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By: Chris Dalton

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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

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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

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

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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

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

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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)

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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.

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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)

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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

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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

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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

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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

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Questions?

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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 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

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