Biomechanics is the application of classical mechanics to biological systems such as the human body. Although this comprises many branches of mechanics, in the context of ergonomics, we will deal only with dynamics and to a limited extent the mechanics of materials.
In physical ergonomics, the human body can be seen as a mechanical system or rather a part of a mechanical system comprising also the tools, objects, and environment with which the human operator interacts. Inverse dynamics can be applied to the analysis of this mechanical system to estimate forces and moments being produced by or acting on thehuman body, whereas mechanics of materials contributes toward understanding the effects of these mechanical loads on the body. Direct measurement of forces and moments in the human is not feasible for practical and ethical reasons. Consequently the vast majority of available methods and data rely to some extent on inverse dynamical models.
Estimating Joint Moments
The principles of inverse dynamics will probably be known to any mechanical engineer and can be found in dynamics textbooks or specialty books on biomechanics (see Additional References). To summarize, application of the equations of motion based on Newton’s second law ( F ma) and Euler’s extension of this law to angular motions ( M l ) to a system of linked segments is used to yield forces and moments acting at each of the segments in each of the links. In biomechanical analyses, moments about the joints of the human body are usually of interest, since these reflect the combined effect of all muscles spanning the
joint. Note that physically these moments are thus the effect of muscle forces. In actual analysis, the moments of force of the muscles appear as a lumped moment in the moment equilibrium equation, and they do not appear in the force equilibrium equation. To perform this type of analysis, masses and moments of inertias of the segments and the accelerations of the segments need to be known. Finally, if two or more external forces act on the system, all but one of these need to be known. If all external forces are known, redundant information is available which can be used to validate the model with respect to anthropometric assumptions
or to decrease the estimation errors that would result from assuming accelerations to be zero.
A simplified example of a linked segment model that was used to estimate the moment on the knee while climbing ladders with different rung separations is given in Fig. 1. Video data were used to approximate the positions of centers of mass of the foot and lower leg as well as the joint rotation centers of the knee and ankle. Forces on a rung were measured with a force transducer. Segment masses were estimated on the basis of anthropometric data.
First, a free-body diagram of the foot was created, and the reaction force at the ankle was calculated by equating the sum of the forces on this segment to its mass times acceleration. Next, the moment at the ankle was calculated from equating the sum of the moments to inertia times angular acceleration. Subsequently, the opposites of this force and moment were used as input for a free-body diagram of the lower leg and the reaction force and moment at the knee were calculated. Segment masses and moments of inertias cannot be directly measured when dealing with the human body. Therefore estimations need to be made on the basis of anthropometric models (see the discussion of fundamentals in Section 2.2). Obviously these estimations may introduce errors, and the magnitude of such errors can be gauged by making use of redundant information when all external forces have been measured. For example, the moment about the low back in lifting can be calculated on the basis of a model of the lower body (legs and pelvis) using measured ground reaction forces on each foot as input. This same moment can also be estimated using a model of the upper body (arms and trunk) and the object lifted. It has been shown that with a careful choice of anthropometric assumptions, errors in moment estimates will generally be below 10 N m. Accelerations can be measured or calculated from position data by double differentiation.
This involves labor-intensive measurements and is only feasible when at least a mockup of the situation to be analyzed is available. Consequently, in many ergonomic applications, accelerations are assumed to be zero, in which case only the static configuration of the human body needs to be known or predicted. This simplification will lead to underestimation of mechanical loads on the human body in dynamic tasks, which in some cases can be substantial (e.g., in manual lifting, the moments around the low back may be underestimated by a factor of 2). Such errors may lead to questionable conclusions, even in a comparative analysis. For instance, earlier studies comparing stoop and squat lifting techniques appear to have been biased toward favoring the squat technique due to the application of static models.
