Zeitschriftenartikel: „Mechanical constraint“

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ANGELES, J., und SANGKOO LEE. „THE MODELLING OF HOLONOMIC MECHANICAL SYSTEMS USING A NATURAL ORTHOGONAL COMPLEMENT“. Transactions of the Canadian Society for Mechanical Engineering 13, Nr. 4 (Dezember 1989): 81–89. http://dx.doi.org/10.1139/tcsme-1989-0014.

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A computationally efficient and systematic algorithm for the modelling of constrained mechanical systems is developed and implemented in this paper. With this algorithm, the governing equations of mechanical systems comprised of rigid bodies coupled by holonomic constraints are derived by means of an orthogonal complement of the matrix of the velocity-constraint equations. The procedure is applicable to all types of holonomic mechanical systems, and it can be extended to cases including simple nonholonomic constraints. Holonomic mechanical systems having a simple Kinematic-chain structure, such as single-loop linkages and serial-type robotic manipulators, are analysed regarding the derivation of the matrix of the constraint equations and its orthogonal complement, and the computation of the constraint forces.

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GRILLO, S., F. MACIEL und D. PÉREZ. „CLOSED-LOOP AND CONSTRAINED MECHANICAL SYSTEMS“. International Journal of Geometric Methods in Modern Physics 07, Nr. 05 (August 2010): 857–86. http://dx.doi.org/10.1142/s0219887810004580.

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In this paper, we study the relationship between closed-loop mechanical systems (CLMS) and higher-order constrained systems (HOCS). We show that second-order constraints, i.e. constraints in acceleration, can be used to construct a CLMS, where the control law is given by the related constraint force. As an example we show that, by means of appropriate constraints of this kind, stabilization can be achieved for the inertia wheel pendulum. We also consider the inverse problem, that is to say: can every CLMS be constructed from a HOCS, i.e. can every control law be seen as the constraint force related to a given set of constraints? We answer this question affirmatively, reflecting a deep connection between feedback systems and systems with constraints. Also, we study when these constraints can be integrated to constraints in velocities. We prove that this is possible for CLMSs constructed by means of linear methods and also by some global ones, as the kinetic shaping method with symmetry.

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Adams, Jeffrey D., und Daniel E. Whitney. „Application of Screw Theory to Constraint Analysis of Mechanical Assemblies Joined by Features“. Journal of Mechanical Design 123, Nr. 1 (01.08.1999): 26–32. http://dx.doi.org/10.1115/1.1334858.

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Screw Theory is used to provide mathematical models of assembly features, allowing the determination of positioning constraints imposed on one part in an assembly by another part based on the geometry of the features that join them. Several feature types have been modeled, and it is easy to model new ones. A user of this theory is able to combine members of this set to join two parts and then determine whether or not the defined feature set over-, under-, or fully-constrains the location and orientation of the part. The ability to calculate the state of constraint of parts in an assembly is useful in supporting quantitative design of properly constrained assemblies in CAD systems. Locational over-constraint of parts can lead to assembleability problems or require deformation of parts in order to complete the assembly.

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Kim, S. S., und M. J. Vanderploeg. „QR Decomposition for State Space Representation of Constrained Mechanical Dynamic Systems“. Journal of Mechanisms, Transmissions, and Automation in Design 108, Nr. 2 (01.06.1986): 183–88. http://dx.doi.org/10.1115/1.3260800.

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This paper presents a numerical solution method for dynamic analysis of constrained mechanical systems. This method reduces a coupled set of differential and algebraic equations to state space form. The reduction uses an independent set of velocities which lie on the tangent plane of the constraint surface. The tangent plane is defined by the nullspace of constraint Jacobian matrix. The nullspace basis is found using QR decomposition of the constraint Jacobian matrix. Because the nullspace basis is not unique, directional continuity of the nullspace is difficult to preserve each time the Jacobiar is decomposed. This paper presents an updating algorithm that is used instead oj repeated decomposition. This preserves directional continuity of the Jacobian matrix and increases efficiency. State equations are then derived in terms of independent accelerations and therefore can efficiently be integrated. Generalized velocities are integrated with constraints to obtain positions. This method has demonstrated minimal constraint violations and improved efficiency. Numerical examples with singular configurations and redundant constraints are presented to demonstrate the effectiveness of the method.

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Barhorst, A. A., und L. J. Everett. „Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems“. Journal of Dynamic Systems, Measurement, and Control 117, Nr. 4 (01.12.1995): 559–69. http://dx.doi.org/10.1115/1.2801115.

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The multiple motion regime (free/constrained) dynamics of hybrid parameter multiple body (HPMB) systems is addressed. Impact response has characteristically been analyzed using impulse-momentum techniques. Unfortunately, the classical methods for modeling complex HPMB systems are energy based and have proven ineffectual at modeling impact. The problems are exacerbated by the problematic nature of time varying constraint conditions. This paper outlines the reformulation of a recently developed HPMB system modeling methodology into an impulse-momentum formulation, which systematically handles the constraints and impact. The starting point for this reformulation is a variational calculus based methodology. The variational roots of the methodology allows rigorous equation formulation which includes the complete nonlinear hybrid differential equations and boundary conditions. Because the methodology presented in this paper is formulated in the constraint-free subspace of the configuration space, both holonomic and nonholonomic constraints are automatically satisfied. As a result, the constraint-addition/deletion algorithms are not needed. Generalized forces of constraint can be directly calculated via the methodology, so the condition for switching from one motion regime to another is readily determined. The resulting equations provides a means to determine after impact velocities (and velocity fields for distributed bodies) which provide the after collision initial conditions. Finally the paper demonstrates, via example, how to apply the methodology to contact/impact in robotic manipulators and structural systems.

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Khusanov, Kahramanjon. „Selecting Control Parameters of Mechanical Systems with Servoconstraints“. E3S Web of Conferences 264 (2021): 04085. http://dx.doi.org/10.1051/e3sconf/202126404085.

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The research results on the derivation of equations of motion (a mathematical model) of a mechanical system constrained by holonomic constraints of the first and second kind, which contains only tangential components of the constraint of the second kind, are presented in the article. These tangential components are taken as control parameters. Besides, the controllability of the plate, considered in the Appel problem, is investigated.

