Model-Based Design and Optimization of Passive Shoulder Exoskeletons

2021 ◽  
Author(s):  
Ali Nasr ◽  
Spencer Ferguson ◽  
John McPhee
Keyword(s):  
Elevation Angle ◽  
Differential Algebraic Equations ◽  
Joint Torque ◽  
Algebraic Equations ◽  
Joint Torques ◽  
Design And Optimization ◽  
Passive Mechanism ◽  
Wide Range ◽  
Passive Exoskeleton ◽  
Selection Of

Abstract To physically assist workers in reducing musculoskeletal strain or to develop motor skills for patients with neuromuscular disabilities, recent research has focused on Exoskeletons (Exos). Designing active Exos is challenging due to the complex human geometric structure, the human-Exoskeleton wrench interaction, the kinematic constraints, and the selection of power source characteristics. Because of the portable advantages of passive Exos, designing a passive shoulder mechanism has been studied here. The study concentrates on modeling a 3D multibody upper-limb human-Exoskeleton, developing a procedure of analyzing optimal assistive torque profiles, and optimizing the passive mechanism features for desired tasks. The optimization objective is minimizing the human joint torques. For simulating the complex closed-loop multibody dynamics, differential-algebraic equations (DAE)s of motion have been generated and solved. Three different tasks have been considered, which are common in industrial environments: object manipulation, over-head work, and static pointing. The resulting assistive Exoskeleton’s elevation joint torque profile could decrease the specific task’s human shoulder torque. Since the passive mechanism produces a specific torque for a given elevation angle, the Exoskeleton is not versatile or optimal for different dynamic tasks. We concluded that designing a passive Exoskeleton for a wide range of dynamic applications is impossible. We hypothesize that augmenting an actuator to the mechanism can provide the necessary adjustment torque and versatility for multiple tasks.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Comparison of Modeling Techniques for a Landing Gear

2010 ◽  
Author(s):  
Rebecca Margetts ◽  
Roger F. Ngwompo
Keyword(s):  
Block Diagram ◽  
Differential Algebraic Equations ◽  
Landing Gear ◽  
Algebraic Equations ◽  
Bond Graphs ◽  
Aircraft Landing ◽  
Aircraft Landing Gear ◽  
Wide Range ◽  
Modeling Techniques ◽  
Computational Errors

A wide range of modeling techniques is available to the engineer. The objective of this paper is to compare some typical modeling techniques for the simulation of a multi-domain mechatronic system. Usual dynamic modeling methods, such as block diagrams and iconic diagrams, can cause problems for the engineer. Differential algebraic equations (DAEs) and algebraic loops can significantly increase simulation times and cause numeric errors. Bond graphs are less common in industry, and are presented here as a method which allows the engineer to easily identify causal loops and elements in differential causality. These can indicate DAEs in the underlying equations. An aircraft landing gear is given as an example of a multi-domain system, and is modeled as a block diagram, an iconic diagram and as a bond graph. The time to construct the model, time to solve and problems faced by the analyst are presented. Bond graphs offer distinct advantages in terms of the ease of implementing algebraic equations and visibility of causality. The time taken to model a system can be significantly reduced and the results appear free from computational errors. Bond graphs are therefore recommended for this type of multi-domain systems analysis.

scholarly journals An α-Model Parametrization Algorithm for Optimization with Differential-Algebraic Equations

2022 ◽  
Vol 12 (2) ◽  
pp. 890
Author(s):  
Paweł Dra̧g
Keyword(s):  
Optimization Algorithm ◽  
Numerical Optimization ◽  
Differential Algebraic Equations ◽  
Multiple Shooting ◽  
Small Range ◽  
Algebraic Equations ◽  
New Approach ◽  
Highly Nonlinear ◽  
Special Cases ◽  
Wide Range

