Moshe B. Fuchs

A myosignal-based powered exoskeleton system

This paper studies the integration of a human arm with a powered exoskeleton (orthotic device) and its experimental implementation in an elbow joint, naturally controlled by the human. The human-machine interface was set at the neuromuscular level, by using the neuromuscular signal (EMG) as the primary command signal for the exoskeleton system. The EMG signal along with the joint kinematics were fed into a myoprocessor which in turn predicted the muscle moments on the elbow joint. The moment-based control system integrated myoprocessor moment prediction with feedback moments measured at the human arm/exoskeleton and external load/exoskeleton interfaces. The exoskeleton structure under study was a two-link, two-joint mechanism, corresponding to the arm limbs and joints, which was mechanically linked by the human operator. Four indices of performance were used to define the quality of the human/machine integration and to evaluate the operational envelope of the system. Experimental results indicate the feasibility of an EMG-based power exoskeleton system as an integrated human-machine system using high-level neurological signals.

Performances of Hill-type and neural network muscle models—toward a myosignal-based exoskeleton

Muscle models are the essential components of any musculoskeletal simulation. In addition, muscle models which are incorporated in neural-based prosthetic and orthotic devices may significantly improve their performance. The aim of the study was to compare the performances of two types of muscle models in terms of predicting the moments developed at the human elbow joint complex based on joint kinematics and neuromuscular activity. The performance evaluation of the muscle models was required to implement them in a powered myosignal-driven exoskeleton (orthotic device). The experimental setup included a passive exoskeleton capable of measuring the joint kinematics and dynamics in addition to the muscle myosignal activity (EMG). Two types of models were developed and analyzed: (i) a Hill-based model and (ii) a neural network. The task, which was selected for evaluating the muscle models performance, was the flexion-extension movement of the forearm with a hand-held weight. For this task the muscle model inputs were the normalized neural activation levels of the four main flexor-extensor muscles of the elbow joint, and the elbow joint angle and angular velocity. Using this inputs, the muscle model predicted the moment applied on the elbow joint during the movement. Results indicated a good performance of the Hill model, although the neural network predictions appeared to be superior. Relative advantages and shortcomings of both approaches were presented and discussed.

Trabecular bone adaptation with an orthotropic material model

Most bone adaptation algorithms, that attempt to explain the connection between bone morphology and loads, assume that bone is effectively isotropic. An isotropic material model can explain the bone density distribution, but not the structure and pattern of trabecular bone, which clearly has a mechanical significance. In this paper, an orthotropic material model is utilized to predict the proximal femur trabecular structure. Two hypotheses are combined to determine the local orientation and material properties of each element in the model. First, it is suggested that trabecular directions, which correspond to the orthotropic material axes, are determined locally by the maximal principal stress directions due to the multiple load cases (MLC) the femur is subject to. The second hypothesis is that material properties in each material direction can be determined using directional stimuli, thus extending existing adaptation algorithms to include directionality. An algorithm is utilized, where each iteration comprises of two stages. First, material axes are rotated to the direction of the largest principal stress that occurs from a multiple load scheme applied to the proximal femur. Next, material properties are modified in each material direction, according to a directional stimulus. Results show that local material directions correspond with known trabecular patterns, reproducing all main groups of trabeculae very well. The local directional stiffnesses, degree of anisotropy and density distribution are shown to conform to real femur morphology.

Optimal design of infinite repetitive structures

An approach for designing optimal repetitive structures under arbitrary static loading is presented. It is shown that the analysis of such infinite structures can be reduced to the analysis of the repeating module under transformed loading and boundary conditions. Consequently, both the design parameters and the analysis variables constitute a relatively small set which facilitates the optimization process. The approach hinges on the representative cell method. It is based on formulating the analysis equations and the continuity conditions for a sequence of typical modules. Then, by means of the discrete Fourier transform this problem translates into a boundary value problem of a representative cell in transformed variables, which can be solved by any appropriate analytical or numerical method. The real structural response any-where in the structure is then obtained by the inverse transform. The sensitivities can also be calculated on the basis of the sensitivities of the representative cell. The method is illustrated by the design for minimum compliance with a volume constraint of an infinite plane truss. It is shown that by employing this analysis method within an optimal design scheme one can incorporate a reduced analysis problem in an intrinsically small design space.

Explicit optimum design

Abstract The optimization of a trussed type structure of given geometry and material properties can be formulated as an exact and explicit mathematical programming problem in a mixed space of design variables and behaviour variables. Three techniques are presented, corresponding to the three classical analysis methods of structural theory. In the case of a single loading condition without variables linking, the proposed method is very efficient since it eliminates the problem of multiple reanalysis without increasing the dimensionality of the problem and the number of constraints. In the other cases the numerical efficiency of the technique depends on the specific problem to be solved.

Unimodal formulation of the analysis and design problems for framed structures

Abstract Traditionally the analysis of framed and trussed structures is carried out along similar, albeit different, paths. This is true chiefly in the force approach. The difference is to be attributed to the truss element having essentially one deformation mode, whereas bending elements are bimodal. It is shown that by means of an eigenvalue analysis, a uniform Timoshenko bending element can be decomposed into its constituent unimodal components. Consequently, frame and truss analysis are united into an identical set of equations, and solution techniques. Such an approach is shown to be beneficial, even for the automated design of framed structures.

