By: Chris Dalton. 3-dimensional movement can be described by the use of 6 Degrees of Freedom ◦ 3...
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Transcript of By: Chris Dalton. 3-dimensional movement can be described by the use of 6 Degrees of Freedom ◦ 3...
Coordinate SystemsBy: 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
Key Ideas
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
Motion in 2-Dimensions
Coordinate systems are generally:◦ Cartesian◦ Orthogonal◦ Right-Handed
Purpose:◦ To quantitatively define the position of a
particular point or rigid body
Coordinate Systems
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
Definition:◦ Refers to axes that are perpendicular (at 90°) to
one another at the point of intersection
Orthogonal
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
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
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
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
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
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
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
Application of Joint Coordinate Systems to the Knee
Questions?
The End
Grood, E.S. & Suntay, W.J. (1983). A Joint Coordinate System for the Clinical Description of Three- Dimensional Motions: Application to the Knee. Journal of Biomechanical Engineering, 105. 136- 144. Retrieved from http://www.biomech.uottawa.ca/english/teaching/apa6905/lectures/2012/Grood%20and%20Suntay%201983.pdf
Karduna, A.R., McClure, P.W., & Michener, L.A. (2000). Scapular Kinematics: Effects of Altering the Euler Angle Sequence of Rotation. Journal of Biomechanics, 33. 1063-1068. doi. 10.1016/S0021-9290(00)00078-6
Mantovani, G. (2013, September). 3-D Kinematics. Lecture conducted from University of Ottawa, Ottawa,ON.
Pennestri, E., Cavacece, M., & Vita, L. (2005). Proceedings from IDETC’05: ASME International Design Engineering Technical Conference and Computers and Information in Engineering Conference. Long Beach, California.
Robertson, Gordon E. (2004). Introduction to Biomechanics for Human Motion Analysis: Second Edition. Waterloo: Waterloo Biomechanics
Roberston, G.E., Caldwell, G.E., Hamill, J., Kamen, G., & Whittlesey, S.N. (2004). Research Method in Biomechanics: Second Edition. Windsor: Human Kinetics.
Routh, Edward J. (1877). An Elementary Treatise on the Dynamics of a System of Rigid Bodies. London: MacMillan and Co.
Zalvaras, C.G., Vercillo, M.T., Jun, B.J., Otarodifard, K., Itamura, J.M., & Lee, T.Q. (2011). Biomechanical Evaluation of Parallel Versus Orthogonal Plate Fixation of Intra-Articular Distal Humerus Fractures. Journal of Shoulder and Elbow
Surgery, 20. 12-20. doi. 10.1016/j.jse.2010.08.005
References