Force plates are a powerful tool for examining the kinetic characteristics of an athletes movement. The plates offer a large variety of information about the external forces involved, but have very specific characteristics that define the potential quality of collected data. Through proper understanding of these qualities, and sound use of calibration, filtering, and sampling procedures, the user can ensure that the error disguising the signal of interest is minimized. Thus, the collected data is at its highest possible quality, and inference about the athlete in question is strongest. This paper deals with the aforementioned topics related to force plate design and use, including a section describing an example laboratory set-up.
Keywords: force plate, filtering, sampling, data collection, kinetic
Force is the entity that results in movement- it can be understood as a push, or pull, or simply, a tendency to distort a material. Measurement of force can allow a coach or sport scientist to quantitatively understand an athlete’s execution of a skill, or to assess an athlete’s physical progress. For example, assessment of the external forces applied to the ground by an athlete in a vertical jump provide a very good picture of the explosive abilities of an athlete, as well a very good indicator of the progress of those abilities if measured at multiple time points in a training program.
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Force plates and other force measurement devices are widely used to assess the external forces generated by athletes. Force plates in particular measure external ground reaction forces in up to three planes -vertical, anterior-posterior, and medial lateral. This data provides a picture of the interaction within an athlete-ground system, something extremely difficult to do without a force plate. It is important to distinguish between kinetic and kinematic analysis. Kinematics is related to movement, what is visually observable, e.g. positions velocities and directions, while kinetics refers to what causes the movement to occur (i.e. torques and forces), and is not directly observable. Force plates allow one to see the kinetic characteristics of a skill, and thus the forces that cause the precise execution of that skill.
Force Plate Design and Use
Force plates measure external forces based on the principles of Newton’s third law- that an object exerting a force on another object has a simultaneous force exerted upon it that is equal in magnitude and opposite in direction to the original force exerted. Thus, the force plate measures ground reaction force (GRF). GRF is the force the ground exerts as a reaction (equal, opposite, and simultaneous) to the forces applied to the ground or other object by the athlete’s body (see Figure 1). This principle allows the researcher to determine the forces exerted by an athlete while in contact with the force plate. In a vertical jump for example, the athlete’s body mass and propulsion forces from the jump exert a push on the plate, causing a tendency of the plate to distort. This tendency is measured as GRF.
The kinetic information obtained from force plate data then provides an understanding of the kinematic characteristics through a derivation of Newton’s second law – that the force on a body is directly proportional to the mass of the body and the acceleration of the body, represented by the equation force = mass X acceleration. Given that the forces can be measured by a force plate, and the mass of the athlete is known, a very good understanding of the kinematic characteristics of the skill can be obtained through calculation of the acceleration of the athlete using the aforementioned equation.
Five important pieces of information can be obtained from a modern full featured force plate: force in the X, Y, and Z directions, the center of pressure, and moment (torque) around each of the axes. Each of these variables shows a picture of the forces exerted by an object (i.e. a limb) on the force plate. This data allows the investigator to determine a multitude of measures. For example, force plates have been used to study the take-off forces in pole vault technique (3) and the forces involved in the second pull in weightlifters (7); as it stands, the uses for force plates are numerous.
Before analysis and use of the collected data, processing of the analog signal must occur. Figure 2 shows the complete flow of the force plate data, from the initial analog signal output (continuous voltage) from the force plate, to the final digital input signal leading into the final analysis. Force is applied to the force plate, which changes the excitation charge sent through the force plate in proportion to the force applied. That new charge is sent to an amplifier. Analog signal processing (some kind of filtering or smoothing of the signal) can occur. After the signal has been amplified, the current goes to a data acquisition device, where it enters an analog-digital converter which converts the continuous analog signal to a discrete digital signal. The newly-converted digital data is recorded as evenly spaced samples, and more processing of the digital signal can occur. It is at this point that the recorded digital signal can be analyzed.
