Transform from FCS to LCS

Transforming the force signals from the Force Platform Coordinate System to the Laboratory Coordinate System

C3D Parameter FORCE_PLATFORM:CORNERS

The force platform corners are numbered from 1 to 4. The values are specified in the Laboratory Coordinate System in units consistent with the POINT data. The order is specified by the quadrant numbers in the force platform coordinate system. The order is (+x,+y), (-x, +y), (-x, -y), ( +x, -y).

Computing the Transformation

Visual3D calculates the transformation matrix from the force platform coordinate system to the laboratory coordinate system using the force platform corners. This transformation matrix is then used to transform the force vector from the force platform coordinate system (in which it was collected) into the laboratory coordinate system where it is used for the analysis.

The Force Platform corners can be modified using the Modify Force Platform Parameters selection under the Visual3D File Menu Transforming the Ground Reaction Force into the Laboratory Coordinate System

The following pseudo-code describes the algorithm for computing the transformation from the Force Platform Coordinate System (FPCS) to the Laboratory Coordinate System (LCS)

x_vector = unit_vector(corner4 - corner3)

y_vector = unit_vector(corner2 - corner3)

z_vector = cross_product(x_vector , y_vector)

y_vector = cross_product(z_vector , x_vector)

Rotation Matrix - FPCS to LCS

fpcs_to_lcs column1= x_vector

fpcs_to_lcs column2= y_vector

fpcs_to_lcs column3= z_vector

location of top center of force platform in LCS

platform_top_center_lcs= average(corner1, corner2, corner3, corner4)

vector from plate origin to top center relative to lab

Rotate_to_Lab(forceplatform_origin)

vector from LCS origin to platform origin

platform_origin_lcs= platform_top_center_lcs- vector from plate origin to top center