ASTM F3109-23

Standard Practice for Verification of Multi-Axis Force Measuring Platforms

SIGNIFICANCE AND USE
5.1 Multi-axis force measuring platforms are used to measure the ground reaction forces produced at the interface between a subject's foot or shoe and the supporting ground surface. These platforms are used in various settings ranging from research laboratories to healthcare facilities. The use of force platforms has become particularly important in gait analysis where clinical evaluations have become a billable clinical service.  
5.2 Of particular importance is the application of force platforms in the treatment of cerebral palsy (CP) (1, 2).3 An estimated 8000 to 10 000 infants born each year will develop CP (3) while today’s affected population is over 764 000 patients (4). Quantitative gait analysis, using force platforms and motion capture systems, provides a valuable tool in evaluating the pathomechanics of children with CP. This type of mechanical evaluation provides a quantitative basis for treating neuromuscular conditions. In other words, surgical decisions are in part guided by information gained from the use of force platform measurements (5, 6).  
5.3 Another application is treatment of spina bifida. According to the Gait and Clinical Movement Analysis Society (GCMAS) (7), an instrumented gait analysis is the standard of expert care for children with gait abnormalities secondary to spina bifida. The main objective of diagnostic gait analysis is to define the pathological consequences of neural tube defects as they relate to gait. The use of instrumented gait analysis allows physicians to determine which surgical or non-surgical interventions would provide the best outcome.  
5.4 More recently, force platforms have been used for pre- and post-surgical evaluation of TKA (total knee arthroplasty) and THA (total hip arthroplasty) patients. Such data provides an objective measure of the mechanical outcome of the surgical procedure.  
5.5 In addition to the clinical applications there are numerous medical and human performance research activities which r...
SCOPE
1.1 This standard recommends practices for performance verification of multi-axis force platforms commonly used for measuring ground reaction forces during gait, balance, and other activities.  
1.1.1 This standard provides a method to quantify the relationship between applied input force and force platform output signals across the manufacturer’s defined spatial working surface and specified force operating range.  
1.1.2 This standard provides definitions of the critical parameters necessary to quantify the behavior of multi-axis force measuring platforms and the methods to measure the parameters.  
1.1.3 This standard presents methods for the quantification of spatially distributed errors and absolute measuring performance of the force platform at discrete spatial intervals and discrete force levels on the working surface of the platform.  
1.1.4 This standard further defines certain important derived parameters, notably COP (center of pressure) and methods to quantify and report the measuring performance of such derived parameters at spatial intervals and force levels across the working range of the force platform.  
1.1.5 This standard defines the requirements for a report suitable to characterize the force platform’s performance and provide traceable documentation to be distributed by the manufacturer or calibration facility to the users of such platforms.  
1.1.6 Dynamic characteristics and applications where the force platform is incorporated in other equipment, such as instrumented treadmills and stairs, are beyond the scope of this standard.  
1.1.7 This standard is written for purposes of multi-axis force platform verification. However, the methods and procedures are applicable to calibration of force platforms by manufacturers.  
1.2 The values stated in SI units are to be regarded as the standard. Other metric and inch-pound values are regarded as equivalent when required.  
1.3 This standard does n...

General Information

• Status: Published
• Publication Date: 28-Feb-2023
• ICS: 17.100 - Measurement of force, weight and pressure
• Technical Committee: F04 - Medical and Surgical Materials and Devices
• Drafting Committee: F04.15 - Material Test Methods