Forces must be measured through indirect means, through a force transducer. A force transducer functions to”convert physical states into electrical signals” (21). The load cells in a force plate transduce the force applied to the plate into a measureable electrical voltage and current. There are a variety of load cell types. Two commonly used load cells in force plates are piezoelectric transducers and strain-gauge load cells. Both types of load cells receive an “excitation” voltage input, and output an different electrical current which is proportional to the load experienced by the cell (based on Ohm’s Law: current = voltage / resistance) (1). The operation of each differs in a few distinct ways. Piezoelectric cells operate based on the fact that when a piezoelectric material has a force applied to it, a charge appears on the face of the material; This charge is proportional to the force applied. Recording of the resultant voltage allows calculation of the applied force.
The strain gauge load cells operate on the fact that changes in electrical current occur when a metal or semiconductor is deformed (1, 19). A thin sheet of metal or semiconductor material is bonded to a metal object, which provides a solid structural device on which to apply the force. Deformations in the device and the bonded sheet result in changes of the electrical resistance of the bonded sheet, thus modifying the current that moves through the bonded sheet. Monitoring of these changes allow for calculation of the force applied to the device.
A common form of the strain gauge is the shear beam load cell (1, 19). One end of the beam is anchored to a stable platform, while the other is extended so that it can receive a load. A foil sheet or semiconductor is bonded to the beam, and an electrical current is run through the sheet. Force applied at the end of the beam (perpendicular to the plane of the sheet) causes deformation of the beam, resulting in electrical resistance changes across the sheet bonded to the beam. This results in a different electrical current and allows measurement of the applied force. Shear beam load cells have the advantage of a high force capacity and accurate measurement, which can make them a good candidate for use in force plates.
A typical tri-planar force plate is constructed with four three-component load cells (14). Each three-component cell measures force in the X, Y and Z direction, and the placement of the load cells allow for calculation of center of pressure, center of force and torque about the axes. The four load cells are arranged in each of the four quadrants of the force plate, evenly spaced from each other and from the edges. Moment about the axes, center of pressure and center of force can be calculated based from measurements from data from individual load cells and their respective locations on the forceplate.
Typically, the forces that are transduced from force plates are summed from measurements from individual force transducers on the plate. For example, in a force plate with four load cells, one in each corner, vertical ground reaction force is calculated from the sum of the forces measured on each cell. Likewise, in a force plate that is capable of anterior-posterior measurement or medial-lateral forces, the forces of interest are the summed composed of the total of the load cells of the plate.
Monitoring the changes in force applied to the force plate requires sampling at regular intervals. Sampling frequencies of 500 to 2000 hertz (Hz) have been noted in the more recent sport science literature, however a sampling frequency of 1000 Hz is perhaps most common (14). While substantial research has examined sampling frequency in a wide variety of applications (engineering, for example), substantially less has been done to examine sampling frequency in sport science, although several authors have evaluated the variability of vertical jump performance data with different sampling frequencies. Vanrenterghem, et al. (24) found that sampling frequencies of above 100 Hz were adequate and Hori, et al. (10) found that sampling at about 200 Hz was accurate enough for accurate measurement. Contrary to the previous authors, Street, et al. (23) found that sampling rates of less than 1080 Hz could lead to an underestimation of jump height (calculated via the impulse method) by up to 4.4%. Other authors have recommended a sampling frequency of 500 Hz or 1000 Hz in force plate research to ensure accuracy, especially when impact is involved (2).
Sampling frequencies must be high enough to ensure accuracy of measurement and reduction of signal aliasing (where the recorded digital signal fails to accurately show the original signal due to inadequate sampling). The Nyquist Theorum suggests that the absolute minimum sampling frequency is two times the frequency of interest. Bartlett (2) recommends a sampling frequency of at least 500 Hz, however 1000 Hz is a common choice for force plate capture of human motion (14).
High sampling frequency is especially important when creating force-time curves in the early time segments of the curve. For example, some performance monitoring testing evaluates forces applied in the first 50ms of application of force in the isometric mid-thigh pull (12). At a sampling frequency of only 200 ms, if one were to construct a force-time curve, only 11 data points could be used for constructing this 50ms long curve. While a polynomial function could be applied to the 11 data points, a greater degree of accuracy for the curve will be obtained with a frequency of 500 Hz or 1000 Hz, because there would be 26 and 51 data points, respectively, from which to construct a curve.