Consequently, early studies have often reported a lower low-back load in squat lifting as compared to stoop lifting, whereas more recent studies using dynamic models have reported the opposite.5 If an analysis of a dynamic task is performed assuming acceleration to be ze zro but inputting the measured external forces on the body into the analysis—the so-called quasidynamic approach—reasonable estimates of joint moments result. A second simplification often used is to assume that all movement and force exertion takes place in a single plane, which allows application of a 2D model. In analyses of asymmetric lifting tasks, this can cause significant and substantial errors in estimated moments around the low back (roughly 20% when the load is placed 30 outside of the primary plane of movement). At 10 of asymmetry, differences between 2D and 3D analyses have been found to be insignificant.
Data collection required for the estimation of net moments is usually not prohibitive in
a comparative analysis of working methods and techniques, since this can be done in a
laboratory mock-up setting. However, for monitoring and identification of the most stressful
tasks or task elements, field measurements covering long periods are desirable. In this case,
use of an inverse dynamics approach usually is prohibitive. Methods have been developed
to estimate moments based on measurements of the electrical activity of muscles, the latter
using electrodes applied on the skin overlying the muscle group of interest (electromyography,
or EMG). However, it has been shown that additional kinematic data and extensive
calibrations are needed to obtain valid estimates. Currently miniature kinematic sensors and
efficient calibration procedures are being developed and tested to facilitate this type of measurements.
Finally estimation of mechanical loads in the design stage can be done using
inverse dynamics when external forces are known and postures (and movements) can be
predicted. Several software programs which can in some cases be integrated with computeraided
design (CAD) applications allow for such analyses. Note that these models usually are
static (assume accelerations to be zero), and the validity of the analysis will depend on the
validity of the posture predictions made by the software or the user.
An indication of how load magnitude, as expressed by the moment about a joint, relates
to the capacity of the musculoskeletal system can be obtained by comparison of the moments
during a task to maximum voluntary moments. Usually such comparisons are made with the
results of isometric strength tests (see Section 2.3). For example, lifting a 20-kg load manually
has been predicted to exceed the shoulder strength of about 30% of the general population,
whereas the same task performed with a hoist allowed over 95% to have sufficient
strength.6 Since many tasks are dynamic in nature and both joint angle and angular velocity
strongly affect the moment capacity, dynamic reference data are needed. As noted earlier,
however, such reference data are only partially available. Some commercial software packages
provide a comparison of joint moments with population strength data, though the latter
are usually static. Several studies have shown that inverse dynamics of human movement can provide
reliable and accurate estimates of joint moments. It should be noted, though, that joint
moments do not always provide a definitive answer as to the actual extent of musculoskeletal
loading, as will be discussed in the next paragraph. Further, since human motor behavior
can be quite variable, the reliability of moment estimates derived from limited numbers of
measurements, and more so when derived from model simulations, should be considered
with care. When comparative analyses are done, substantial differences in net moments (e.g.,
10%) will usually allow conclusions to be drawn with respect to musculoskeletal loading.
For normative interpretation of joint moments with data on muscle strength, it is recommended
that a margin of safety be included in view of the variability and sources of error
both in moment estimates and strength data.
First, a free-body diagram of the foot was created, and the reaction force at the ankle was calculated by equating the sum of the forces on this segment to its mass times acceleration. Next, the moment at the ankle was calculated from equating the sum of the moments to inertia times angular acceleration. Subsequently, the opposites of this force and moment were used as input for a free-body diagram of the lower leg and the reaction force and moment at the knee were calculated. Segment masses and moments of inertias cannot be directly measured when dealing with the human body. Therefore estimations need to be made on the basis of anthropometric models (see the discussion of fundamentals in Section 2.2). Obviously these estimations may introduce errors, and the magnitude of such errors can be gauged by making use of redundant information when all external forces have been measured. For example, the moment about the low back in lifting can be calculated on the basis of a model of the lower body (legs and pelvis) using measured ground reaction forces on each foot as input. This same moment can also be estimated using a model of the upper body (arms and trunk) and the object lifted. It has been shown that with a careful choice of anthropometric assumptions, errors in moment estimates will generally be below 10 N m. Accelerations can be measured or calculated from position data by double differentiation.