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Cyril, X., J. Angeles und A. Misra. „DYNAMICS OF FLEXIBLE MULTIBODY MECHANICAL SYSTEMS“. Transactions of the Canadian Society for Mechanical Engineering 15, Nr. 3 (September 1991): 235–56. http://dx.doi.org/10.1139/tcsme-1991-0014.

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In this paper the formulation and simulation of the dynamical equations of multibody mechanical systems comprising of both rigid and flexible-links are accomplished in two steps: in the first step, each link is considered as an unconstrained body and hence, its Euler-Lagrange (EL) equations are derived disregarding the kinematic couplings; in the second step, the individual-link equations, along with the associated constraint forces, are assembled to obtain the constrained dynamical equations of the multibody system. These constraint forces are then efficiently eliminated by simple matrix multiplication of the said equations by the transpose of the natural orthogonal complement of kinematic velocity constraints to obtain the independent dynamical equations. The equations of motion are solved for the generalized accelerations using the Cholesky decomposition method and integrated using Gear’s method for stiff differential equations. Finally, the dynamical behaviour of the Shuttle Remote Manipulator when performing a typical manoeuvre is determined using the above approach.

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Zhang, Cheng-Yin, und Neng-Hui Zhang. „Mechanical Constraint Effect on DNA Persistence Length“. Molecules 27, Nr. 22 (11.11.2022): 7769. http://dx.doi.org/10.3390/molecules27227769.

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Persistence length is a significant criterion to characterize the semi-flexibility of DNA molecules. The mechanical constraints applied on DNA chains in new single-molecule experiments play a complex role in measuring DNA persistence length; however, there is a difficulty in quantitatively characterizing the mechanical constraint effects due to their complex interactions with electrostatic repulsions and thermal fluctuations. In this work, the classical buckling theory of Euler beam and Manning’s statistical theories of electrostatic force and thermal fluctuation force are combined for an isolated DNA fragment to formulate a quantitative model, which interprets the relationship between DNA persistence length and critical buckling length. Moreover, this relationship is further applied to identify the mechanical constraints in different DNA experiments by fitting the effective length factors of buckled fragments. Then, the mechanical constraint effects on DNA persistence lengths are explored. A good agreement among the results by theoretical models, previous experiments, and present molecular dynamics simulations demonstrates that the new superposition relationship including three constraint-dependent terms can effectively characterize changes in DNA persistence lengths with environmental conditions, and the strong constraint-environment coupling term dominates the significant changes of persistence lengths; via fitting effective length factors, the weakest mechanical constraints on DNAs in bulk experiments and stronger constraints on DNAs in single-molecule experiments are identified, respectively. Moreover, the consideration of DNA buckling provides a new perspective to examine the bendability of short-length DNA.

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Hasanoglu, Mehmet Sinan, und Melik Dolen. „Feasibility enhanced particle swarm optimization for constrained mechanical design problems“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, Nr. 2 (08.12.2016): 381–400. http://dx.doi.org/10.1177/0954406216681593.

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Constrained optimization problems constitute an important fraction of optimization problems in the mechanical engineering domain. It is not uncommon for these problems to be highly-constrained where a specialized approach that aims to improve constraint satisfaction level of the whole population as well as finding the optimum is deemed useful especially when the objective functions are very costly. A new algorithm called Feasibility Enhanced Particle Swarm Optimization (FEPSO), which treats feasible and infeasible particles differently, is introduced. Infeasible particles in FEPSO do not need to evaluate objective functions and fly only based on social attraction depending on a single violated constraint, called the activated constraint, which is selected at each iteration based on constraint priorities and flight occurs only along dimensions of the search space to which the activated constraint is sensitive. To ensure progressive improvement of constraint satisfaction, particles are not allowed to violate a satisfied constraint in FEPSO. The highly-constrained four-stage gear train problem and its two variants introduced in this paper are used to assess the effectiveness of FEPSO. The results suggest that FEPSO is effective and consistent in obtaining feasible points, finding good solutions, and improving the constraint satisfaction level of the swarm as a whole.

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Phong, Dinh Van. „Successive algorithm for construction of equation of motion of constrained mechanical systems“. Vietnam Journal of Mechanics 24, Nr. 2 (30.06.2002): 101–14. http://dx.doi.org/10.15625/0866-7136/24/2/6612.

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The article devotes to the construction of equations of motion of constrained mechanical systems. The constraint conditions are successively appended to the already defined systems. Therefore the algorithm is very flexible and allows studying the separate constraints more in detail. For illustration of consequent steps of the algorithm one simple example is shown.

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LALLOUET, ARNAUD, und ANDREÏ LEGTCHENKO. „Partially defined constraints in constraint-based design“. Artificial Intelligence for Engineering Design, Analysis and Manufacturing 20, Nr. 4 (November 2006): 297–311. http://dx.doi.org/10.1017/s0890060406060227.

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In constraint-based design, components are modeled by variables describing their properties and subject to physical or mechanical constraints. However, some other constraints are difficult to represent, like comfort or user satisfaction. Partially defined constraints can be used to model the incomplete knowledge of a concept or a relation. Instead of only computing with the known part of the constraint, we propose to complete its definition by using machine-learning techniques. Because constraints are actively used during solving for pruning domains, building a classifier for instances is not enough: we need a solver able to reduce variable domains. Our technique is composed of two steps: first we learn a classifier for the constraint's projections and then we transform the classifier into a propagator. We show that our technique not only has good learning performances but also yields a very efficient solver for the learned constraint.

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Lv, Gang, Shou Wen Fan, Lian Xu Zhou und Xin Nuo He. „Design Defects Immune Identification Methodology for Mechanical Products Based on Directed Graph of Assembly Constraint Relationship“. Applied Mechanics and Materials 365-366 (August 2013): 104–10. http://dx.doi.org/10.4028/www.scientific.net/amm.365-366.104.

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In order to identify design defects in mechanical product quickly and accurately, geometric constraints relationships between mechanical parts are formulated as critical functions, assembly constraint relationship (ACR) matrix is established based on encoding of geometric constraints between mechanical parts. Directed graph is employed to describe constraint relationship of ACR matrix, the node in directed graph denotes parts number, data structure of node stores the design parameters of mechanical parts, weights of directed graph arcs represents geometric constraint type. Weights of directed graph arcs are treated as antigen, design defects for mechanical parts are treated as antibody, mutation rules such as trimming, splicing and replacement is employed to identify design defects of antigen gene. Identification example of spherical mechanism demonstrates effectiveness and accuracy of above methodologies.