Relations

• Refers: ASTM E4-14 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Jun-2014
• Refers: ASTM E74-13a - Standard Practice of Calibration of Force-Measuring Instruments for Verifying the Force Indication of Testing Machines
• Effective Date: 01-May-2013
• Refers: ASTM E74-13 - Standard Practice of Calibration of Force-Measuring Instruments for Verifying the Force Indication of Testing Machines
• Effective Date: 01-Mar-2013
• Refers: ASTM E74-12 - Standard Practice of Calibration of Force-Measuring Instruments for Verifying the Force Indication of Testing Machines
• Effective Date: 01-Dec-2012
• Refers: ASTM E4-10 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Jun-2010
• Refers: ASTM E4-09a - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Nov-2009
• Refers: ASTM E4-09 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Apr-2009
• Refers: ASTM E4-08 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Dec-2008
• Refers: ASTM E4-07 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 01-Jan-2007
• Refers: ASTM E74-06 - Standard Practice of Calibration of Force-Measuring Instruments for Verifying the Force Indication of Testing Machines
• Effective Date: 01-Mar-2006
• Refers: ASTM E74-04 - Standard Practice of Calibration of Force-Measuring Instruments for Verifying the Force Indication of Testing Machines
• Effective Date: 01-Dec-2004
• Refers: ASTM E4-03 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 10-Aug-2003
• Refers: ASTM E4-02 - Standard Practices for Force Verification of Testing Machines
• Effective Date: 10-Nov-2002
• Refers: ASTM E74-00a - Standard Practice of Calibration of Force-Measuring Instruments for Verifying the Force Indication of Testing Machines
• Effective Date: 05-Apr-2002
• Refers: ASTM E74-02 - Standard Practice of Calibration of Force-Measuring Instruments for Verifying the Force Indication of Testing Machines
• Effective Date: 05-Apr-2002

Overview

ASTM F3109-23 defines the standard practice for verification of multi-axis force measuring platforms. These platforms are essential devices for accurately measuring ground reaction forces at the interface between a subject’s foot (or shoe) and the supporting ground surface. Such measurements are critical in a range of settings-including research laboratories, hospitals, and clinical gait analysis centers.

The verification practices outlined ensure that multi-axis force platforms deliver precise, reliable, and traceable results. The standard covers key definitions, verification methodology, error quantification, and documentation requirements, thereby supporting both end users and manufacturers in ensuring measurement integrity.

Key Topics

• Performance Verification: The standard prescribes how to verify that the force platform's outputs correlate accurately with applied input forces across the manufacturer’s defined spatial working surface and operational force range.
• Critical Parameters and Definitions: Definitions such as center of pressure (COP), crosstalk, force platform origin, and multi-axis force are provided to support standardized measurement and analysis.
• Error Quantification: Methods are included to quantify spatially distributed errors and absolute measurement performance at various grid points and force levels on the platform’s surface.
• COP Measurement: Techniques to quantify the measurement performance of the center of pressure and report COP errors at discrete intervals.
• Reporting Requirements: Specifies the format and key content for verification reports, including graphical presentations of results, making the data useful for traceability and compliance.
• Applicability: Although focused on verification, the procedures are also applicable for the calibration of multi-axis force platforms by manufacturers.

Applications

ASTM F3109-23 is highly relevant for several practical applications:

• Gait Analysis: Utilized in clinical settings for the quantitative evaluation of walking patterns, especially for patients with neurological disorders such as cerebral palsy (CP) and spina bifida. Quantitative gait data support evidence-based clinical decision-making and treatment planning.
• Orthopedic Surgery Evaluation: Used for objective measurement of patient function before and after procedures such as total knee arthroplasty (TKA) and total hip arthroplasty (THA), allowing for assessment of surgical outcomes.
• Biomechanics and Human Performance Research: Supports research into human motion, balance, and load distribution by providing accurate force and moment data.
• Healthcare Facilities and Rehabilitation: Assists clinicians and therapists in the evaluation and monitoring of neuromuscular and musculoskeletal conditions.

Related Standards

To ensure comprehensive force measurement and calibration in alignment with ASTM F3109-23, the following standards are frequently referenced:

• ASTM E4: Practices for Force Calibration and Verification of Testing Machines
• ASTM E74: Practices for Calibration and Verification for Force-Measuring Instruments

These references guide traceable calibration protocols and ensure compatibility and accuracy across different force measurement systems.

