Week 2 Flashcards
Position
• Definition
• Measurement
Displacement
-Definition
• Measurement
• Terminology and application
POSITION OF A POINT IN SPACE
• Mechanics analyses the movement of objects.
• Step 1 - Determine and define the position of these objects.
• Position referred to from a point of reference
• Starting point, reference frame, grid
• Definition specifies how to get from the reference point to the point that we are tracking.
• In 3D, we need three pieces of information (coordinates) to know exactly how to travel from the reference point to the point being tracked.
Relative positions
POSITION IN THE CARTESIAN COORDINATE SYSTEM
• Origin of the coordinate system is the reference point.
• To get from the origin to the point being tracked, move specific distances along each of the axes. These distances are referred to as (x,y, and z) coordinates of the point being tracked.
POSITION VECTOR(r->)
• In mechanics, position is usually defined via the “position vector”. This is the vector that has its tail in the referent point and its head in the point being tracked.
Note that:
The components of the position vector are the coordinates of the point being tracked.
The magnitude of the position vector is the distance between the referent point and the point being tracked .
Distance of P from the referent point
->
r = x2p+y2p+z2p
TRAJECTORY
The collection of successive positions of a moving point is called trajectory.
•It can also be said that the trajectory is a line drawn by the head of the position vector as the point moves.
POSITION OF A POINT IN SPACE VIA THE CARTESIAN COORDINATE SYSTEM
Y= mediallateral
X- forwards backwards
Z=verticales
POSITION TRACKING FROM 2D VIDEO CLIPS
• Simple position tracking methods can be used if the movement occurs in a single plane.
• Position is determined by relating image pixels to real-life distances.
ERRORS IN 2D ANALYSIS
• Parallax Error – apparent change in position from different viewpoints
—Defined by distance from optical axis of camera
—Minimised by increasing distance to keep motion
close to optical axis
• Perspective Error – apparent change in length due to changing distance from camera
—Caused by out of plane motion
— Minimised by perpendicular placement of camera
relative to plane of motion (also benefits from increased distance)
• Reference/scaling object required has to be in same plane of motion
• Low frame rates (how many pictures per second)may miss key timepoints
• Digitising error from low zoom or blurred image (slow shutter speed)(how long the shutter is open)
3D POSITION TRACKING: INFRA-RED CAMERA SYSTEMS
• An array of infra-red cameras detecting and tracking positions of reflective markers
•The synchronised output from the cameras is fed into a computer for processing. At least two cameras have to detect a marker to determine 3D coordinates
WHAT DO WE MEASURE FROM COORDINATE DATA?
• Relative positions of key landmarks (joints, anatomical features, objects, centre of mass)
• Changes in positions of key landmarks over time
• Orientations of body segments/objects from relative
positions of points on the segment/object
• Angles between body segments from relative positions of points on the segment/object
Linear Kinematics
• The description of linear motion through time, without consideration of the cause of the motion
• Distance and Displacement
• Distance (l) = The length of a path taken by a body
• Units = m (km, cm, mm)
DISPLACEMENT
Displacement (d) = The change in position of a body during motion (distance between start and finish positions)
= Final position – Initial position
(SIZE AND DIRECTION)
Units = m (km, cm, mm)
Angular displacement
Final joint position - initial joint position
The question defines the variable
» Suitability of measurement
• Instantaneous
• Average
• Phased
CALCULATION OF DISPLACEMENT
Calculation of Magnitude:
Resultant displacement (dR)
Use Pythagorus’ Theorem H2 =A2 + B2
=
= =
• Calculation of Direction: Use Trigonometry Angle to horizontal (θ)