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Yang, B. „Eigenvalue Inclusion Principles for Distributed Gyroscopic Systems“. Journal of Applied Mechanics 59, Nr. 3 (01.09.1992): 650–56. http://dx.doi.org/10.1115/1.2893773.

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In his famous treatise The Theory of Sound, Rayleigh enunciated an eigenvalue inclusion principle for the discrete, self-adjoint vibrating system under a constraint. According to this principle, the natural frequencies of the discrete system without and with the constraint are alternately located along the positive real axis. Although it is commonly believed that the same rule also applied for distributed vibrating systems, no proof has been given for the distributed gyroscopic system. This paper presents several eigenvalue inclusion principles for a class of distributed gyroscopic systems under pointwise constraints. A transfer function formulation is proposed to describe the constrained system. Five types of nondissipative constraints and their effects on the system natural frequencies are studied. It is shown that the transfer function formulation is a systematic and convenient way to handle constraint problems for the distributed gyroscopic system.

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Skakoon, James G. „Exact Constraint“. Mechanical Engineering 131, Nr. 09 (01.09.2009): 32–36. http://dx.doi.org/10.1115/1.2009-sep-2.

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This article discusses the significance of knowing exact constraint in successful design. Although not traditionally taught in mechanical engineering curricula, and not universally known among mechanical engineers, principles of exact constraint have been around for over a century. Designers of precision instruments have for decades used exact constraint, without which they simply would not achieve the precision required by many devices. Exact constraint has a well-developed theory applicable for design engineers. Applying it improves designs by avoiding over-constraint. Over-constrained designs lead to high stresses, tight tolerances, looseness, binding, and difficult assembly. Exact constraint is easier to picture in two dimensions than in three. In two dimensions, there are three degrees of freedom: two translations and one rotation. Some useful compromises to exact constraint are pinned and bolted connections, ball bearings, and tapered roller bearings. Another is in-situ adjustment of over-constraint as in, for example, the thread-adjusted foot pads of a clothes dryer or washing machine.

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Zeidis, Igor, Klaus Zimmermann, Steffen Greiser und Julia Marx. „Analysis of Kinematic Constraints in the Linkage Model of a Mecanum-Wheeled Robot and a Trailer with Conventional Wheels“. Applied Sciences 13, Nr. 13 (23.06.2023): 7449. http://dx.doi.org/10.3390/app13137449.

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Mechanical systems that consist of a four-wheeled or two-wheeled robot with Mecanum wheels and a two-wheeled trailer with conventional wheels are considered. The kinematic characteristics of the mechanical systems under consideration of holonomic and non-holonomic constraints are presented and compared. From this, it is shown that the structure of the kinematic constraint equations for mobile systems with a trailer does not apply to Chaplygin’s dynamic equations. If the mechanical system is not Chaplygin’s system, then the dynamic equations cannot be integrated separately from the equations of kinematic constraints. This is the difference between the kinematic constraint equations for the robot-trailer system and the constraint equations for a single robot with Mecanum wheels. Examples of numerical calculations using the equations of kinematic constraints are given.

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Blajer, W., D. Bestle und W. Schiehlen. „An Orthogonal Complement Matrix Formulation for Constrained Multibody Systems“. Journal of Mechanical Design 116, Nr. 2 (01.06.1994): 423–28. http://dx.doi.org/10.1115/1.2919396.

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A method is proposed for the automatic generation of an orthogonal complement matrix to the constraint matrix for the dynamic analysis of constrained multibody systems. The clue for this method lies in the determination of local constraint matrices and their orthogonal complements relative to the local reference frames of particular constrained points. These matrices are then transformed into the system’s configuration space in order to form the final constraint matrix and its orthogonal complement. The avoidance of singularities in the formulation is discussed. The method is especially suited for the dynamic analysis of multibody systems with many constraints and/or closed-loops.

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Djerassi, S., und H. Bamberger. „Constraint Forces and the Method of Auxiliary Generalized Speeds“. Journal of Applied Mechanics 70, Nr. 4 (01.07.2003): 568–74. http://dx.doi.org/10.1115/1.1572902.

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This paper deals with noncontributing forces, usually called constraint forces or reaction forces, arising in simple, nonholonomic multibody systems. These forces are related to two kinds of constraints, namely, kinematical constraints—derived from kinematical requirements, and auxiliary constraints, introduced for the purpose of constraint forces determination. Here, the method of “auxiliary generalized speeds” is used to bring into evidence constraint forces related to the two kinds of constraints. It is shown that auxiliary generalized speeds can always be chosen in a way that gives rise to additional equations each having one measure number of a constraint force as an unknown. Motion equations can thus be generated and solved without regard to constraint forces determination; and constraint forces can be determined with no matrix inversion, at a minimal computational cost.

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Udwadia, F. E., und R. E. Kalaba. „Explicit Equations of Motion for Mechanical Systems With Nonideal Constraints“. Journal of Applied Mechanics 68, Nr. 3 (09.10.2000): 462–67. http://dx.doi.org/10.1115/1.1364492.

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Since its inception about 200 years ago, Lagrangian mechanics has been based upon the Principle of D’Alembert. There are, however, many physical situations where this confining principle is not suitable, and the constraint forces do work. To date, such situations are excluded from general Lagrangian formulations. This paper releases Lagrangian mechanics from this confinement, by generalizing D’Alembert’s principle, and presents the explicit equations of motion for constrained mechanical systems in which the constraints are nonideal. These equations lead to a simple and new fundamental view of Lagrangian mechanics. They provide a geometrical understanding of constrained motion, and they highlight the simplicity with which Nature seems to operate.

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Shi, Heng, Yanbing Liang und Zhaohui Liu. „An approach to the dynamic modeling and sliding mode control of the constrained robot“. Advances in Mechanical Engineering 9, Nr. 2 (Februar 2017): 168781401769047. http://dx.doi.org/10.1177/1687814017690470.

