By: Chris Dalton

 3-dimensional movement can be described by the use of 6 Degrees of Freedom ◦ 3 translational Degrees of Freedom ◦ 3 rotational Degrees of Freedom  What are Degrees of Freedom? ◦ “The number of independent variables that must be specified to define completely the condition of the system”  Purpose of a coordinate system ◦ To quantitatively define the position of a particular point

 In planar motion ◦ There are two ways to report 2-D motion  Cartesian coordinates  Polar coordinates  In space ◦ A way to determine the position of a body in space

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

 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

 Definition: ◦ Refers to axes that are perpendicular (at 90°) to one another at the point of intersection

 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)

 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.

 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)

 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

 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

 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

 The knee joint focuses on tibial and femoral motion  First, need to establish your Cartesian coordinate system  Second, want to determine a motion of interest for each bone  Third, want to determine the perpendicular reference direction  Last, complete the system using the right-handed rule

Questions?

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