A
  • head moves
  • sleep
63
Q

When does Listing’s law hold?

A
  • fixation
  • saccades with head fixed
64
Q

What area of the brain causes saccades that obey Listing’s law?

A

stimulating the superior colliculus (at the midbrain)

65
Q

What area of the brain causes saccades that doesn’t obey Listing’s law?

A

stimulating short-lead burst neurons in the brainstem

66
Q

Where isthe control system for Listing’s law?

A

between the midbrain (superior colliculus) and brainstem (short-lead burst neurons)

67
Q

What is 1 example where you obey Donders’ law but not Listing’s?

A

Fick Pattern:

  • pan horizontally by pivoting arbout vertical axis
  • pan veritcally about horizontal axis
68
Q

motions intermediate between Fick and Listings are seen in…

A
  • straight arm pointing
  • head motion during spontaneous eye-head gaze shifts
69
Q

Purpose of Listing’s law

A
  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
Q

Proof that Listing’s law is important

A

animals use it (e.g. chameleons)

PSL304 (10 decks)

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