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Keywords: multi-axis force platform, force plate verification, ground reaction force measurement, center of pressure, biomechanical analysis, crosstalk, gait analysis, ASTM F3109, accuracy, force calibration, clinical biomechanics.

This standard is essential for users and manufacturers seeking reliable, traceable, and standardized practice in the verification and calibration of multi-axis force measuring platforms, ensuring data quality in clinical, research, and engineering applications.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: F3109 − 23
Standard Practice for
Verification of Multi-Axis Force Measuring Platforms
This standard is issued under the fixed designation F3109; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* 1.2 The values stated in SI units are to be regarded as the
standard. Other metric and inch-pound values are regarded as
1.1 This standard recommends practices for performance
equivalent when required.
verification of multi-axis force platforms commonly used for
1.3 This standard does not purport to address all of the
measuring ground reaction forces during gait, balance, and
safety concerns, if any, associated with its use. It is the
other activities.
responsibility of the user of this standard to establish appro-
1.1.1 This standard provides a method to quantify the
priate safety, health, and environmental practices and deter-
relationship between applied input force and force platform
mine the applicability of regulatory limitations prior to use.
output signals across the manufacturer’s defined spatial work-
1.4 This international standard was developed in accor-
ing surface and specified force operating range.
dance with internationally recognized principles on standard-
1.1.2 This standard provides definitions of the critical pa-
ization established in the Decision on Principles for the
rameters necessary to quantify the behavior of multi-axis force
Development of International Standards, Guides and Recom-
measuring platforms and the methods to measure the param-
mendations issued by the World Trade Organization Technical
eters.
Barriers to Trade (TBT) Committee.
1.1.3 This standard presents methods for the quantification
2. Referenced Documents
of spatially distributed errors and absolute measuring perfor-
mance of the force platform at discrete spatial intervals and
2.1 ASTM Standards:
discrete force levels on the working surface of the platform.
E4 Practices for Force Calibration and Verification of Test-
1.1.4 This standard further defines certain important derived ing Machines
parameters, notably COP (center of pressure) and methods to
E74 Practices for Calibration and Verification for Force-
quantify and report the measuring performance of such derived Measuring Instruments
parameters at spatial intervals and force levels across the
3. Terminology
working range of the force platform.
3.1 Definitions of Terms Specific to This Standard:
1.1.5 This standard defines the requirements for a report
suitable to characterize the force platform’s performance and 3.1.1 center of pressure (COP), n—the spatial point on the
surface of a force platform at which a single equivalent force
provide traceable documentation to be distributed by the
manufacturer or calibration facility to the users of such has the same static effect as the sum of the distributed forces
and the distributed moments acting on the system.
platforms.
1.1.6 Dynamic characteristics and applications where the
3.1.2 COP error, n—difference between the COP x-y posi-
force platform is incorporated in other equipment, such as tion reported by the force platform (or calculated from the
force platform outputs) and the actual x-y location of the
instrumented treadmills and stairs, are beyond the scope of this
standard. applied Fz verification force.
1.1.7 This standard is written for purposes of multi-axis 3.1.3 crosstalk or crosstalk error, n—response of an output
force platform verification. However, the methods and proce-
channel corresponding to an unloaded axis when a force or a
dures are applicable to calibration of force platforms by moment is applied to a different axis.
manufacturers.
3.1.4 force platform origin, n—the position on the force
platform, specified by the manufacturer, where x, y, and z = 0.
The origin serves as a reference position for the COP x and
This practice is under the jurisdiction of ASTM Committee F04 on Medical and
Surgical Materials and Devices and is the direct responsibility of Subcommittee
F04.15 on Material Test Methods. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved March 1, 2023. Published March 2023. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 2016. Last previous edition approved in 2022 as F3109 – 22. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/F3109-23. the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F3109 − 23
