Three dimensional kinematics

Question 1

what is 3d calibration establishing?

Answer 1

collects information to establish DLT parameters

Question 2

DLT parameters

Answer 2

Direct linear transformation
-where cameras are
-in which directions do cameras point

Question 3

3D analysis: Step 1

Answer 3

obtain series of vectors which describe object and image coordinates in different reference systems

Question 4

3D analysis: Step 2

Answer 4

Make multiple vector substitutions and transformations

Question 5

3D analysis: Step 3

Answer 5

u= (Ax+By+Cz+D)/(Ex+Fy+Gz+1)
v= (Hx+Iy+Jz+K)/(Ex+Fy+Gz+1)

Question 6

3D analysis: Step 4

Answer 6

Calibration Experiment

Question 7

3D analysis: Step 5

Answer 7

Final Step
2 cameras to record points at same moment in time (time-synchronus)

Question 8

Issues with 3D calibration

Answer 8

• ## Redundancy: number of control points vs number of cameras

Question 9

When is Global Coordinate System determined?

Answer 9

Determined during calibration of motion analysis system

Question 10

How is Dynamic Calibration accomplished, when is it processed?

Answer 10

Wand dance
Processed first

Question 11

what does Static Calibration accomplish?

Answer 11

establishes constant for variable (0,0,0)

Question 12

Residuals

Answer 12

numbers that indicate the quality of calibration

Question 13

Linearization

Answer 13

the process of correcting for lens distortion

Question 14

bundle adjustment

Answer 14

an algorithm that performs the linearization process by optimizing the camera parameters to give the best reprojection error

Question 15

Dynamic calibration algorithmic assumptions

Answer 15

-known distance to orgins
-no extraneous markers
-2d marker images seen by different cameras originate from the same 3d position

Question 16

Wand dance tips

Answer 16

-avoid breaking cameras view with body
-position body so wand can be seen by as many cameras as possible
-move around the entire volume
-collect ~1000 or more samples
*rotate and move wand up and down and back and fourth

Question 17

Residuals limit

Answer 17

<.18

Question 18

What does tripleton establish?

Answer 18

establishes direction of first x axis

Question 19

What does singleton establish?

Answer 19

-establishes position of origin
-combines with first axis to establish second
resultatnt cross product is third

Question 20

Common causes of failed calibrations

Answer 20

Bad wand dance

Poor camera position

Background static noise

Question 21

Local Coordinate System Guidelines

Answer 21

• 3 non colinear markers on segment (GTC, ASIS, PSIS)

Question 22

LCS determination (j’)

Answer 22

Sets AP axis
denominator is magnitude of difference

Question 23

LCS determination (i’)

Answer 23

Sets ML axis

Question 24

LCS Determination (k’)

Answer 24

sets longitudinal axis

Question 25

What does this image represent?

Answer 25

Static 3D coordinates of transformation matrix

Question 26

what does this formula represent?

Answer 26

rotational matrix

Question 27

Types of transformations

Answer 27

1. linear transformations 2. rotational transformations *both have a rigid body assumption

Question 28

What do Linear Transformations assume?

Answer 28

no rotation

Question 29

rotational transformations

Answer 29

assumes no translations

Question 30

What do A and B represent

Answer 30

A. rotational transformation unit vector for proximal segment B. rotational transformation unit vector for distal segment

Question 31

Methods for determining joint angles (which is primarily used in Biomechanics?)

Answer 31

1. Cardan*/Euler 2 Joint coordinate system 3. Helical Axes

Question 32

Cardan/Euler angles

Answer 32

both provide methods of describing the orientation of rigid body segments in space. Biomechanics uses Cardan

Question 33

Cardan/Euler angle sequencing

Answer 33

1. About an axis in LCS' (x'y'z') 2. About a floating axis (changes according to orientation of 1st and 3rd axis) 3. about an axis in LCS'' (x'',y'',z'')

Question 34

6 of 12 sequences have terminal axes that are the same as the first rotation axis

Answer 34

Euler Angles

Question 35

6 of 12 sequences have terminal axes that are different from the first rotation axes

Answer 35

Cardan Angles (actually describe what happend during movement)

Question 36

Answer 36

Cardan sequence of rotation xyz

Question 37

Cardan sequence: Alpha Beta Gamma

Answer 37

Alpha: Flexion/extension Beta: add/abduction Gamma: internal/external rotation

Question 38

Answer 38

cardan beta

Question 39

Answer 39

cardan alpha

Question 40

Answer 40

cardan gamma

Question 41

What does the wand dance do?

Answer 41

determines camera and lens variables, sets x,y,z for all cameras

Question 42

What does static calibration do?

Answer 42

-determines origin (absolute reference point only -depends on successful dynamic calibration

Question 43

What do linear transformations represent?

Answer 43

represent P in LCS

Question 44

Where is the singleton origin specified?

Answer 44

CRO file

Question 45

When is static calibration processed?

Answer 45

last

Question 46

What does calibration of the GCS require?

Answer 46

1. Geometrical structure with at least 6 points 2. Dynamic or static calibration