Force transducer design: a new approach combining nonlinear finite element analysis and robust design.

Designing a strain gage based force transducer is considered more of an art than an engineering process. Only general guidelines are available, and many trial and error iterations are needed to optimize the geometry and minimize the errors caused by nonlinear behavior of the structure. A new method, based on nonlinear finite element analysis and robust design principles, is proposed. A matrix of experiments considers relevant geometric and loading parameters. The behavior of the structure under different combinations of these parameters is determined by calculating the strain at different locations (suitable for strain gage installation) using finite element models. The nonlinear behavior of the transducer is identified by comparing the results of the nonlinear finite element analysis with those obtained using a linear finite element analysis. A signal-to-noise ratio is defined to quantify the nonlinearities and how the considered parameters affect them. An analysis of variance is employed to determine their relative influence. Based on the results of the statistical analysis, it is possible to identify the best value for each geometric parameter that would reduce, if not eliminate the nonlinearities. Once these optimal geometric parameters are chosen, a prototype can be built, instrumented with strain gages, and tested, to validate the obtained design. To illustrate this new proposed methodology, and appreciate its advantages over current practice of designing a force transducer, an example of the step-by-step procedure is illustrated considering a thin-wall cylindrical transducer.

Comparison of methods for the calculation of energy storage and return in a dynamic elastic response prosthesis.

The standard method used to calculate the ankle joint power contains deficiencies when applied to dynamic elastic response prosthetic feet. The standard model, using rotational power and inverse dynamics, assumes a fixed joint center and cannot account for energy storage, dissipation, and return. This study compared the standard method with new analysis models. First, assumptions of inverse dynamics were avoided by directly measuring ankle forces and moments. Second, the ankle center of rotation was corrected by including translational power terms. Analysis with below-knee amputees revealed that the conventional method overestimates ankle forces and moments as well as prosthesis energy storage and return. Results for efficiency of energy return were varied. Large differences between models indicate the standard method may have serious inadequacies in the analysis of certain prosthetic feet. This research is the first application of the new models to prosthetic feet, and suggests the need for additional research in gait analysis with energy-storing prostheses.

Inertially compensated force plate: a means for quantifying subject's ground reaction forces in non-inertial conditions.

A system for the measurement of forces in noninertial reference systems, and a possible solution to compensate force plate readings by means of accelerometers were investigated. If the force plate can be considered a rigid body, six linear accelerometers can measure all linear and angular accelerations of the instrument in 3-D space. However, by using nine accelerometers in a proper layout, the force and moment generated by the movement of the plate can be quantified in a way that eliminates the errors due to the time integration of the accelerations. By doing so, no temporal limits are imposed to the compensation. A one degree of freedom numerical model was implemented to evaluate the importance of main error sources in the estimation of inertial forces using accelerometers with different technical characteristics. The inertial compensation of the force plate along one axis was tested, and the performances of a piezoelectric accelerometer and a capacitive accelerometer were compared. With the proposed inertially compensated force plate, accelerations up to 5 g's in amplitude and frequencies from 0 to 100 Hz can be compensated by means of capacitive accelerometers. Such a device can be used for force measurements in moving vehicles, or any situation where the surface on which the instrument is mounted is moving or vibrating.

Significance of nonsagittal power terms in analysis of a dynamic elastic response prosthetic foot.

Dynamic elastic response prosthetic feet generally utilize a solid ankle, limiting dominant motion to the sagittal plane. However, researchers often use total rotational ankle joint power in the analysis of these feet. This investigation measured joint power terms in each plane for the Carbon Copy High Performance prosthetic foot. The significance of the frontal and transverse plane terms was assessed. Addition of these terms to the dominant sagittal power term revealed only slight differences, indicating that the sagittal power term is likely sufficient.

How force plate size influences the probability of valid gait data acquisition.

