W29 - Rotations and Translations Flashcards
Define a global coordinate system - what is it used for?
Fixed coordinate system in the lab from where all positions are derived
Gives us a zero point
What calibration is needed for GCS?
L frame
Define a local coordinate system - what is it used for?
A reference system that is fixed within a body and moves with the body
Gives us the position of a rigid body (e.g. coordinates)
Where is the LCS usually placed on a rigid body? (one of two places)
Centre of Mass
Proximal joint centre
What is the difference between GCS ad LCS?
Global is stuck, local moves around
Define a rigid body:
Theoretical body that is not deformable, non moveable and has constant mass
What does a rigid body allow us to do?
Calculate movement more efficiently
What properties does a rigid body have?
Fixed inertial properties
What are the two categories that rigid bodies can fall into?
Translation (forwards/backwards or side-to-side)
Rotation (x, y, z - can move in circular path about axis of rotation
Define Degrees of Freedom:
The number of independent parameters that define the location of a point/body
What pieces of info do you need to describe a rigid body’s motion?
6
X, Y, Z location of CoM or proximal joint centre
3 angles that describe its orientation
For the right hand rule, which finger corresponds to which axis?
X = Thumb Y = Index finger Z = Middle finger
What is a matrices, and what are the two types?
Used to specify/represent geometrical translations (such as rotations) and coordinate changes
Similar to vectors
Translational and Rotational
Explain how translational matrices work:
Translation broken down into movement along X,Y,Z axes
Order of movement does not matter
E.g. Co-ordinate: (5,6,7) with matrix (2,3,7) -> New co-ordinates (7,9,14)
What is a problem with using translational matrices?
Means we don’t know if any rotation has occured
Explain how rotational matrices work:
Order of rotation does matter
Order = X, Y, Z for rows and columns
What are the results of rotating 3D around each axis?
Rot 3D around X axis = 2D rot in YZ plane
Rot 3D around Y axis = 2D rot in XZ plane
Rot 3D around Z axis = 2D rot in XY plane
What is a joint angle and how can you describe it?
Transformation between 2 coordinate systems
Rotational matrix
Why is a rotation matrix rarely used for reporting joint angles?
Because it doesn’t tell you anything on its own
What methods are used to determine relative orientation of 2 coordinate systems or joint angles?
Cardan/ Euler (like oiler)
Joint Coordinate System
Helical Axis