COP y locations, locations for uniaxial forces applied during 3.1.11 serialized calibration values, n—calibration values
verification, and for calculating output moments due to input that apply to a specific force platform with a specific serial
forces. The origin may be at a different x-y-z position from the number. The calibration values may be used in the force
force platform’s geometric center. The force platform origin is platform, in an amplifier, or in a computer that makes up a
sometimes called the electro-mechanical origin. calibrated force-measuring platform system.
3.1.5 Fx and Fy, n—forces orthogonal to Fz, assigned per 3.1.12 traceable force standard, n—a force transducer or
Fig. 1 which follows the right-hand coordinate system (“right- dead weight that is traceable to national standards and is more
hand rule”) convention for directionality. accurate than the instrumentation that is being verified. In this
method, if dead weights are used then corrections for gravity
3.1.6 Fz, n—force that is orthogonal to the working surface
shall be applied per Practice E4 and their center of mass shall
of the platform. Fz and z distances are positive going down-
be spatially balanced around the axis of loading such that
ward when the force platform is mounted on the floor.
forces applied to the force platform are applied at a known
3.1.7 moment, n—a vector equal to the cross product of a
location.
position vector and a force vector. Given a position vector d =
3.1.13 uniaxial force, n—force that is only in the direction
{x, y, z} that indicates a point, relative to a given origin, which
of the intended axis without imparting forces in the two
is on the line of action of a force F = {Fx, Fy, Fz} then the
orthogonal axes. For example, applying Fz uniaxially shall not
components of the moment vector M = {Mx, My, Mz} relative
cause Fx or Fy forces greater than 10 % of the Fz to Fx or Fz
to the origin are:
to Fy crosstalk specified by the force platform’s manufacturer.
Mx = y · Fz – z · Fy
My = z · Fx – x · Fz 3.1.14 working surface, n—the flat area of the platform
Mz = x · Fy – y · Fx
where ground reaction forces are measured while patients or
If the point indicated by d lies on the surface of the force subjects perform activities such as walking, standing, running,
platform, then that point is also the COP of F.
and other activities. In most applications the working surface is
oriented horizontally and is the top surface of the force
3.1.8 Mx, My, and Mz, n—moments around the x, y, and z
platform.
axes, respectively, following the right-hand coordinate system
convention for directionality.
3.1.15 x-y-z position, n—the position where the force veri-
fication vector is applied with respect to the force platform’s
3.1.9 multi-axis force plate, n—synonym for multi-axis
origin.
force platform.
3.1.10 multi-axis force platform, n—a transducer with a flat
4. Summary of Practice
measuring surface capable of measuring three orthogonal force
components, three orthogonal moment components, and di- 4.1 This standard practice has three sections:
rectly or indirectly measuring the center of pressure x-y 4.1.1 Uniaxial test forces are applied to the force platform
position. using traceable force standards. The forces are applied for at
FIG. 1 Force Platform Orthogonal Coordinate Conventions
F3109 − 23
least five force values over a range of positions spanning the estimated 8000 to 10 000 infants born each year will develop
manufacturer’s specified working surface dimensions. The CP (3) while today’s affected population is over 764 000
force platform’s outputs are recorded at each force and patients (4). Quantitative gait analysis, using force platforms
position. To ensure adequate quality of measurement at all and motion capture systems, provides a valuable tool in
locations of force application, the spatial errors should be evaluating the pathomechanics of children with CP. This type
sampled by test forces at appropriately small spatial intervals. of mechanical evaluation provides a quantitative basis for
In this standard, a grid pattern to ensure proper spatial treating neuromuscular conditions. In other words, surgical
characterization of errors is presented (see Fig. 2). decisions are in part guided by information gained from the use
4.1.2 The recorded force platform outputs are analyzed at all of force platform measurements (5, 6).
forces and positions to compare the force platform’s Fx, Fy, Fz,
5.3 Another application is treatment of spina bifida. Accord-
Mx, My, Mz, COP x, and COP y measuring errors and
ing to the Gait and Clinical Movement Analysis Society
crosstalk performance with the manufacturer’s specifications.
