The FORCE_PLATFORM:CAL_MATRIX parameter is an array of floating-point values, supplied by the force platform manufacturer, that contain force platform calibration matrices.  This allows for greater accuracy in the calculation of forces, powers and moments from the recorded analog data as the full calibration matrices are now stored within the C3D file and are available to any application that reads the analog data from the C3D file.

This parameter is only applicable to TYPE-4 force platforms having six channel outputs.  A calibration matrix enables software applications to correct for cross talk between outputs of the force platform; software applications that use the full calibration matrix to correct for cross talk will typically provide more accurate results when compared to applications that only have access to the major diagonal component.  As a result, it is recommended that the CAL_MATRIX parameter be  always included with force data from TYPE-4 plates if possible – software applications may choose which correction method they wish to use when the CAL_MATRIX is present in a C3D file. 

Since the CAL_MATRIX parameter will be ignored, even if present, unless the force platform type is 4, its inclusion in a C3D file does not automatically imply that it must be applied to the stored force data.  Force data from TYPE-1 and TYPE-2 force plates is scaled using the ANALOG:SCALE factors as described in detail in the chapter entitled Calculating SCALE values for force plates.  When the CAL_MATRIX parameter is present for TYPE-2 and TYPE-4 plates, all software applications must reset the scaling data stored in the appropriate ANALOG:SCALE parameters to their “unscaled” values before applying the CAL_MATRIX parameter information.

Note that most force plate systems include some degree of variable amplification of the signals from the plate.  The amount of amplification applied to each force signal must be taken into account when applying the calibration matrix and is an important factor is the calculation of the correct ANALOG:SCALE value for each force plate channel.

If a calibration matrix is entered for a force platform, it should be used in addition to the individual channel scales.  The 6 x 6 calibration matrix for each force platform should be applied to the measured channel outputs to obtain the corrected channel outputs according to the matrix equation:

[CAL_MATRIX] Fmeasured = Fcorrected

where the F’s are 6-element column vectors.  Hence, the elements of the calibration matrix must be entered in column order, i.e. for the first force platform:

·      CAL_MATRIX(1,1,1) must contain the first element of the matrix.

·      CAL_MATRIX(6,1,1) the last element of the first column.

·      CAL_MATRIX(1,2,1) must contain the first element of the second column, etc.

Typically, the calibration matrix is supplied with units of N/V for the force channels and N•m/V for the moment channels.  If you are using distance units of millimeters in your reference coordinate system, then the last three rows of the calibration matrix must be multiplied by 1000 before being entered into CAL_MATRIX as shown below:

Note that, unlike Type-2 force platforms, the analog channels associated with Type-4 force platforms are not pre-scaled – see the earlier discussions for full details on calculating the analog scale values for each force platform type.  Sample data files and spreadsheets are available from http://www.c3d.org that implement the full CAL_MATRIX parameter calculations.

Unfortunately, at the time of writing, this parameter is relatively uncommon in C3D files.  Its use is recommended for all future 6-channel force platforms as it provides additional information that improves the quality of the force data and removes the need to calculate individual ANALOG:SCALE values for each force platform channel.