Signal Amplification and Conditioning
Data collected from the force plate is not useable until amplification and signal processing occurs. Typically, analog signals (the raw voltage values) from the force plate are amplified and sent to an analog to digital (AD) converter (14). The AD converter then converts the analog voltage signal into a scaled digital signal, a signal that is able to be processed by computer software. Custom software developed in programs like LabVIEWTM (National Instruments, Austin, TX, USA) or Matlab (Mathworks Incorporated, Natick, MA, USA) can perform signal processing to clean up some of the noise from the data for use. Other methods exist for smoothing data that can be done in spreadsheet software such as Microsoft ExcelTM (Microsoft Corporation, Redmond, WA, USA). Many force plates come with proprietary software with filtering and smoothing methods included.
Through the collection process, amplification and A/D conversion, there are a number of electrical noise sources that may contaminate the data (5). A number of methods exist for filtering the noise in the signal, in order to best isolate and identify the signal of interest. This filtering can be done on either the analog or digital signal, or both. A low-pass filter eliminates frequencies above a certain level defined in the method, while a high-pass filter eliminates frequencies below a designated level. As noise often occurs at higher frequencies, a low pass filter is able to eliminate much of the noise in the signal. Sometimes it is necessary to restrict the data collected to within a range of frequencies, during which time a band-pass filter can be used. Other times it is necessary to eliminate a certain range of frequencies from a signal; a notch filter will be able to accomplish that task.
There are a multitude of signal processors and conditioners that are used in digital signal processing. Three common methods of reducing signal noise are Butterworth filters, splines and frequency domain techniques, such as Fourier Analysis (5). Yet another method is a moving average, which is relatively simple to calculate in Excel. Each of these methods operates differently, and provided that the optimal filter is applied to a signal, the end result is the same: the signal is less choppy and smoother, thus data is cleaner and easier to analyze (for more detailed information, the reader is directed toward Bartlett (2), Challis (5)) and Street, et al. (23). The general recommendation for filter choice is the one that most effectively and accurately isolates the signal of interest.
Force plate calibration is necessary to establish a regression equation to calculate ground reaction forces from output voltage, as well as to ensure accuracy of data obtained from testing. Because force plates only provide an output voltage, a calibration equation must be used to calculate what the ground reaction forces actually are. Unfortunately, often little is done by researchers to address the proper calibration of force plates (9). While calibration of some of the testable variables of the force plate can be difficult, calibration is absolutely necessary given the immense error that can be introduced even with small errors in calibration (9). The general idea behind calibration is that a range of known forces is applied to the force plate to see the resultant voltage given by the load cells, allowing the creation of a regression equation (1). For the Z-direction, a common method of calibration is to place a range of “dead weights” of known mass on top of the force plate, which allows the researcher to calibrate based on the resulting output voltage of the known mass. Calibration of the horizontal forces, torque and center of pressure can be a more difficult endeavor. However, researchers have proposed methods of calibration that are possible in the laboratory environment, such as a pulley system for X- and Y-direction calibration as proposed by Hall, et al. (9). In the pulley system, a regression equation is built from the output voltages with progressively higher (horizontally) applied loads. A pendulum system for dynamic calibration designed by Fairburn, et al. (6) is also a possibility for more advanced calibration. In-laboratory testing would allow a laboratory to avoid the potentially expensive calibration that is done by the force plate companies and private metricians.
Technical Information of Note
Force plate technical reports typically contain a data table with information about some or all of the following: linearity, hysteresis, crosstalk, and/or natural frequency. Each of these items provides valuable information about the characteristics of the force plate, as each affects the data obtained from it. Refer to Table 1 for recommended ranges.
Linearity is the maximum deviation of collected force plate data from a straight line (2). Perfect linearity is ideal, but is not necessarily a requirement for accurate data collection and analysis, as it can be calibrated for by applying a higher order polynomial to the data points(2). Linearity can be expressed as:
Where y=maximum deviation from linearity, and Y=full scale deflection (8). Full scale deflection refers to the voltage output with the highest load within the limit of the force plate. Dividing deviation from linearity by the highest voltage achieved gives a relative measure of linearity, and allows comparison to a standard.