An optimization task with nonlinear differential-algebraic equations (DAEs) was approached. In special cases in heat and mass transfer engineering, a classical direct shooting approach cannot provide a solution of the DAE system, even in a relatively small range. Moreover, available computational procedures for numerical optimization, as well as differential- algebraic systems solvers are characterized by their limitations, such as the problem scale, for which the algorithms can work efficiently, and requirements for appropriate initial conditions. Therefore, an αDAE model optimization algorithm based on an α-model parametrization approach was designed and implemented. The main steps of the proposed methodology are: (1) task discretization by a multiple-shooting approach, (2) the design of an α-parametrized system of the differential-algebraic model, and (3) the numerical optimization of the α-parametrized system. The computations can be performed by a chosen iterative optimization algorithm, which can cooperate with an outer numerical procedure for solving DAE systems. The implemented algorithm was applied to solve a counter-flow exchanger design task, which was modeled by the highly nonlinear differential-algebraic equations. Finally, the new approach enabled the numerical simulations for the higher values of parameters denoting the rate of changes in the state variables of the system. The new approach can carry out accurate simulation tests for systems operating in a wide range of configurations and created from new materials.

A Computer-Aided Environment for Analysis and Design of Mechanical Systems

1991 ◽  
Author(s):  
Hamid M. Lankarani ◽  
Behnam Bahr ◽  
Saeid Motavalli
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
General Purpose ◽  
Design System ◽  
Integrated Analysis ◽  
Algebraic Equations ◽  
Efficient Design ◽  
Analysis And Design ◽  
Wide Range

Abstract This paper presents the description of an ideal tool for analysis and design of complex multibody mechanical systems. It is in the form of a general-purpose computer program, which can be used for simulation of many different systems. The generality of this computer-integrated environment allows a wide range of applications with significant engineering importance. No matter how complicated the mechanical system under consideration is, a numerical multibody model of the system is constructed. The governing mixed differential/algebraic equations of motion are automatically formulated and numerically generated. State-of-the-art numerical techniques and computational methods are employed and developed which produce in the response of the system at discrete time junctures. Postprocessing of the results in the form of graphical images or real-time animations provides an enormous aid in visualizing motion of the system. The analysis package may be merged with an efficient design optimization algorithm. The developed integrated analysis/design system is a valuable tool for researchers, design engineers, and analysts of mechanical systems. This computer-integrated tool provides an important bridge between the classical decision making process by an engineer and the emerging technology of computers.

scholarly journals Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations—Part 2: the discrete least-squares problem

2021 ◽  
Author(s):  
Michael Hanke ◽  
Roswitha März
Keyword(s):  
Least Squares ◽  
Differential Algebraic Equations ◽  
Collocation Methods ◽  
Discrete Problem ◽  
Algebraic Equations ◽  
Least Squares Collocation ◽  
Least Squares Problem ◽  
Ill Posed ◽  
Natural Settings ◽  
Selection Of

AbstractIn the two parts of the present note we discuss questions concerning the implementation of overdetermined least-squares collocation methods for higher index differential-algebraic equations (DAEs). Since higher index DAEs lead to ill-posed problems in natural settings, the discrete counterparts are expected to be very sensitive, which attaches particular importance to their implementation. We provide in Part 1 a robust selection of basis functions and collocation points to design the discrete problem whereas we analyze the discrete least-squares problem and substantiate a procedure for its numerical solution in Part 2.

scholarly journals Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations—Part 1: basics and ansatz function choices

2021 ◽  
Author(s):  
Michael Hanke ◽  
Roswitha März
Keyword(s):  
Least Squares ◽  
Differential Algebraic Equations ◽  
Collocation Methods ◽  
Discrete Problem ◽  
Algebraic Equations ◽  
Least Squares Collocation ◽  
Ill Posed ◽  
Present Part ◽  
Natural Settings ◽  
Selection Of

AbstractIn the two parts of the present note we discuss several questions concerning the implementation of overdetermined least-squares collocation methods for higher index differential-algebraic equations (DAEs). Since higher index DAEs lead to ill-posed problems in natural settings, the discrete counterparts are expected to be very sensitive, which attaches particular importance to their implementation. In the present Part 1, we provide a robust selection of basis functions and collocation points to design the discrete problem. We substantiate a procedure for its numerical solution later in Part 2. Additionally, in Part 1, a number of new error estimates are proven that support some of the design decisions.