Acquiring valid data is one of the major difficulties in gait analysis. Our previous study proved that, using the currently commercially available force plates, there is a low probability that every trial will be successful, and some subjects will have to alter their gait pattern to have a successful trial. In the present study the possibility of using an instrumented floor consisting of more than two force places of small size was investigated. This appears as the most promising solution to simultaneously solve the contrasting requirements of avoiding double contact on each element while acquiring complete gait cycles. In this work the set of mathematical equations previously developed for systems of two force plates was extended to consider any number of plates. Using gait data of 280 subjects from The Ohio State University Gait Laboratory, a software simulation was developed and performed to analyze different combinations of element and system sizes, and to calculate the probability of a successful gait analysis trial.

Design and testing of a 6-component ballistocardiographic bed.

Ballistocardiography is a non-invasive technique for the assessment of the cardiac function. It consists in studying the resultant forces generated by the blood mass flowing in the cardio-circulatory system while the subject lies on an instrumented bed. In the past, ballistocardiography was in large part limited by the signal processing and data acquisition capabilities. Technology improvements have countered these limitations. Previous studies by the authors using a regular size force plate have shown the capability of detecting cardiac activity in the human body. However, many patients with severe disorders cannot stand on a force plate for the duration required to acquire adequate data. Thus, a force plate, which performs as a ballistocardiographic bed, would allow patients to lie down in a stable position while body tremor data are acquired. To evaluate this idea, a highly sensitive ballistocardiographic bed was built using strain gage technology. Then, using high-resolution data acquisition software, the sensitivity of the instrument and the capability to obtain ballistocardiographic data were tested. Future developments include the analysis of ballistocardiographic data obtained from the bed to search their possible relation with cardio-circulatory and neurologic pathologies.

A viscoelastic sphere model for the representation of plantar soft tissue during simulations.

Simulations of human body during locomotion require a realistic representation of the foot which is the major interacting part of the body with the environment. Most simulation models consider the foot to be a rigid link, and impose unrealistic kinematic conditions. This study utilizes a viscoelastic sphere model with realistic properties, which can be used to represent the plantar surface of the foot during locomotion. The mechanical properties of the sphere are identified using experimental data on heel pads (Valiant, 1984). To check the validity of the model the results of the experimental study are reproduced by simulating the impact tests. Sensitivity analyses of the model parameters are carried out. The model is found to be insensitive to variations in stiffness and damping properties. The change in the thickness of the soft tissue, however, affected the maximum force of deformation proportionally. A symmetrical pressure distribution for the sphere during impact is calculated. It is concluded that the viscoelastic sphere model, presented here, can be incorporated into a foot model to represent the plantar surface of the foot.

Average power spectral density of physiological tremor in normal subjects.

The measurement technologies currently available to quantitatively evaluate neurological tremors have several limitations. For this reason the assessment of disorders involving tremor is largely based on subjective clinical evaluation of the patient. The availability of a high-sensitivity, portable and easy to use instrument based on force plate technology, coupled with a customized data analysis protocol could represent a useful tool for the clinician. To verify such a hypothesis, baseline physiological tremor information in a standing posture was collected from normal subjects. A lightweight portable force plate was built and used in collecting vertical ground reaction force data, which was subsequently analyzed for frequency content and power spectral distribution. Repeatability of results in a group of subjects without any diagnosed neurological disorders, and intra-subject repeatability, as well as influence of footwear were investigated.

Oversampling data acquisition to improve resolution of digitized signals.

The ability to capture analog signals in a digital format suitable for subsequent storage, processing and analysis by a computer has revolutionized many scientific fields, including biomechanics. In the process of going from the analog signal to its digital representation, it is essential to maintain as much of the original signal content as possible. There is always a loss of information associated with the conversion from analog to digital, independently of how it is actually performed. The only possibility to reduce the loss of information is to increase the number of states or the resolution of the digital signal. The method presented here, based on the same theory used in oversampling analog to digital converters, is applicable to digital signals acquired using any converter. In most situations this method provides a feasible and inexpensive technique to significantly improve the amplitude resolution of the analog to digital conversion. This can be of fundamental importance when the information of interest is small in amplitude compared to the overall signal, or when subsequent ill-conditioned operations, like the computation of the derivatives of the signal, are to be performed.

Probability of valid gait data acquisition using currently available force plates.