(GCMAS) (7), an instrumented gait analysis is the standard of
These comparisons determine whether the force platform is
expert care for children with gait abnormalities secondary to
successfully verified.
spina bifida. The main objective of diagnostic gait analysis is to
4.1.3 A report which includes graphical presentation of the
define the pathological consequences of neural tube defects as
results shall be prepared.
they relate to gait. The use of instrumented gait analysis allows
physicians to determine which surgical or non-surgical inter-
5. Significance and Use
ventions would provide the best outcome.
5.1 Multi-axis force measuring platforms are used to mea-
5.4 More recently, force platforms have been used for pre-
sure the ground reaction forces produced at the interface
and post-surgical evaluation of TKA (total knee arthroplasty)
between a subject’s foot or shoe and the supporting ground
and THA (total hip arthroplasty) patients. Such data provides
surface. These platforms are used in various settings ranging
an objective measure of the mechanical outcome of the surgical
from research laboratories to healthcare facilities. The use of
procedure.
force platforms has become particularly important in gait
analysis where clinical evaluations have become a billable
5.5 In addition to the clinical applications there are numer-
clinical service.
ous medical and human performance research activities which
rely on accurate measurement of ground reaction forces by
5.2 Of particular importance is the application of force
using multi-axis force platform measurement instruments.
platforms in the treatment of cerebral palsy (CP) (1, 2). An
5.6 As a standards organization, ASTM has historically
provided excellent standards for the calibration of force trans-
The boldface numbers in parentheses refer to the list of references at the end of
ducers and force-measuring instrumentation. Force platforms,
this standard.
FIG. 2 Illustration of Spatial Grid Pattern Used to Apply Forces for Force Platform Verification
F3109 − 23
however, are different from force transducers. Force platforms 7.4.1 Apply Fz at points making up an evenly spaced grid
typically provide a large active working surface, whereas force spanning the force platform’s working surface. Grid count
transducers provide more or less a single point of interaction should be 100 or more grid points, and the x and y grid spacing
with the load-applying environment. Moreover, force plat- should be approximately 25 mm (1 in. in U.S. customary units)
forms typically provide six-axis measurements and are ex- or less. Use of fewer positions or larger spacing increments
pected to be used in environments causing multi-axial loading. shall be noted and justified in the report. The spacing between
measurements shall be sufficiently close so that the uncertainty
6. Apparatus of the force platform’s outputs due to interpolation between
positions is less than the force platform’s specified accuracy.
6.1 The apparatus shall have the following attributes:
The x and y positions where Fz is applied shall be measured
6.1.1 The apparatus shall apply all Fx, Fy, and Fz forces
with an accuracy of 60.1 mm.
using a traceable force standard. See Practice E74–13a, Sec-
7.4.2 At each x-y position, apply five or more different Fz
tions 5 and 6.
forces. Begin with a minimum force that is no less than 5 %
6.1.2 The apparatus shall apply all forces using a single, flat
and no greater than 10 % of the force platform’s Fz full scale.
contact pad to concentrate force distribution as might be
Monotonically increase the applied force and end at the force
encountered during heel strike. The shape and dimensions of
platform manufacturer’s specified Fz full-scale capacity. For
the contact pad shall be specified in the report.
each applied Fz and x-y position, record the force applied by
6.1.3 The apparatus shall apply all forces uniaxially in an
the force standard (either the output of the standard force
axis that is coincident with the axis of the force platform being
transducer cell or the force applied by the standard weights);
verified. For example, Fz shall be applied perpendicular to the
the x and y positions of Fz; and the force platform’s outputs Fx,
force platform’s working surface without causing Fx or Fy
Fy, Fz, Mx, My, Mz, and, if provided by the force platform,
forces greater than 10 % of the Fz to Fx or Fz to Fy crosstalk
COP x and COP y. The COP is frequently not a direct output
specified by the force platform’s manufacturer.
of the force platform but is calculated from the force and
6.1.4 The apparatus shall measure and report the position of
moment outputs of the platform. Each recorded value at each
the applied forces with an accuracy of 60.1 mm.
Fz and x-y position shall consist of an average of several