Hysteresis is the difference in output values seen during the loading and unloading of a material (2). This is a quality that should also be minimized, as many force plate measurements involve both a loading and unloading component (see Figure 3). For example, large hysteresis in a load cell might over-estimate the forces in the eccentric portion of a squat, while correctly estimating the forces during the concentric portion. Hysteresis is sometimes seen as a result of a mechanical lag in deformity return to normal shape occurring during loading of the force transducers. Hysteresis can be calculated with the equation:
Where XL = output voltage for a given load during loading, XU = output voltage for the same given load during unloading, and Z =full scale deflection (2).
Many force plates measure forces in multiple planes; the components required to measure the different directions generally have at least a minor amount of cross-talk. Cross-talk refers to the interference of force in one component direction with the measurement of force by a component in another direction (2). It is important that this quality is minimized, so that forces from one plane are not measured on another, thus falsely attributing forces to an incorrect source. Bartlett (2) stated that less than 3% of full-scale deflection is preferable.
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Natural Frequency & Maximum Frequency Ratio
When struck, every object has a frequency at which it will tend to vibrate, (5). Force plates, as they are constructed of multiple materials, sometimes have multiple natural frequencies. Force plate manufacturers often report the natural frequency of the force plate when set up according to manufacturer specifications. This natural frequency should be significantly higher than that of the measurement, as it greatly increases the ease of isolating the measurement signal from the plate vibration. Force plates generally have high natural frequencies to aid in the ease of isolation through filtering. For example, the Kistler Type 9281E Triplanar force plate has a natural frequency of 1000 Hz (Kistler Group, Winterthur, Switzerland). The high natural frequency of this force plate is high enough to measure the impact activities of sports, which can surpass 100 Hz (2). The ratio of frequency of the measured skill to natural frequency (Maximum Frequency Ratio) should be less or equal to 0.2, so that the information of interest in the signal can be effectively isolated from the natural frequency of the plate.
The possibility of inaccurate measurements must be minimized if accurate conclusions are to be drawn. Certain steps can be taken to reduce the possibility of error, although even the most optimal setup will have at least a small amount of error. First and foremost, if a user does not know how to properly use the force plate and the software associated with it, the largest source of error may be the user himself. In this article, it is emphasized that with a proper education and the right information, the reader of this paper should be able to understand the basics of using a force platform, thus severely reducing potential for user error.
Adherence to the recommendations by Bartlett (2) will also serve to ensure accuracy of the data collected by the plate. Any deviance of the force plate characteristics outside of the recommendations increases the risk of inaccuracy. For example, Lees and Lake (14) and Hall, et al. (9) showed how cross-talk of even 1% could introduce a large amount of error in certain gait measurements.
Calibration should occur over a range of loads, from unloaded to above the highest expected load, within the manufacturer-specified loads of the force plate (if the expected loads are outside of the range, then a new plate with greater load range is necessary). For example, in an isometric pull, where measurements of vertical ground reaction force can exceed 7000 N or more (4), the force plate should be calibrated in the Z-axis with loads ranging from 0kg to more than 700kg. For horizontal calibration, a pulley system, like the one designed by Hall, et al. (9) would suffice. Dynamic calibration can be a bit more tricky, requiring expensive equipment or complex methodology. This can be done by major force plate companies or by private metricians.
It is also extremely important to install and adjust force plates based on manufacturer recommendations. Manufacturer-reported technical data about the force plate (e.g. hysteresis, linearity) are measured and determined under set conditions. Recommendations for where the force plate is installed, the type of flooring installed on and which floor level it is installed on must all be followed. A level surface for installation is required. Should the conditions during use deviate from those specified by the manufacturer, there is the possibility that those reported qualities (linearity, hysteresis) are no longer accurate.