A major difficulty in using force plates for gait analysis is to have a foot fall completely on the instrument while not having the other foot in contact with the same device. This translates into more trials (and time) required to obtain valid data. In order to estimate the probability of a successful trial, which is related to the overall number of trials required, the dimensional relationships between force plate, foot and gait cycle were investigated. In particular, it was analyzed how the dimensions of the plate, the size of foot, the step length and width affect the probability of having a successful trial when acquiring one or two subsequent foot falls using one or two force plates respectively. The equations obtained can also be used to estimate the force plate dimensions that allow for the minimum number of trials for a specific group of subjects. To illustrate this approach, commercially available force plate sizes were statistically evaluated using gait data collected in recent years at The Ohio State University Gait Laboratory from patients with different pathologies. The force plate length maximizing the probability of a successful trial was identified for this specific population.

The realization of a haptic (force feedback) interface device for the purpose of angioplasty surgery simulation.

Simulation is becoming an increasingly accepted method for training personnel for complex or high risk tasks. With the advent of modern Virtual Reality (VR) technology, such simulations are becoming more and more immersive. One significant limitation to the advance of this science is the challenges associated with simulating the touch or feel of various tasks in conjunction with VR simulations. This work has focused on creating and assessing the feasibility of haptic technology for high fidelity surgery simulation. It has culminated in a prototypical interface device to provide tactile feedback during the simulation of complex interventional radiology procedures such as Angioplasty. This device extends state of the art motion control, distributed computing processes, high resolution sensors for real-time feedback, and modular design techniques to accomplish these goals. The realization of the device, its capabilities, interfacing requirements, its limitations, and future extensions will be presented here.

The mechanics of drop landing on a flat surface--a preliminary study.

In an effort to investigate the mechanics of drop landing on a flat surface, bilateral performance characteristics during the landing were investigated. Two force plates were used as landing surfaces, and the six component kinetic time histories and the path of the center of pressure were measured for both feet. The forces were combined to obtain the resultant ground reaction force, allowing comparison between the global resultant and the forces developed by each leg. The results highlighted an asymmetry, and the presence of one dominant leg during the landing: the contact with the plate occurred with a delay between the dominant and non-dominant legs, and the forces applied to the plate were also unequal. Furthermore, due to the high rate of data acquisition and sensitivity of the force plates used, it was possible to correlate the peaks present in the global vertical reaction force with the impact of the different anatomical segments of each foot. The availability of such high resolution information presents to researchers and clinicians with more key identifiers to quantify various phenomena, potentially injury prevention, pathological diagnosis or quantification, and others.

Measurement of angular displacements using Hall effect transducers.

Hall effect transducers were studied as an alternative to limited-wear precision potentiometers and optical encoders in measuring angular displacements. Various design parameters are identified, and the optimum Hall effect transducer configuration is presented. Using this configuration, it was possible to measure an angular rotation of 140 degrees with a standard deviation of 0.5 degrees. Within the +/- 35 degrees mid-range of the total 140 degrees, the standard deviation improved to 0.1 degrees.

Quantitative assessment of gait determinants during single stance via a three-dimensional model--Part 1. Normal gait.

In this two-part paper, a variety of three-dimensional, dynamical models are constructed for simulating the single support phases of normal and pathological human gait. A major objective of this work is to quantify the influence of individual gait determinants on the ground reaction forces generated during normal, level walking. To this end, Part 1 presents a three-dimensional, seven degree-of-freedom model incorporating five of the six fundamental determinants of gait. On the basis of crude muscle-force and/or joint-moment trajectories, body-segmental motions and ground reaction forces are synthesized open loop. Through a quantitative comparison with experimental gait data, the model's predictions are evaluated. Our simulation results suggest that pelvic list is not as dominant a dynamical determinant as either stance knee flexion-extension or foot and knee interaction. Transverse pelvic rotation, however, makes an important contribution by limiting the magnitude of the horizontal ground reaction prior to opposite heel-strike.

Quantitative assessment of gait determinants during single stance via a three-dimensional model--Part 2. Pathological gait.

