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Joint Coordinate System.  Coordinate systems are generally: Cartesian Orthogonal Right-Handed  Purpose: To quantitatively define the position of a particular.

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Presentation on theme: "Joint Coordinate System.  Coordinate systems are generally: Cartesian Orthogonal Right-Handed  Purpose: To quantitatively define the position of a particular."— Presentation transcript:

1 Joint Coordinate System

2  Coordinate systems are generally: Cartesian Orthogonal Right-Handed  Purpose: To quantitatively define the position of a particular point or rigid body Coordinate Systems

3  Purpose: used to establish a Frame of Reference  Generally, this system is defined by 2 things: An origin: 2-D coordinates (0,0) or 3-D location in space (0,0,0) A set of 2 or 3 mutually perpendicular lines with a common intersection point  Example of coordinates: 2-D: (3,4) – along the x and y axes 3-D: (3,2,5) – along all 3 axes Cartesian Coordinate Systems

4  Definition: Refers to axes that are perpendicular (at 90°) to one another at the point of intersection Orthogonal

5  Coordinate systems tend to follow the right-hand rule This rule creates an orientation for a coordinate system  Thumb, index finger, and middle finger X-axis = principal horizontal direction (thumb) Y-axis = orthogonal to x-axis (index) Z-axis = right orthogonal to the xy plane (middle) Right-Handed Rule

6  A reference system for an entire system. When labelling the axes of the system, upper case (X, Y, Z) may be useful in a GCS Example – a landmark from a joint in the body (lateral condyle of the femur for the knee joint)  Within a global coordinate system, the origin is of utmost importance  Using a global coordinate system, the relative orientation and position of a rigid body can be defined. Not only a single point. Global Coordinate Systems

7  A reference system within the larger reference system (i.e. LCS is within the GCS)  This system holds its own origin and axes, which are attached to the body in question  Additional information: Must define a specific point on or within the body Must define the orientation to the global system  Origin and orientation= secondary frame of reference (or LCS) Local Coordinate Systems

8  A reference system for joints of the body in relation to larger GCS(the whole body) and to other body segments (LCS)  Purpose To be able to define the relative position between 2 bodies. Relative position change = description of motion  Orientation  Origin Could be the centre of mass of a body segment (ex. The thigh) Could be the distal and proximal ends of bones Joint Coordinate Systems

9 Joint Angles  Methods Used Within Biomechanics »Euler/Cardan Angles »Joint Coordinate System »Helical Axes >Each method has specific advantages and disadvantages and the best method to use for a project depends on numerous factors Human Movement Biomechanics Lab

10 Euler’s Angles  Leonhard Euler (1707-1783) http://www-history.mcs.st-andrews.ac.uk/PictDisplay/Euler.html 3D finite rotations are non-commutative –They must be performed in specific ORDER –Ex: book on desk The order of rotations is precisely described in biomechanics depending on the application –12 possible sequences of rotations First rotation defined relative to a GLOBAL axis Third rotation defined about an axis in rotating body (LOCAL) Second rotation defined about a floating axis in the second body Ex: (X global, Y local, X local ) When the terminal rotation is the same it is known as an EULER ROTATIONS (6) When the terminal rotations are NOT the same these are considered CARDAN ROTATIONS (6) http://www.strubi.ox.ac.uk/strubi/fuller/docs/spider2003/euler.gif Human Movement Biomechanics Lab

11  Purpose: A method used to describe 3-dimensional motion of a joint  `Represent three sequential rotations about anatomical axes`  Important to note about Euler angles is that they are dependent upon sequence of rotation  Classified into two or three axes Euler Angles

12  Sequence dependency differs depending on which system is being looked at in order to describe 3-dimensional rotation about axes  Standard Euler Angles: Dependent upon the order in which rotations occur Classified into rotations about 2 or 3 axes  Euler Angle in a Joint Coordinate Systems: Independent upon the order in which rotations occur All angles are due to rotations about all 3 axes Standard Euler Angles and Euler Angle of JCS

13 Common Cardan Sequence in biomechanics studies  Xyz sequence »Rotation about medially-directed X axis (Global CS) »Rotation about anteriorly-directed y axis (Local CS) »Rotation about vertical axis (Local CS) »See Fig 2.12 in text  This sequence chosen to represent joint angles and recommended within biomechanics (Cole et al., 1993) »Rotations occur about: flexion-extension axis, ab/adduction axis, and axial rotation  Major Disadvantage: Gimbal Lock  when middle rotation equals π/2 it results in mathematical singularity and causes computational problems Human Movement Biomechanics Lab

14 Cardan Sequence Application  Movement of a joint is defined as the motion of the distal (far) segment to the proximal segment (near) >Ex (knee): »thigh (proximal segment) »Shank (distal segment) »Find T TS »Decompose rotation matrix into the three Cardan angles of flexion-extension, ab-adduction, axial rotation Human Movement Biomechanics Lab

15 Joint Coordinate System (JCS)  Grood & Suntay (1983) >Describe the motion of the knee joint  Purpose: to insure that all three rotations had functional meaning for the knee  How is it different than an Euler/Cardan rotation? »NOT an orthogonal system »Two segment-fixed axes and a FLOATING axis  Essentially we must define the anatomical axes of interest from bony markers, the clinical axes of rotation, and the origin of the joint coordinate system for a complete analysis of motion Human Movement Biomechanics Lab

16 Helical Angles  Woltring (1985, 1991)  Another method to describe the orientation (both rotation & translation) between two reference systems  Any two reference systems can be “ matched ” up through a single rotation and a translation about a single axi >This axis does not necessarily have to line up with one of the axis of the local CS  Good for joints that are hinge-like >i.e. talocrural joint Human Movement Biomechanics Lab


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