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

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References