Analytic representation of member forces in linear elastic redundant trusses

Abstract The process of designing a truss of given geometry and material properties, where the design variables are the cross-sectional areas of the bars is hampered by the need to reanalyse the structure many times until an acceptable design is obtained. Currently, approximate explicit analysis models, based on truncated linear Taylor series expansions, are used to evaluate the structural response at the various candidate design points. Due to the approximate nature of the analysis model, the structure is designed iteratively until convergence of both the analysis equations and the design process. This paper presents for the first time the exact analytic expressions of the internal loads in a truss which is subjected to static loads. The stress resultants are the ratio of two multilinear polynomials in the element stillness. The number of terms of the polynomials is equal to the number of combinations of statically determinate stable structures which can be derived from the original structures. The coefficients of the polynomial expansions can be obtained from equilibrium considerations and from enforcing “global” compatibility of deformations. The expressions are explicit in both the external loads and the element stiffness. The applicability of the analytic equations hinges on the number of combinations of statically determinate stable substructures. In the case of small size structures, the present explicit equations circumvent the need for approximate reanalysis. In common engineering structures, the number of stable subsets is prohibitively large, which renders the analytic expressions intractable. The exact analytic expressions may, however, constitute a starting point for constructing approximate explicit analysis equations of improved quality.

The explicit inverse of the stiffness matrix

Abstract In two recent papers the author has given the exact analytic expression of the internal forces in linear elastic structures composed of uniform prismatic elements. It was shown that the member forces are the ratios of two multilinear homogeneous polynomials in the unimodal stiffnesses of the elements of the structure. The order of the polynomials is equal to the number of nodal degrees of freedom of the structure. The number of terms of each polynomial is equal to the number of statically determinate stable substructures which can be derived from the original structure. The coefficients of the polynomials can be computed by employing the equilibrium equations and by enforcing global compatibility of deformations. It was found empirically that the coefficients of the polynomial in the denominator were numerically equal to the square of the determinants of the statics matrices of the respective statically determinate substructures. As a consequence, the denominator became the sum of the stiffness matrices of the statically determinate substructures. This is in fact the Binet-Cauchy form of the determinant of the stiffness matrix of the structure. Bearing in mind that the inverse of the stiffness matrix can be expressed as the ratio of the adjoint matrix of the stiffness matrix divided by the determinant of the stiffness matrix it became clear that the expressions of the stress resultants stem from an explicit expression of the adjoint. The explicit expression of the adjoint of the stiffness matrix lies at the heart of this paper. It is shown that the adjoint is a congruent transformation of the ( N -1) compound of the stiffness matrix, where N is the number of degrees of freedom of the structure. This cleared the way to use the Binct Cauchy theorem on the product of compound matrices to obtain an explicit expression for the adjoint and ipso facto , for the inverse of the stiffness matrix. Having now the displacements of the structure, the expression of the stress resultants, which was obtained independently, emerges in a very elegant manner. The member forces in a structure can be expressed as the weighted sum of the member forces in all its determinate substructures, when subjected to the applied loads. The weighting factors are the ratios of the determinants of (he stiffness matrices of the substructures, to the determinant of the stiffness matrix of the original structure. Both the explicit inverse of the stiffness matrix and the expression of the internal forces in the structure are, at present, of a theoretical nature. The number of terms involved in the polynomials is simply excessive for common engineering structures. However, ongoing reseach may yield more applicable expressions to be used, for instance, in (he field of automated design of structures. The theory is illustrated with the explicit analysis of a stayed mast.

The Explicit Expression of Internal Forces in Prismatic Membered Structures

ABSTRACT Analytic expressions for member forces in linear elastic redundant trusses have recently been given by the author. It was shown that the internal forces in a truss are the ratios of two multilinear homogeneous polynomials in the longitudinal stiffnesses of the elements of the structure. The order of the polynomials is equal to the number of nodal degrees of freedom of the structure. The number of terms of each polynomial is equal to the number of statically determinate stable substructures that can be derived from the original structure. It was shown that coefficients of the polynomials can be computed through the equilibrium equations and by enforcing global compatibility of deformations. This paper generalizes these results to the case of linear elastic structures, composed of uniform prismatic elements that have extensional, flexural, and torsional stiffness. This is done by replacing each bi-modal bending element with a unimodal moment element and a unimodal shear element. This allows the rep...

Norm Optimization Method in Structural Design

A general method for the minimization of a class of nondifferenti able merit functions is presented. The merit functions are defined as the maximum absolute value of the components of a vector of functions. These merit functions have gradient discontinuities in the design space and cannot be minimized by efficient algorithms of mathematical programming. The technique consists of sequential minimizations of an appropriate family of substitute merit functions, namely, the pth order norm of the vector. The efficiency of the technique is illustrated by the design of continuous beams for optimum geometry and is shown to give good results. It is further indicated that the method could be applied to general nonlinear inequality constrained mathematical programming problems and a few encouraging numerical examples are presented.