This involves labor-intensive measurements and is only feasible when at least a mockup of the situation to be analyzed is available. Consequently, in many ergonomic applications, accelerations are assumed to be zero, in which case only the static configuration of the human body needs to be known or predicted. This simplification will lead to underestimation of mechanical loads on the human body in dynamic tasks, which in some cases can be substantial (e.g., in manual lifting, the moments around the low back may be underestimated by a factor of 2). Such errors may lead to questionable conclusions, even in a comparative analysis. For instance, earlier studies comparing stoop and squat lifting techniques appear to have been biased toward favoring the squat technique due to the application of static models.
Consequently, early studies have often reported a lower low-back load in squat lifting as compared to stoop lifting, whereas more recent studies using dynamic models have reported the opposite.5 If an analysis of a dynamic task is performed assuming acceleration to be ze zro but inputting the measured external forces on the body into the analysis—the so-called quasidynamic approach—reasonable estimates of joint moments result. A second simplification often used is to assume that all movement and force exertion takes place in a single plane, which allows application of a 2D model. In analyses of asymmetric lifting tasks, this can cause significant and substantial errors in estimated moments around the low back (roughly 20% when the load is placed 30 outside of the primary plane of movement). At 10 of asymmetry, differences between 2D and 3D analyses have been found to be insignificant.
Data collection required for the estimation of net moments is usually not prohibitive in
a comparative analysis of working methods and techniques, since this can be done in a
laboratory mock-up setting. However, for monitoring and identification of the most stressful
tasks or task elements, field measurements covering long periods are desirable. In this case,
use of an inverse dynamics approach usually is prohibitive. Methods have been developed
to estimate moments based on measurements of the electrical activity of muscles, the latter
using electrodes applied on the skin overlying the muscle group of interest (electromyography,
or EMG). However, it has been shown that additional kinematic data and extensive
calibrations are needed to obtain valid estimates. Currently miniature kinematic sensors and
efficient calibration procedures are being developed and tested to facilitate this type of measurements.
Finally estimation of mechanical loads in the design stage can be done using
inverse dynamics when external forces are known and postures (and movements) can be
predicted. Several software programs which can in some cases be integrated with computeraided
design (CAD) applications allow for such analyses. Note that these models usually are
static (assume accelerations to be zero), and the validity of the analysis will depend on the
validity of the posture predictions made by the software or the user.
An indication of how load magnitude, as expressed by the moment about a joint, relates
to the capacity of the musculoskeletal system can be obtained by comparison of the moments
during a task to maximum voluntary moments. Usually such comparisons are made with the
results of isometric strength tests (see Section 2.3). For example, lifting a 20-kg load manually
has been predicted to exceed the shoulder strength of about 30% of the general population,
whereas the same task performed with a hoist allowed over 95% to have sufficient
strength.6 Since many tasks are dynamic in nature and both joint angle and angular velocity
strongly affect the moment capacity, dynamic reference data are needed. As noted earlier,
however, such reference data are only partially available. Some commercial software packages
provide a comparison of joint moments with population strength data, though the latter
are usually static. Several studies have shown that inverse dynamics of human movement can provide
reliable and accurate estimates of joint moments. It should be noted, though, that joint
moments do not always provide a definitive answer as to the actual extent of musculoskeletal
loading, as will be discussed in the next paragraph. Further, since human motor behavior
can be quite variable, the reliability of moment estimates derived from limited numbers of
measurements, and more so when derived from model simulations, should be considered
with care. When comparative analyses are done, substantial differences in net moments (e.g.,
10%) will usually allow conclusions to be drawn with respect to musculoskeletal loading.
For normative interpretation of joint moments with data on muscle strength, it is recommended
that a margin of safety be included in view of the variability and sources of error
both in moment estimates and strength data.
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