Ultraspherical Differentiation Method for Solving System of Initial Value Differential Algebraic Equations

2009 ◽  
Vol 9 (3) ◽  
pp. 226-237 ◽  
Author(s):  
M. El-kady ◽  
M.A. Ibrahim
Keyword(s):  
Nonlinear Programming ◽  
Differential Equations ◽  
Spectral Method ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Initial Value ◽  
Numerical Examples ◽  
Ultraspherical Polynomials ◽  
Differentiation Method ◽  
Wide Range

AbstractIn this paper, we introduce a new spectral method based on ultraspherical polynomials for solving systems of initial value differential algebraic equations. Moreover, the suggested method is applicable for a wide range of differential equations. The method is based on a new investigation of the ultraspherical spectral differentiation matrix to approximate the differential expressions in equations. The produced equations lead to algebraic systems and are converted to nonlinear programming. Numerical examples illustrate the robustness, accuracy, and efficiency of the proposed method.

Controlling a Dynamic System With Open and Closed Loops: Application to Ladder Climbing

1997 ◽  
Author(s):  
Janzen Lo ◽  
Dimitris Metaxas ◽  
Norman I. Badler
Keyword(s):  
Dynamic System ◽  
Closed Loop ◽  
Step Length ◽  
Initial Position ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Step Frequency ◽  
Joint Torques ◽  
Closed Loops ◽  
Baumgarte Stabilization

Abstract We develop a method for animating systems with open and closed loops and in particular ladder climbing for virtual world applications. Ladder climbing requires the modeling of dynamic open and closed-loop chains. We model the stance phase and the associated closed-loop dynamics, through the use of the Lagrange multiplier method which results in a system of differential algebraic equations (DAE). We use the Lagrange method for the dynamic formulation of the swing phase. The input to the algorithm is a given forward velocity, step length, step frequency and a chosen gait. The algorithm then determines the initial and final positions for each phase of ladder climbing. We use the Newton-Ralphson method to find the vector of joint torques that drives the dynamic system from the initial position to the final position. We use the Baumgarte stabilization method to achieve stability of the numerical integration. We present a series of real-time animations involving ladder climbing.

Torque-Angle Relationship for a 2D RRR-Type Serial Link Manipulator

2020 ◽  
Vol 12 (10) ◽  
pp. 1296-1299
Author(s):  
Anil Kumar Gillawat ◽  
Hemant Jayantilal Nagarsheth
Keyword(s):  
Joint Torque ◽  
Serial Links ◽  
Serial Link ◽  
Joint Torques ◽  
Serial Manipulators ◽  
Revolute Joints ◽  
Euler Approach ◽  
Torque Values ◽  
Torque Angle ◽  
Selection Of

This paper presents an application of Lagrange–Euler approach for dynamic analysis of three link with revolute type (RRR-type) rigid serial manipulators. MATLAB code is programmed for Lagrange– Euler approach for RRR-type serial manipulator for generating joint torque equations and plotting these joint torque values for given range of angular rotations. This study is useful for understanding the effect of combinations of link rotation on joint torque behaviour. Maximum value of required joint torques obtained can be used for selection of motors for any mechanism with serial links with revolute joints performing given task.

Stabilization of Baumgarte’s Method Using the Runge-Kutta Approach

2002 ◽  
Vol 124 (4) ◽  
pp. 633-641 ◽  
Author(s):  
Shih-Tin Lin ◽  
Jiann-Nan Huang
Keyword(s):  
Equations Of Motion ◽  
Constraint Equation ◽  
Correct Choice ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Runge Kutta Method ◽  
Dae Systems ◽  
Numerical Integration Methods ◽  
Runge Kutta ◽  
Selection Of

The dynamic equations of motion of the constrained multibody mechanical system are mixed differential-algebraic equations (DAE). The DAE systems cannot be solved using numerical integration methods that are commonly used for solving ordinary differential equations. To solve this problem, Baumgarte proposed a constraint stabilization method in which a position and velocity terms were added in the second derivative of the constraint equation. The disadvantage of this method is that there is no reliable method for selecting the coefficients of the position and velocity terms. Improper selection of these coefficients can lead to erroneous results. In this study, stability analysis methods in digital control theory are used to solve this problem. Correct choice of the coefficients for the Runge-Kutta method is found.

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