6.1.5 The apparatus shall be located in an environment with
readings. The readings for each recorded value shall be of
sufficient stability that verification results are unaffected by
sufficient quantity that variability due to noise is characterized.
environmental variations.
Additionally, the readings shall be sufficiently stable that the
6.1.6 The apparatus shall be at a steady-state operating
variability of the readings at each Fz and x-y position is less
conditio
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: F3109 − 22 F3109 − 23
Standard Practice for
Verification of Multi-Axis Force Measuring Platforms
This standard is issued under the fixed designation F3109; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
1.1 This standard recommends practices for performance verification of multi-axis force platforms commonly used for measuring
ground reaction forces during gait, balance, and other activities.
1.1.1 This standard provides a method to quantify the relationship between applied input force and force platform output signals
across the manufacturer’s defined spatial working surface and specified force operating range.
1.1.2 This standard provides definitions of the critical parameters necessary to quantify the behavior of multi-axis force measuring
platforms and the methods to measure the parameters.
1.1.3 This standard presents methods for the quantification of spatially distributed errors and absolute measuring performance of
the force platform at discrete spatial intervals and discrete force levels on the working surface of the platform.
1.1.4 This standard further defines certain important derived parameters, notably COP (center of pressure) and methods to quantify
and report the measuring performance of such derived parameters at spatial intervals and force levels across the working range of
the force platform.
1.1.5 This standard defines the requirements for a report suitable to characterize the force platform’s performance and provide
traceable documentation to be distributed by the manufacturer or calibration facility to the users of such platforms.
1.1.6 Dynamic characteristics and applications where the force platform is incorporated in other equipment, such as instrumented
treadmills and stairs, are beyond the scope of this standard.
1.1.7 This standard is written for purposes of multi-axis force platform verification. However, the methods and procedures are
applicable to calibration of force platforms by manufacturers.
1.2 The values stated in SI units are to be regarded as the standard. Other metric and inch-pound values are regarded as equivalent
when required.
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.4 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
This practice is under the jurisdiction of ASTM Committee F04 on Medical and Surgical Materials and Devices and is the direct responsibility of Subcommittee F04.15
on Material Test Methods.
Current edition approved Sept. 1, 2022March 1, 2023. Published October 2022March 2023. Originally approved in 2016. Last previous edition approved in 20162022 as
F3109 – 16.F3109 – 22. DOI: 10.1520/F3109-22.10.1520/F3109-23.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
F3109 − 23
2. Referenced Documents
2.1 ASTM Standards:
E4 Practices for Force Calibration and Verification of Testing Machines
E74 Practices for Calibration and Verification for Force-Measuring Instruments
3. Terminology
3.1 Definitions of Terms Specific to This Standard:
3.1.1 center of pressure (COP), n—the spatial point on the surface of a force platform at which a single equivalent force has the
same static effect as the sum of the distributed forces and the distributed moments acting on the system.
3.1.2 COP error, n—difference between the COP x-y position reported by the force platform (or calculated from the force platform
outputs) and the actual x-y location of the applied Fz verification force.
3.1.3 crosstalk or crosstalk error, n—response of an output channel corresponding to an unloaded axis when a force or a moment
is applied to a different axis.
3.1.4 force platform origin, n—the position on the force platform, specified by the manufacturer, where x, y, and z = 0. The origin
serves as a reference position for the COP x and COP y locations, locations for uniaxial forces applied during verification, and for
calculating output moments due to input forces. The origin may be at a different x-y-z position from the force platform’s geometric
center. The force platform origin is sometimes called the electro-mechanical origin.
3.1.5 Fx and Fy, n—forces orthogonal to Fz, assigned per Fig. 1 which follows the right-hand coordinate system (“right-hand
rule”) convention for directionality.