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An approach to the dynamic modeling and sliding mode control of the constrained robot is proposed in this article. On the basis of the Udwadia–Kalaba approach, the explicit equation of the constrained robot system is obtained first. This equation is applicable to systems with either holonomic or non-holonomic constraints, as well as with either ideal or non-ideal constraint forces. Second, fully considering the uncertainty of the non-ideal force, that is, the dynamic friction in the constrained robot system, the sliding mode control algorithm is put forward to trajectory tracking of the end-effector on a vertical constrained surface to obtain actual values of the unknown constraint force. Moreover, model order reduction method is innovatively used in the Udwadia–Kalaba approach and sliding mode controller to reduce variables and simplify the complexity of the calculation. Based on the demonstration of this novel method, a detailed robot system example is finally presented.

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Agrawal, R., G. L. Kinzel, R. Srinivasan und K. Ishii. „Engineering Constraint Management Based on an Occurrence Matrix Approach“. Journal of Mechanical Design 115, Nr. 1 (01.03.1993): 103–9. http://dx.doi.org/10.1115/1.2919305.

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In many mechanical systems, the mathematical model can be characterized by m nonlinear equations in n unknowns. The m equations could be either equality constraints or active inequality constraints in a constrained optimization framework. In either case, the mathematical model consists of (n-m) degrees of freedom, and (n-m) unknowns must be specified before the system can be analyzed. In the past, designers have often fixed the set of (n-m) specification variables and computed the remaining n variables using the n equations. This paper presents constraint management algorithms that give the designer complete freedom in the choice of design specifications. An occurrence matrix is used to store relationships among design parameters and constraints, to identify dependencies among the variables, and to help prevent redundant specification. The interactive design of a torsion bar spring is used to illustrate constraint management concepts.

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Lin, Shih-Tin, und Ming-Chong Hong. „Stabilization Method for Numerical Integration of Multibody Mechanical Systems“. Journal of Mechanical Design 120, Nr. 4 (01.12.1998): 565–72. http://dx.doi.org/10.1115/1.2829316.

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The object of this study is to solve the stability problem for the numerical integration of constrained multibody mechanical systems. The dynamic equations of motion of the constrained multibody mechanical system are mixed differential-algebraic equations (DAE). In applying numerical integration methods to this equation, constrained equations and their first and second derivatives must be satisfied simultaneously. That is, the generalized coordinates and their derivatives are dependent. Direct integration methods do not consider this dependency and constraint violation occurs. 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 Adams method are found for both fixed and variable integration step size.

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Yoon, S., R. M. Howe und D. T. Greenwood. „Geometric Elimination of Constraint Violations in Numerical Simulation of Lagrangian Equations“. Journal of Mechanical Design 116, Nr. 4 (01.12.1994): 1058–64. http://dx.doi.org/10.1115/1.2919487.

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Conventional holonomic or nonholonomic constraints are defined as geometric constraints. The total enregy of a dynamic system can be treated as a constrained quantity for the purpose of accurate numerical simulation. In the simulation of Lagrangian equations of motion with constraint equations, the Geometric Elimination Method turns out to be more effective in controlling constraint violations than any conventional methods, including Baumgarte’s Constraint Violation Stabilization Method (CVSM). At each step, this method first goes through the numerical integration process without correction to obtain updated values of the state variables. These values are then used in a gradient-based procedure to eliminate the geometric and energy errors simultaneously before processing to the next step. For small step size, this procedure is stable and very accurate.

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Gilmore, B. J., und R. J. Cipra. „Simulation of Planar Dynamic Mechanical Systems With Changing Topologies—Part 1: Characterization and Prediction of the Kinematic Constraint Changes“. Journal of Mechanical Design 113, Nr. 1 (01.03.1991): 70–76. http://dx.doi.org/10.1115/1.2912753.

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Due to changes in the kinematic constraints, many mechanical systems are described by discontinuous equations of motion. This paper addresses those changes in the kinematic constraints which are caused by planar bodies contacting and separating. A strategy to automatically predict and detect the kinematic constraint changes, which are functions of the system dynamics, is presented in Part 1. The strategy employs the concepts of point to line contact kinematic constraints, force closure, and ray firing together with the information provided by the rigid bodies’ boundary descriptions, state variables, and reaction forces to characterize the kinematic constraint changes. Since the strategy automatically predicts and detects constraint changes, it is capable of simulating mechanical systems with unpredictable or unforessen changes in topology. Part 2 presents the implementation of the characterizations into a simulation strategy and presents examples.

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Udwadia, Firdaus E., und Phailaung Phohomsiri. „Explicit Poincaré equations of motion for general constrained systems. Part I. Analytical results“. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, Nr. 2082 (06.03.2007): 1421–34. http://dx.doi.org/10.1098/rspa.2007.1825.

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This paper gives the general constrained Poincaré equations of motion for mechanical systems subjected to holonomic and/or nonholonomic constraints that may or may not satisfy d'Alembert's principle at each instant of time. It also extends Gauss's principle of least constraint to include quasi-accelerations when the constraints are ideal, thereby expanding the compass of this principle considerably. The new equations provide deeper insights into the dynamics of multi-body systems and point to new ways for controlling them.

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Rajagopal, K. R., und A. R. Srinivasa. „On the nature of constraints for continua undergoing dissipative processes“. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, Nr. 2061 (28.07.2005): 2785–95. http://dx.doi.org/10.1098/rspa.2004.1385.

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When dealing with mechanical constraints, it is usual in continuum mechanics to enforce ideas that stem from the seminal work of Bernoulli and D'Alembert and require that internal constraints do no work. The usual procedure is to split the stress into a constraint response and a constitutively determined response that does not depend upon the variables that appear in the constraint response (i.e. the Lagrange multiplier), and further requiring that the constraint response does no work. While this is adequate for hyperelastic materials, it is too restrictive in the sense that it does not permit a large class of useful models such as incompressible fluids whose viscosity depends upon the pressure—a model that is widely used in elastohydrodynamics. The purpose of this short paper is to develop a purely mechanical theory of continua with an internal constraint that does not appeal to the requirement of worklessness. We exploit a geometrical idea of normality of the constraint response to a surface (defined by the equation of constraint) in a six-dimensional Euclidean space to obtain (i) a unique decomposition of the stress into a determinate and a constraint part such that their inner product is zero, (ii) a completely general constraint response—even constraint equations that are nonlinear in the symmetric part of the velocity gradient D as well as when the coefficients in the determinate part depend upon the constraint response and (iii) a second order partial differential equation for the determination of the constraint response. The geometric approach presented here is in keeping with the ideas of Gauss concerning constraints in classical particle mechanics.