A three-dimensional model for normal gait formulated in Part 1 is now altered to simulate the dynamics of pathological walking. Mechanisms fundamental to the production of a normal gait pattern are systematically removed, in order to assess contributions from individual gait determinants. Four separate pathological cases are studied: a model neglecting ankle plantarflexor activity; absence of stance knee flexion-extension and foot and knee interaction; both pelvic list and transverse pelvic rotation removed; and finally, a model with all major gait determinants missing. These are used collectively to show that stance knee flexion-extension and foot and knee interaction successively dominate lower-extremity dynamical response during the single support phase of normal gait. The hip abductor muscles, while effecting pelvic list, serve to stabilize this limb, rather than actively determine whole-body vertical acceleration. Mechanisms compensating for a loss in joint motion are also explored. Complete ankle loss may be successfully compensated with increased hip abductor muscle activity; the loss of both ankle and knee, however, demand unacceptable levels of vertical pelvic displacement.

The dynamics of quadrupedal locomotion.

This paper presents a dynamical analysis of quadrupedal locomotion, with specific reference to an adult Nubian goat. Measurements of ground reaction forces and limb motion are used to assess variations in intersegmental forces, joint moments, and instantaneous power for three discernible gaits: walking, running, and jumping. In each case, inertial effects of the torso are shown to dominate to the extent that lower-extremity contributions may be considered negligible. Footforces generated by the forelimbs exceed those exerted by the hindlimbs; and, in general, ground reactions increase with speed. The shoulder and hip dominate mechanical energy production during walking, while the knee plays a more significant role in running. In both cases, however, the elbow absorbs energy, and by so doing functions primarily as a damping (control) element. As opposed to either walking or running, jumping requires total horizontal retardation of the body's center of mass. In this instance, generating the necessary vertical thrust amounts to energy absorption at all joints of the lower extremities.

On the construction, circuitry and properties of liquid metal strain gages.

A quick and easy method by which reliable and accurate liquid metal strain gages (LMSG) can be manufactured for use in measuring large strains within biological tissues has been developed. The circuitry used to power the gages is also simple and allows gage voltages to be recorded without the need for instrumentation amplifiers. An added advantage is that the gage output indicates absolute gage length rather than change in gage length. Lastly, evaluation of these gages error sensitivity has shown them to be acceptable for measurement of strains of magnitudes occurring within many soft tissues.

A numerical method for simulating the dynamics of human walking.

This paper presents a general method for simulating the movement of the lower extremity during human walking. It is based upon two separate algorithms: one for single support (an open kinematic chain), and the other for the double support phase (a closed-loop linkage). Central to each of these is the recursive Newton-Euler inverse dynamics algorithm, applicable, as given, to any serial, spatial linkage. For the unconstrained single support model, the Newton-Euler scheme is applied directly to numerically generate the equations of motion. In the case of double support, however, the kinematic constraint equations are used to first eliminate the redundant degrees of freedom, and then solve for the unknown ground reactions under the constrained limb. The attractiveness of the method is that it offers a compact alternative to manually deriving the equations defining a mathematical model for human gait.

An experimental and analytical study of impact forces during human jumping.

Impact forces during landing in dismounts from the horizontal bar onto regulation gymnastic mats and in jumping from a height of 0.45 m onto a hard surface were measured. A two degree-of-freedom dynamic model was developed to predict the forces in landing on the hard surface. The periods of the two peaks that can be identified from experimental data were used in the determination of the system parameters. The peak forces recorded in gymnasts' landing ranged from 8.2 to 11.6 times the body weight. Maximum forces in jumping from 0.45 m, which ranged from 5.0 to 7.0 times the body weight, were accurately predicted by the model.

Synthesis of human walking: a planar model for single support.

A mathematical model for the single support phase of normal, level, human walking is formulated. The motion of the lower extremity is synthesized using a preprogrammed set of inputs, recognized by the model as a simple collection of applied joint moments. Two mechanisms are forwarded as candidates for producing the observed peaks in the vertical ground reaction. The first, stance knee flexion-extension, generates the necessary level of whole-body vertical acceleration during the initial region of single support (opposite toe-off to heel-off). A model accounting for the determinants of foot and knee interaction then predicts the second peak to be the result of an increasing ankle moment in the region from heel-off to opposite heel-strike.