3.1.6 Fz, n—force that is orthogonal to the working surface of the platform. Fz and z distances are positive going downward when
the force platform is mounted on the floor.
FIG. 1 Force Platform Orthogonal Coordinate Conventions
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
F3109 − 23
3.1.7 moment, n—a vector equal to the cross product of a position vector and a force vector. Given a position vector d = {x, y,
z} that indicates a point, relative to a given origin, which is on the line of action of a force F = {Fx, Fy, Fz} then the components
of the moment vector M = {Mx, My, Mz} relative to the origin are:
Mx = y · Fz – z · Fy
My = z · Fx – x · Fz
Mz = x · Fy – y · Fx
If the point indicated by d lies on the surface of the force platform, then that point is also the COP of F.
3.1.8 Mx, My, and Mz, n—moments around the x, y, and z axes, respectively, following the right-hand coordinate system
convention for directionality.
3.1.9 multi-axis force plate, n—synonym for multi-axis force platform.
3.1.10 multi-axis force platform, n—a transducer with a flat measuring surface capable of measuring three orthogonal force
components, three orthogonal moment components, and directly or indirectly measuring the center of pressure x-y position.
3.1.11 serialized calibration values, n—calibration values that apply to a specific force platform with a specific serial number. The
calibration values may be used in the force platform, in an amplifier, or in a computer that makes up a calibrated force-measuring
platform system.
3.1.12 traceable force standard, n—a force transducer or dead weight that is traceable to national standards and is more accurate
than the instrumentation that is being verified. In this method, if dead weights are used then corrections for gravity shall be applied
per Practice E4 and their center of mass shall be spatially balanced around the axis of loading such that forces applied to the force
platform are applied at a known location.
3.1.13 uniaxial force, n—force that is only in the direction of the intended axis without imparting forces in the two orthogonal
axes. For example, applying Fz uniaxially shall not cause Fx or Fy forces greater than 10 % of the Fz to Fx or Fz to Fy crosstalk
specified by the force platform’s manufacturer.
3.1.14 working surface, n—the flat area of the platform where ground reaction forces are measured while patients or subjects
perform activities such as walking, standing, running, and other activities. In most applications the working surface is oriented
horizontally and is the top surface of the force platform.
3.1.15 x-y-z position, n—the position where the force verification vector is applied with respect to the force platform’s origin.
4. Summary of Practice
4.1 This standard practice has three sections:
4.1.1 Uniaxial test forces are applied to the force platform using traceable force standards. The forces are applied for at least five
force values over a range of positions spanning the manufacturer’s specified working surface dimensions. The force platform’s
outputs are recorded at each force and position. To ensure adequate quality of measurement at all locations of force application,
the spatial errors should be sampled by test forces at appropriately small spatial intervals. In this standard, a grid pattern to ensure
proper spatial characterization of errors is presented (see Fig. 2).
4.1.2 The recorded force platform outputs are analyzed at all forces and positions to compare the force platform’s Fx, Fy, Fz, Mx,
My, Mz, COP x, and COP y measuring errors and crosstalk performance with the manufacturer’s specifications. These comparisons
determine whether the force platform is successfully verified.
4.1.3 A report which includes graphical presentation of the results shall be prepared.
5. Significance and Use
5.1 Multi-axis force measuring platforms are used to measure the ground reaction forces produced at the interface between a
subject’s foot or shoe and the supporting ground surface. These platforms are used in various settings ranging from research
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FIG. 2 Illustration of Spatial Grid Pattern Used to Apply Forces for Force Platform Verification
laboratories to healthcare facilities. The use of force platforms has become particularly important in gait analysis where clinical
evaluations have become a billable clinical service.
5.2 Of particular importance is the application of force platforms in the treatment of cerebral palsy (CP) (1, 2). An estimated 8000
to 10 000 infants born each year will develop CP (3) while today’s affected population is over 764 000 patients (4). Quantitative
gait analysis, using force platforms and motion capture systems, provides a valuable tool in evaluating the pathomechanics of