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YANG, C., Q. WU und G. JOYCE. „EFFECTS OF CONSTRAINTS ON BIPEDAL BALANCE CONTROL DURING STANDING“. International Journal of Humanoid Robotics 04, Nr. 04 (Dezember 2007): 753–75. http://dx.doi.org/10.1142/s0219843607001230.

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In this work, the effects of the gravity constraint, friction constraint, center of pressure (COP) constraint, and tip-over constraint on balance control of a simplified two-dimensional biped during standing are investigated. The bounds imposed on the control torque due to the constraints are first determined. Such control bounds have significant effects on designing balance control laws and can be used to predict the type of falls if the constraint is violated. It is found that there exists a critical angular velocity, above which, regardless of the control torque, the constraints will be violated. It is also found that the gravity constraint is the least important since it is always satisfied when the friction constraint is satisfied. For the biped under study, the friction constraint determines the critical angular velocity in most of the region around the upright position, while the COP constraint dictates the bounds of the control torque. Since the tip-over constraint is equivalent to the COP constraint as both feet are on the same level ground, it is concluded that the tip-over constraint is the most important when the magnitude of the angular velocity is below the critical value.

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Yang, Wei, Liang Lifu und Liang Zhongwei. „On mechanical property of constraint“. Applied Mathematics and Mechanics 16, Nr. 11 (November 1995): 1095–103. http://dx.doi.org/10.1007/bf02484376.

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Liu, Min, Xianmin Zhang und Sergej Fatikow. „Design of flexure hinges based on stress-constrained topology optimization“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, Nr. 24 (30.09.2016): 4635–45. http://dx.doi.org/10.1177/0954406216671346.

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Stress concentration is one of the disadvantages of flexure hinges. It limits the range of motion and reduces the fatigue life of mechanisms. This article designs flexure hinges by using stress-constrained topology optimization. A weighted-sum method is used for converting the multi-objective topology optimization of flexure hinges into a single-objective problem. The objective function is presented by considering the compliance factors of flexure hinges in the desired and other directions. The stress constraint and other constraint conditions are developed. An adaptive normalization of the P-norm of the effective von Mises stresses is adopted to approximate the maximum stress, and a global stress measure is used to control the stress level of flexure hinges. Several numerical examples are performed to indicate the validity of the method. The stress levels of flexure hinges without and with stress constraints are compared. In addition, the effects of mesh refinement and output spring stiffness on the topology results are investigated. The stress constraint effectively eliminates the sharp corners and reduces the stress concentration.

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Wang, J. T. „Inverse Dynamics of Constrained Multibody Systems“. Journal of Applied Mechanics 57, Nr. 3 (01.09.1990): 750–57. http://dx.doi.org/10.1115/1.2897087.

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A method for analyzing constrained multibody systems is presented. The method is applicable to a class of problems in which the multibody system is subjected to both force and kinematic constraints. This class of problems cannot be solved by using the classical methods. The method is based upon the concept of partial velocity and generalized forces of Kane’s method to permit the choice of constraint forces for fulfilling both kinematic and force constraints. Thus, the constraint forces or moments at convenient points or bodies may be specified in any desired form. For many applications, the method also allows analysts to choose a constant coefficient matrix for the undetermined force term to greatly reduce the burden of repeatedly computing its orthogonal complement matrix in solving the differential algebraic dynamic equations. Two examples illustrating the concepts are presented.

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Wong, R., und D. B. Cherchas. „Hybrid Constraint Space Dynamics and Control for Robot Manipulators“. Journal of Vibration and Control 10, Nr. 11 (November 2004): 1563–84. http://dx.doi.org/10.1177/1077546304042025.

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In this paper we present the development of a hybrid constraint space dynamics modeling technique and position/force controller for robotic manipulator control in constrained environments. The method utilizes a constraint space dynamic model in which the model coordinates are displacement along the constraint trajectory and the normal force between the manipulator end-effector and the environment. The dynamic model is constructed by transforming the conventional joint space manipulator dynamics equations into their constraint space equivalents through the application of mapping functions, which relate differential displacements and velocities in the constraint space coordinate system to the joint space coordinate system. Control algorithms may then be applied to the simplified dynamic structure of the constraint space equations of motion in order to produce a vector of manipulator joint torques which will satisfy both position and force requirements along the environmental constraint. Actuator constraints and momentum compensating techniques are also used to ensure that the position and force control problems are completely decoupled from one another. A computer torque control algorithm is then applied to a two-degrees-of-freedom prismatic robot and simulations are carried out with two different constraint surfaces, i.e. a planar, and a concave circular environment. The results of these simulations show that the controller, implemented in hybrid constraint space provides good position and force control.

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Liang, C. G., und George M. Lance. „A Differentiable Null Space Method for Constrained Dynamic Analysis“. Journal of Mechanisms, Transmissions, and Automation in Design 109, Nr. 3 (01.09.1987): 405–11. http://dx.doi.org/10.1115/1.3258810.

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A geometric approach to the solution of the dynamic response of constrained mechanical systems is proposed. A continuous and differentiable basis of the constraint null space is automatically generated using the Gram-Schmidt process. The independent coordinates are obtained by transforming the physical velocity coordinates to the tangent hyperplane of the constraint surface. As a result the independent coordinates lie on the constraint surface and no constraint violation control is necessary.

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Sehitoglu, Huseyin. „Constraint Effect in Thermo-Mechanical Fatigue“. Journal of Engineering Materials and Technology 107, Nr. 3 (01.07.1985): 221–26. http://dx.doi.org/10.1115/1.3225805.

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Many structural members in service experience fluctuating loads and temperatures. Thermal stresses devlop on a contrained element if the temperature is cycled. Constraint exists in structural components due to temperature gradient, material anisotropy, and geometry effects. The equilibrium and compatibility equations determine the degree of constraint on the critcal component of the body. A two-bar structure is employed in this study to simulate different constraint conditions encountered in practice. The constraint types are termed (a) total, (b) partial, (c) over, and (d) notch constraint. Thermo-mechanical fatigue test results indicate that the fatigue lives decrease severely with increasing constraint, increasing temperature range and with the presence of notch or a defect.

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Wu, S. C., und E. J. Haug. „A Substructure Technique for Dynamics of Flexible Mechanical Systems With Contact-Impact“. Journal of Mechanical Design 112, Nr. 3 (01.09.1990): 390–98. http://dx.doi.org/10.1115/1.2912620.