Even with an ideal setup, there remain other sources for error. Other such sources of error are thermal noise, chemical noise, and electrical interference. Thermal noise is associated with the temperature of the device in use. Part of the reason for allowing a device to warm up is so that thermal noise is allowed to stabilize, as rising component temperatures result in changing electrical noise. Chemical noise is random noise that exists everywhere, and comes from variations in temperature, humidity, pressure and other sources. Electrical noise results from devices around the testing area that use electricity, such as lighting and equipment. Electrical noise is at 60 Hz and progressively weaker at its harmonics- 120 Hz, 180 Hz, etc. For example, if a force platform is placed in a room that has fluorescent lights, air conditioning/heat, and the building is located near power lines, electrical noise may be a substantial source of interference.
In all devices, the measured value is the result of the true score plus error. While one can attempt to eliminate as much error as possible, there will always be a degree of error in the collected data. It is up to the tester to eliminate and reduce as many sources of error as possible, and a theoretical judgment as to how much error in the collection is acceptable.
Equipment and Processing
While our laboratory uses tri-directional force plates, the majority of force plates we use are unidirectional, and measure only in the vertical direction (See Figure 4 for a photo). Although it is a drawback to only allow collection in the vertical direction, the plates offer a substantial reduction in cost over other plates offered by KistlerTM or AMTITM, for example. Furthermore, a number of studies have demonstrated that vertical forces and vertically- oriented skills have strong relationships to explosiveness and speed in sporting movements, thus measurement of vertical forces is of substantial importance (12, 20, 22, 25). In addition, we use force plates (0.914 x 0.46 m; 3′ x 1.5′; Rice Lake Weighing Systems, Rice Lake, WI) situated side-by-side to allow for collection of unilateral force data. For bilateral data collection, the forces from each force plate are summed. Each plate sits on a level concrete pad that is on the ground floor of the laboratory, to reduce contamination of data from extraneous sources.
Each force plate in the Sport Science laboratory is attached to Transducer Techniques TM0-2 amplifier and conditioner module (Transducer Techniques, Temecula, CA, USA). The amplifier provides both the excitation signal (the initial current going to the strain gage load cell) and amplification of the analog signal. In addition, the module provides an analog low-pass filter at 16 Hz. In between the amplifier/conditioner and the A/D converter is a shielded connector block. The BNC-2110 (National Instruments, Austin, TX, USA) accepts the analog signal and conveys the signal to the A/D converter. The block then connects to a DAQCard-6063E (National Instruments, Austin TX, USA). The DAQCard-6063E converts the analog signal to a digital signal. The digitized signal is then analyzed with custom software developed in LabVIEWTM (National Instruments, Austin TX, USA).
The custom software we’ve developed in LabVIEWTM samples the analog signal at 1000hz. The custom software has been set up to save the digital signal file and filter the digitized signal using a 4th order low-pass Butterworth filter at 100 Hz. From there, the signal can be analyzed for whatever variables are of interest. Refer to Kraska, et al. (12) for examples of measures of interest for static and countermovement jumps, and Leary, et al. (13) for examples of measures of interest in the isometric mid-thigh pull.
The Data Collection Process
Calibration of our force plates is performed immediately before the data collection process, which ensures that the calibration equation used in data analysis is established under similar environmental conditions as the data collection as well as avoids a potential shift of voltage output over time. Prior to calibration, force plates, amplifiers, A/D converters and computers are all turned on so that all of the collection equipment can warm up (thus stabilizing thermal and instrumentation noise). After this warm up period, the force plates are calibrated using loads from 0 kg to 350kg or 500kg, depending on the specific use of the plate (either jumps or isometric pulls). The plates are progressively loaded in 25kg increments, with the output voltage recorded each time. A linear regression equation is then applied to the calibration load data set in Microsoft Excel. This regression equation is saved, and used in the custom LabVIEWTM program during analysis.
A full understanding of a testing device and its characteristics are an integral part of accuracy, validity and reliability of testing. The force plate is a rather complex device. The complexities of the device and its peripherals allow the user to collect a large variety of high-quality data for analysis that are difficult to obtain via other means. While it is somewhat difficult to master use of the device, the plethora of information that can be obtained from a force plate makes the endeavor more than worthwhile.
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