children with CP. This type of mechanical evaluation provides a quantitative basis for treating neuromuscular conditions. In other
words, surgical decisions are in part guided by information gained from the use of force platform measurements (5, 6).
5.3 Another application is treatment of spina bifida. According to the Gait and Clinical Movement Analysis Society (GCMAS)
(7), an instrumented gait analysis is the standard of expert care for children with gait abnormalities secondary to spina bifida. The
main objective of diagnostic gait analysis is to define the pathological consequences of neural tube defects as they relate to gait.
The use of instrumented gait analysis allows physicians to determine which surgical or non-surgical interventions would provide
the best outcome.
5.4 More recently, force platforms have been used for pre- and post-surgical evaluation of TKA (total knee arthroplasty) and THA
(total hip arthroplasty) patients. Such data provides an objective measure of the mechanical outcome of the surgical procedure.
5.5 In addition to the clinical applications there are numerous medical and human performance research activities which rely on
accurate measurement of ground reaction forces by using multi-axis force platform measurement instruments.
5.6 As a standards organization, ASTM has historically provided excellent standards for the calibration of force transducers and
force-measuring instrumentation. Force platforms, however, are different from force transducers. Force platforms typically provide
a large active working surface, whereas force transducers provide more or less a single point of interaction with the load-applying
environment. Moreover, force platforms typically provide six-axis measurements and are expected to be used in environments
causing multi-axial loading.
The boldface numbers in parentheses refer to the list of references at the end of this standard.
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6. Apparatus
6.1 The apparatus shall have the following attributes:
6.1.1 The apparatus shall apply all Fx, Fy, and Fz forces using a traceable force standard. See Practice E74–13a, Sections 5 and
6.
6.1.2 The apparatus shall apply all forces using a single, flat contact pad to concentrate force distribution as might be encountered
during heel strike. The shape and dimensions of the contact pad shall be specified in the report.
6.1.3 The apparatus shall apply all forces uniaxially in an axis that is coincident with the axis of the force platform being verified.
For example, Fz shall be applied perpendicular to the force platform’s working surface without causing Fx or Fy forces greater
than 10 % of the Fz to Fx or Fz to Fy crosstalk specified by the force platform’s manufacturer.
6.1.4 The apparatus shall measure and report the position of the applied forces with an accuracy of 60.1 mm.
6.1.5 The apparatus shall be located in an environment with sufficient stability that verification results are unaffected by
environmental variations.
6.1.6 The apparatus shall be at a steady-state operating condition before verification begins so that the equipment itself does not
introduce any errors.
6.1.7 Care shall be taken to minimize transient vibrations when verification is being performed.
6.2 Users of this standard shall ensure that the force platform’s serialized calibration information provided by the manufacturer
is in effect. For example, if the force platform requires the end user to apply calibration files from a computer or to use the force
platform with an amplifier as a matched pair, the user of this standard shall ensure that the force platform (or force platform and
amplifier combination) is using the correct force platform’s serialized calibration values before beginning verification.
7. Verification Procedure
7.1 Before proceeding with the verification, a warm-up period with all electronics powered may be necessary to achieve stable
temperatures and outputs. Reviewing the force platform manufacturer’s recommendations regarding a warm-up period is
recommended.
7.2 Before any forces are applied to the force platform, ensure that the traceable force standard is not touching the force platform.
Then, zero the outputs of all six force platform outputs and, if used, the traceable force transducer. This step may be repeated at
each position.
7.3 Note that all x-y-z positions in the verification procedure are relative to the force platform’s origin as defined in 3.1.
7.4 Apply Fz to the working surface of the force platform.
7.4.1 Apply Fz at points making up an evenly spaced grid spanning the force platform’s working surface. Grid count should be
100 or more grid points, and the x and y grid spacing should be approximately 25 mm (1 in. in U.S. customary units) or less. Use
of fewe
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