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A substructure synthesis method is proposed to account for contact-impact effects in flexible components of mechanical systems. Components that may come into contact are divided into substructures, on each of which local deformation modes are defined to describe deformation fields of components. Constraint modes and fixed interface normal modes are used to account for elastic deformation within each substructure. A constraint addition-deletion technqiue is used to determine when contact occurs, account for the effect of contact constraints during the period of contact, and delete constraints after the completion of the contact event. Lagrange multipliers associated with the contact constraints, which represent contact forces, are used to determine the time of separation of contacting nodes. Use of the method is illustrated for longitudinal and transverse impact of elastic bars.

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Chang, C. O., und P. E. Nikravesh. „Optimal Design of Mechanical Systems With Constraint Violation Stabilization Method“. Journal of Mechanisms, Transmissions, and Automation in Design 107, Nr. 4 (01.12.1985): 493–98. http://dx.doi.org/10.1115/1.3260751.

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This paper presents a comprehensive optimal design procedure for constrained dynamic systems. The constraint violation stabilization method for dynamic analysis of mechanical systems is briefly reviewed. A direct differentiation method is used to form the equations of design sensitivity analysis based on a constraint violation stabilization method. The sensitivity equations and the equations of motion are integrated simultaneously to obtain the system response, as well as the state sensitivity matrices. All integrations are performed using a multistep predictor-corrector method. The first order design sensitivity matrix is used to calculate the gradient of cost function and the performance constraint during the optimization procedure. An optimization routine is linked to the analysis/sensitivity algorithm. Two examples are given which illustrate the effectiveness of this method for determining the optimal design of a system.

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Ostrovskaya, S., und J. Angeles. „Nonholonomic Systems Revisited Within the Framework of Analytical Mechanics“. Applied Mechanics Reviews 51, Nr. 7 (01.07.1998): 415–33. http://dx.doi.org/10.1115/1.3099013.

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Nonholonomic mechanical systems are revisited. This review article focuses on Lagrangian formulations leading to a system of governing equations free of constraint forces. While eliminating the constraint forces, the number of scalar Lagrange equations is reduced to a number of independent equations lower than the original system with constraint forces. In the process of constraint-force elimination and dimension-reduction, a matrix that appears to play a relevant role in the formulation of the mathematical models of mechanical systems arises naturally. We call this matrix here the holonomy matrix. It is shown that necessary and sufficient conditions for the integrability of the constraints in Pfaffian form are readily derived using the holonomy matrix. In the same vein, a class of nonholonomic systems is identified, of current engineering relevance, that is termed quasiholonomic. Examples are included to illustrate these concepts. This review article contains 40 references.

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Kabir, Ariyan M., Shantanu Thakar, Rishi K. Malhan, Aniruddha V. Shembekar, Brual C. Shah und Satyandra K. Gupta. „Generation of synchronized configuration space trajectories with workspace path constraints for an ensemble of robots“. International Journal of Robotics Research 40, Nr. 2-3 (31.01.2021): 651–78. http://dx.doi.org/10.1177/0278364920988087.

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We present an approach to generate path-constrained synchronous motion for the coupled ensemble of robots. In this article, we refer to serial-link manipulators and mobile bases as robots. We assume that the relative motion constraints among the objects in the environment are given. We represent the motion constraints as path constraints and pose the problem of path-constrained synchronous trajectory generation as a non-linear optimization problem. Our approach generates configuration space trajectories for the robots to manipulate the objects such that the given motion constraints among the objects are satisfied. We present a method that formulates the problem as a discrete parameter optimization problem and solves it using successive constraint refinement techniques. The method adaptively selects the parametric representation of the configuration variables for a given scenario. It also generates an approximate solution as the starting point for the successive constraint refinement stages to reduce the computation time. We discuss in detail why successive constraint refinement strategies are useful for solving this class of problems. We demonstrate the effectiveness of the proposed method on challenging test cases in simulation and physical environments with high-degree-of-freedom robotic systems.

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Zhang, Ketao, und Jian S. Dai. „Reconfiguration of the plane-symmetric double-spherical 6R linkage with bifurcation and trifurcation“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, Nr. 3 (14.05.2015): 473–82. http://dx.doi.org/10.1177/0954406215584396.

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This study presents a double-spherical 6R overconstrained linkage which is a variant of the Sarrus linkage and investigates its constraint-induced bifurcation and trifurcation. In light of the unique geometry of the double-spherical 6R linkage, which is also a typical plane-symmetric Bricard 6R loop, its parametric constraints are explored. Based on constraint analysis in screw system theory, both design and motion parameters that lead to constraint singularities are revealed and the transitory positions for bifurcation and trifurcation are identified among geometric constraints induced singular positions. The analysis reveals that the presented 6R overconstrained linkage is able to reconfigure its configurations by passing transitory positions and to evolve to distinct motion branches including spherical 4R linkages and serial kinematic chains.

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Sheng, Xiaochao, Chia-Hsiang Menq und Tao Tao. „Analysis of coupled motion constraints and coupling errors for a six-axis magnetic levitation stage“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, Nr. 11 (11.02.2020): 2097–112. http://dx.doi.org/10.1177/0954406220903764.

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This paper presents the coupled motion constraints and coupling errors analysis of a magnetic levitation stage, which are two aspects of the coupling characteristics of magnetic levitation stage caused by force coupling. Aiming at the motion constraint coupling problem, this paper proposes a motion constrain method based on the force distribution matrix of the magnetic levitation stage. By this method, the motion constraint intervals without input saturation for single-degree-of-freedom motion, in-plane motion, and out-of-plane motion of magnetic levitation stage are established. When used for motion control, these constraints can provide the motion constraint specifications for the magnetic levitation stage, avoid the input saturation problem caused by the actuation force coupling, and provide a theoretical basis for magnetic levitation stage trajectory planning. Aiming at reducing the coupling error, this paper proposes a strategy to evaluate the coupling degree of the magnetic levitation stage actuation force by the condition number of the actuation force transfer matrix and the singular value of the force and torque error matrix. On this basis, the force and torque coupling errors caused by the translational and rotational movements of the magnetic levitation stage are studied, and the mechanism and characteristics of the coupling error between the interaction of translational and rotational movements are revealed. Based on the obtained results, the decoupling algorithm of the magnetic levitation stage is designed. Experimental results of the normalized step response demonstrate that the linearity of the magnetic levitation stage will be destroyed by the current saturation, and coupling error can also be introduced. Therefore, it is necessary to study the motion constrain strategy to provide comprehensive criteria for the trajectory planning and controller design. Experimental results of six-axis coupling error analysis show that the coupling error of x- and y-axes translational movement is reduced by 69.34% and 69.60%, respectively. This method provides a theoretical basis for the decoupling of the magnetic levitation stage and reducing the coupling error.

