A simple method for calibrating force plates and force treadmills using an instrumented pole

Abstract

We propose a new method for calibrating force plates to reduce errors in center of pressure locations, forces, and moments. These errors may be caused by imperfect mounting of force plates to the ground or by installation of a treadmill atop a force plate, which may introduce distorting loads. The method, termed the Post-Installation Least-Squares (PILS) calibration, combines features of several previous methods into a simple procedure. It requires a motion capture system and an instrumented pole for applying reference loads. Reference loads may be manually applied to the force plate in arbitrary locations and directions. The instrumented pole measures applied load magnitudes through a single-axis load cell, and load directions through motion capture markers. Reference data and imperfect force plate signals are then combined to form a linear calibration matrix that simultaneously minimizes mean square errors in all forces and moments. We applied the procedure to standard laboratory force plates, as well as a custom-built, split-belt force treadmill. We also collected an independent set of verification data for testing. The proposed calibration procedure was found to reduce force errors by over 20%, and moment errors by over 60%. Center of pressure errors were also reduced by 63% for standard force plates and 91% for the force treadmill. The instrumented pole is advantageous because it allows for fast and arbitrary load application without needing a precise fixture for aligning loads. The linear calibration matrix is simpler than nonlinear correction equations and more compatible with standard data acquisition software, yet it yields error reductions comparable to more complex methods.

Figure 1

Equipment used to demonstrate Post-Installation Least Squares (PILS) calibration procedure. (A) Instrumented pole used for force plate calibration. The pole allows arbitrary directions and magnitudes of force to be manually applied to the force plate in arbitrary locations, using a motion capture system to record kinematics. The pole (Motion Lab Systems MTD-2) is modified to include an axial load cell, similar to [12]. Its ends are tapered so that only axial forces can be applied. A loading plate with a shallow chamfered hole is used to apply loads to the top; a similar, protective plate transmits those loads to the force plate below. The pole’s direction u⃗_p is determined from locations of motion tracking markers, and the axial force F_p is measured by the load cell. These quantities contribute to the reference ground reaction force F⃗_ref that is used for calibration. (B) Custom-built, split-belt, instrumented force treadmill (not to scale). Independent treadmills are mounted atop separate force plates, with a gap of 2 cm between the treadmill belts. The mounting of a force plate to the ground, or of a treadmill to the force plate, can introduce distorting loads that adversely affect the accuracy of the force plate. The PILS procedure is also demonstrated on a standard set of force plates mounted flush with ground (not shown).

Figure 2

Mean center of pressure (COP) locations for validation tests with (left) standard flush-mounted force plates and (right) the split-belt force treadmill. Plus symbols (+) mark reference locations determined through motion capture, squares (□) mark locations determined from the Standard Calibration using manufacturer-specified values, and circles (○) mark the corrected locations following PILS calibration.

Figure 3

Effect of PILS calibration on COP error (plotted as root-mean-square error) for both sets of force plates. Errors were reduced by 63% for the flush-mounted force plates, and 91% for the instrumented force treadmill, comparing PILS to the Standard Calibration.