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Tsai, T. L., und J. Y. Chen. „Investigation of Effect of Endpoint Constraint on Time-Line Cubic Spline Interpolation“. Journal of Mechanics 25, Nr. 2 (Juni 2009): 151–60. http://dx.doi.org/10.1017/s1727719100002604.

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AbstractIn this study, the effects of various endpoint constraints, including the first derivative, natural, quadratic, and not-a-knot endpoint constraints, on the time-line cubic spline interpolation are examined by solving the advection-diffusion equation with constant and variable velocities, and the viscous Burgers equation. The natural endpoint constraint could produce large numerical diffusion. The quadratic endpoint constraint can decrease the numerical diffusion from the natural endpoint constraint, but it could trigger large numerical oscillation. The first derivative endpoint constraint with higher-order central difference approximation has better simulated results than the natural and quadratic endpoint constraints. It can significantly reduce not only the numerical diffusion produced by the natural endpoint constraint, but also the numerical oscillation caused by the quadratic endpoint constraint. The applicability of the time-line cubic spline interpolation together with the not-a-knot endpoint constraint is limited, since the computational instability is caused while the Courant number is greater than unity. Therefore, as far as accuracy and applicability are concerned, the first derivative endpoint constraint with higher-order central difference approximation rather than the commonly used natural endpoint constraint should be a better choice for the time-line cubic spline interpolation.

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Kingston, Zachary, Mark Moll und Lydia E. Kavraki. „Exploring implicit spaces for constrained sampling-based planning“. International Journal of Robotics Research 38, Nr. 10-11 (26.08.2019): 1151–78. http://dx.doi.org/10.1177/0278364919868530.

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We present a review and reformulation of manifold constrained sampling-based motion planning within a unifying framework, IMACS (implicit manifold configuration space). IMACS enables a broad class of motion planners to plan in the presence of manifold constraints, decoupling the choice of motion planning algorithm and method for constraint adherence into orthogonal choices. We show that implicit configuration spaces defined by constraints can be presented to sampling-based planners by addressing two key fundamental primitives, sampling and local planning, and that IMACS preserves theoretical properties of probabilistic completeness and asymptotic optimality through these primitives. Within IMACS, we implement projection- and continuation-based methods for constraint adherence, and demonstrate the framework on a range of planners with both methods in simulated and realistic scenarios. Our results show that the choice of method for constraint adherence depends on many factors and that novel combinations of planners and methods of constraint adherence can be more effective than previous approaches. Our implementation of IMACS is open source within the Open Motion Planning Library and is easily extended for novel planners and constraint spaces.

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Hou, M., Th Schmidt, R. Schu¨pphaus und P. C. Mu¨ller. „Normal Form and Luenberger Observer for Linear Mechanical Descriptor Systems“. Journal of Dynamic Systems, Measurement, and Control 115, Nr. 4 (01.12.1993): 611–20. http://dx.doi.org/10.1115/1.2899188.

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Normal forms are presented for linear mechanical systems with holonomic and/or nonholonomic constraints. These forms provide deep insight into the peculiar system structure of constrained linear mechanical systems or the so-called linear mechanical descriptor systems. Based on these normal forms, an explicit observer design method is proposed under a weaker observability assumption, i.e., finite observability or reachable observability on the linear mechanical descriptor systems. The observer has the Luenberger observer form and provides the estimation of displacements, velocities, and constraint forces simultaneously. The finite observability is shown to be a necessary and sufficient condition for the existence of this type of observer. The reason for the existence of the Luenberger observers for finitely observable linear mechanical descriptor systems is due to the special system structure. Two examples are included to illustrate the design method.

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Nikravesh, P. E., O. K. Kwon und R. A. Wehage. „Euler Parameters in Computational Kinematics and Dynamics. Part 2“. Journal of Mechanisms, Transmissions, and Automation in Design 107, Nr. 3 (01.09.1985): 366–69. http://dx.doi.org/10.1115/1.3260723.

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In this paper a methodology for formulating kinematic constraint equations and equations of motion for constrained mechanical systems is presented. Constraint equations and transformation matrices are expressed in terms of Euler parameters. The kinematic velocity and acceleration equations, and the equations of motion are expressed in terms of physical angular velocity of the bodies. An algorithm for solving the constrained equations of motion using a constraint stabilization technique is reviewed. Significant reduction in computation time can be achieved with this formulation and the accompanying algorithm as compared with the method presented in Part 1.

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Ider, S. K., und F. M. L. Amirouche. „Coordinate Reduction in the Dynamics of Constrained Multibody Systems—A New Approach“. Journal of Applied Mechanics 55, Nr. 4 (01.12.1988): 899–904. http://dx.doi.org/10.1115/1.3173739.

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In this paper a new theorem for the generation of a basis for the null space of a rectangular matrix, with m linearly independent rows and n (n > m) columns is presented. The method is based on Gaussian row operations to transform the constraint Jacobian matrix to an uptriangular matrix. The Gram-Schmidt process is then utilized to identify basis vectors orthogonal to the uptriangular matrix. A complement orthogonal array which forms the basis for the null space for which the algebraic constraint equations are satisfied is then formulated. An illustration of the theorem application to constrained dynamical systems for both Lagrange and Kane’s equations is given. A numerical computer algorithm based on Kane’s equations with embedded constraints is also presented. The method proposed is well conditioned and computationally efficient and inexpensive.

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Langer, F. Dieter, H. Hemami und D. B. Brown. „Constraint forces in holonomic mechanical systems“. Computer Methods in Applied Mechanics and Engineering 62, Nr. 3 (Juni 1987): 255–74. http://dx.doi.org/10.1016/0045-7825(87)90062-4.

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Putkaradze, Vakhtang, und Stuart Rogers. „Constraint Control of Nonholonomic Mechanical Systems“. Journal of Nonlinear Science 28, Nr. 1 (29.07.2017): 193–234. http://dx.doi.org/10.1007/s00332-017-9406-1.

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Wang, Jianfeng, Qingjie Sun, Jiangkun Ma, Peng Jin, Tianzhu Sun und Jicai Feng. „Correlation between wire feed speed and external mechanical constraint for enhanced process stability in underwater wet flux-cored arc welding“. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 233, Nr. 10 (18.11.2018): 2061–73. http://dx.doi.org/10.1177/0954405418811783.

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It is a great challenge to improve the process stability in conventional underwater wet welding due to the formation of unstable bubble. In this study, mechanical constraint method was employed to interfere the bubble generated by underwater wet welding, and the new method was named as mechanical constraint assisted underwater wet welding. The aim of the study was to quantify the combined effect of wire feed speed and condition of mechanical constraint on the process stability in mechanical constraint assisted underwater wet welding. Experimental results demonstrated that the introduction of mechanical constraint not only suppressed the bubble without floating but also stabilized the arc burning process. The degree of influence of mechanical constraint, which changed with wire feed speed, played an important role during the mechanical constraint assisted underwater wet welding process. For all wire feed speeds, the fluctuations of welding electrical signal were decreased through introduction of mechanical constraint. The difference in the proportion of arc extinction process between underwater wet welding and mechanical constraint assisted underwater wet welding became less with increasing wire feed speed. At wire feed speed lower than 7.5 m/min, the improvement of process stability was very significant by mechanical constraint. However, the further improvement produced limited effect when the wire feed speed was greater than 7.5 m/min. The observation results showed that a better weld appearance was afforded at a large wire feed speed, corresponding to a lower variation coefficient.

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Saito, Daichi, Kazuhiro Sasabuchi, Naoki Wake, Atsushi Kanehira, Jun Takamatsu, Hideki Koike und Katsushi Ikeuchi. „Constraint-Aware Policy for Compliant Manipulation“. Robotics 13, Nr. 1 (27.12.2023): 8. http://dx.doi.org/10.3390/robotics13010008.

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Robot manipulation in a physically constrained environment requires compliant manipulation. Compliant manipulation is a manipulation skill to adjust hand motion based on the force imposed by the environment. Recently, reinforcement learning (RL) has been applied to solve household operations involving compliant manipulation. However, previous RL methods have primarily focused on designing a policy for a specific operation that limits their applicability and requires separate training for every new operation. We propose a constraint-aware policy that is applicable to various unseen manipulations by grouping several manipulations together based on the type of physical constraint involved. The type of physical constraint determines the characteristic of the imposed force direction; thus, a generalized policy is trained in the environment and reward designed on the basis of this characteristic. This paper focuses on two types of physical constraints: prismatic and revolute joints. Experiments demonstrated that the same policy could successfully execute various compliant manipulation operations, both in the simulation and reality. We believe this study is the first step toward realizing a generalized household robot.

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Pagilla, P. R., und Masayoshi Tomizuka. „Contact Transition Control of Nonlinear Mechanical Systems Subject to a Unilateral Constraint“. Journal of Dynamic Systems, Measurement, and Control 119, Nr. 4 (01.12.1997): 749–59. http://dx.doi.org/10.1115/1.2802387.

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In this paper, contact transition control of mechanical systems subject to a unilateral constraint is presented. A systematic way is proposed for designing control laws for unilaterally constrained mechanical systems. Three phases of motion (inactive, transition, active) are formulated depending on the activation/deactivation of the constraint. Our framework describes the complete behaviour of the mechanical system under the action of a unilateral constraint. We propose stable control laws for all the phases of the system. Exponential stability in each phase is shown. Of special interest is the contact transition problem. During this phase the dynamics is discontinuous. Nonsmooth Lyapunov techniques are used to show exponential stability in the transition phase. Composite Lyapunov functions are constructed for each phase and these are used to show asymptotic stability of the overall system taking into consideration switching from one phase to another. The proposed method is successfully implemented on robots interacting with an environment, and we present results of those experiments. Experimental results confirm the theoretically predicted behavior.

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Tian, Chunxu, Yuefa Fang, Sheng Guo und Haibo Qu. „A class of reconfigurable parallel mechanisms with five-bar metamorphic linkage“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, Nr. 11 (27.01.2016): 2089–99. http://dx.doi.org/10.1177/0954406216628558.

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This paper presents a planar five-bar metamorphic linkage which has five phases resulting from locking of motors. Reconfigurable limbs are constructed by integrating the five-bar metamorphic linage as sub-chains. The branch transition of metamorphic linkage is analyzed. By adding appropriate joints to the planer five-bar metamorphic linkage, reconfigurable limbs whose constraint can switch among no constraint, a constrained force and a constrained couple are obtained. Serial limb structures that can provide a constraint force and a constraint couple are synthesized based on screw theory. Reconfigurable limbs that have five configurations associated with the five phases of the five-bar metamorphic linkage are assembled with 4-DOF (degrees-of-freedom) serial chains. A class of reconfigurable parallel mechanisms is derived by connecting the moving platform to the base with three identical kinematic limbs. These parallel mechanisms can perform various output motion modes such as 3T, 3R, 2T1R, 1T2R, 3T1R, 2T2R, 1T3R, 2T3R, 3T2R and 3T3R. Finally, the potential application of the proposed mechanisms is analyzed and conclusions are drawn.

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Choi, S.-B. „Compliant Motion Control of a Three-Link Manipulator with Link Flexibility and Joint Constraints“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 219, Nr. 11 (01.11.2005): 1207–17. http://dx.doi.org/10.1243/095440605x32057.

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This article presents a new approach employing constraint Hamiltonian system for the compliant motion control of a three-link manipulator with link flexibility and joint constraints. Two non-linear controllers consisting of force part and position part are first derived from constraint Hamiltonian system obtained by the Lagrange and Hamiltonian methods. The linear feedback controllers that satisfy the Lyapunov stability of the total constraint Hamiltonian system are then designed. Consequently, the compliant motion control system consisting of the sum of two non-linear controllers and corresponding linear feedback controllers is formulated. The compliant motion control strategy is accomplished by steering the end effector of the manipulator onto the constraint surface with the linear controllers, and subsequently, by executing a prescribed desirable motion with the non-linear controllers. Computer simulations are undertaken in order to demonstrate the effectiveness of the proposed control methodology.

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