Determination Du Degre De Liberte Des Chaines Cinematique

Ángeles, Jorge; Gosselin, Cle ́ment M.

doi:10.1139/tcsme-1988-0031

Cited by 26 publications

(21 citation statements)

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“…f e i is the active mobilities in ith joint L comj is the number of loops with common joint j k e K is the dimension of the active motion space f e comj is the active degree of mobility of the jth common joint 32 M = nullity(J) Angeles and Gosselin [32] The mobility equation by using the Jacobian matrix of a simple or multi loop closed kinematic chain without exception…”

Section: Dudita Andmentioning

confidence: 99%

“…During the second half of the 20th century, the productive results to find general methods for determination of the mobility of any mechanisms had been obtained by Moroshkin [15], Voinea and Atanasiu [16], Paul [17], Rö ssner [18], Boden [19], Ozol [20], Waldron [21], Manolescu [22], Bagci [23], Antonescu [24], Freudenstein and Alizade [25], Hunt [26], Herve [27], Gronowicz [28], Davies [29], Agrawal and Rao [30], Dudita and Diaconescu [31], Angeles and Gosselin [32], Alizade [33], McCarthy [34]. In the calculation of mechanism mobility, the following new parameters were used (Table 1), as the rank of linear independent loop equations or the order of the equivalent screw system of the closed loop (r), relative displacements of the joint (m), number of independent, scalar, differential loop-closure equations (k K ), the rank of the coefficient matrix (r(j)), finite dimensional vector space (d(v)), new formula of the number of independent loops (L = j B À B À c b , where j B is the total number of joints on the platforms, and c B is the total number of branches between moving platforms and B is the number of moving platforms), serial open chains connecting to ground or total number of robot legs (c l ), and the degree of constraint of the platform (U).…”

Section: Introductionmentioning

confidence: 99%

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Structural synthesis of serial platform manipulators

Alizade

Bayram

Gezgin

2007

Mechanism and Machine Theory

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In this paper, structural synthesis of serial platform manipulators is considered. Serial platform manipulators are created according to the development of the platforms and closed loops. Also a new structural formula of mobility of parallel Cartesian platform robot manipulators is presented. Structural synthesis of serial platform manipulators with lower and higher kinematic pairs with respect to their structures are also examined. Structural synthesis of parallel Cartesian platform robot manipulators is also introduced. History of structural formulas DOF are presented as a table with equations, authors, years and some commentaries. New and revised methods for structural synthesis of serial platform manipulators and parallel Cartesian platform robot manipulators are illustrated along with examples. Ó 2006 Elsevier Ltd. All rights reserved. Pep.veı gpelcnabkeyyoq pa,one paccvanpbba.ncz ıogpocs cnpyrnypyouo cbynepa gkanaopveyysx vaybgykznopob gockelobaneksyoq cnpyrnyps. Coplaybe gkanaopveyysx vaybgylznopob goclelobanelsyoq cnpyrnyps ocyobaya ya papbbnbb gkanaopv b pavryynsx roynypob. ı pa,one gpelcnabgeya yobaz cnpyrnypyaz aopvyka, a nar;e paccvanpbba.ncz bogpocs cnpyrnypyouo cbynepa gkanaopveyysx vaybgykznopob gockelobaneksyoq cnpyrnyps c ybpobvb b bscobvb gapavb c noxrb ppeybz bx cnpryrnyps. Bcnopbz cnpyrnypys aopvyk cnegeyb golbb;yocnb gpelcnabkeya b bble na,kbws c ypabyeybzvb, aınopavb, uolavb b yeronopsvb roveynapbzvb. Hobse b gepecvonpeyyse venols cnpyrnypyouo cbynepa gkanaopveyysx vaybgykznopob gockelobaneksyoq cnpyrnyps bkk.cnpbpy.ncz papkbxsvb gpbvepavb.

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Section: Dudita Andmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Structural synthesis of serial platform manipulators

Alizade

Bayram

Gezgin

2007

Mechanism and Machine Theory

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“…This implies that the mobility of the system is reduced to zero when its actuators are locked. As outlined in [16], the mobility of the actuated system can be found by considering a particular form of its Jacobian matrix, Jc, given by Since each column of Jc corresponds to a particular joint variable in the system, the mobility of the actuated system is found by partitioning Jc into its actuated and unactuated columns ac = [Ja Jd (12) and evaluating [16] M' = dim[N'(Ju)].…”

Section: Rendering the System Determinatementioning

confidence: 99%

A comparison of methods for the control of redundantly-actuated robotic systems

Nahon

1995

J Intell Robot Syst

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Abstract. Mechanical hands, legged vehicles and cooperating manipulators are robotic systems containing closed kinematic chains which are typically driven by more actuators than required. As a result, the force distribution existing in these systems cannot be determined simply from the governing rigid-body statics or dynamics equations since these equations are underdetermined. Techniques have been proposed to overcome this obstacle -the most common being to formulate an optimization problem whose solution will be a force distribution which is optimal in a prescribed sense. A second approach which has been suggested is one in which the elasticity of the constituent bodies is considered in order to render the force-distribution problem determinate, in a manner analogous to the techniques typically used in structural mechanics to analyze hyperstatic structures. A third approach would be to deactivate certain actuators in order to reduce the number of unknowns so that the problem becomes determinate. In the present paper, these methods are compared and the first is shown to yield the best results.

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“…Considering the null spaces of these matrices, they determine kinematically and statically indeterminate modes of pin-jointed assemblies. Similarly, Angeles and Gosselin [1] consider mechanisms with open and closed loop kinematic chains coupled by either revolute or prismatic pairs. The number of degrees of freedom of the chain is computed from the null space of a suitably defined Jacobian matrix.…”

Section: Introductionmentioning

confidence: 99%

Flexible multibody modelling for exact constraint design of compliant mechanisms

2011

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In high precision equipment, the use of compliant mechanisms is favourable as elastic joints offer the advantages of low friction and no backlash. If the constraints in a compliant mechanism are not carefully dealt with, even small misalignments can lead to changes in natural frequencies and stiffnesses. Such unwanted behaviour can be avoided by applying exact constraint design, which implies that the mechanism should have exactly the required degrees of freedom and non-redundant constraints so that the system is kinematically and statically determinate. For this purpose, we propose a kinematic analysis using a finite element based multibody modelling approach. In compliant mechanisms, the system's degrees of freedom are presented clearly from the analysis of a system in which the deformation modes with a low stiffness are free to deform while the deformation modes with a high stiffness are considered rigid. If the Jacobian matrix associated with the dependent coordinates is not full column or row rank, the system is under-constrained or over-constrained. The rank of this matrix is calculated from a singular value decomposition. For an under-constrained system, any motion in the mechanism that is not accounted for by the current set of degrees of freedom is visualised using data from the right singular matrix. For an over-constrained system, a statically indeterminate stress distribution is derived from the left singular matrix and is used to visualise the over-constraints. The analysis is exemplified for the design of a straight guiding mechanism, where under-constrained and over-constrained conditions are visualised clearly.

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Determination Du Degre De Liberte Des Chaines Cinematique

Cited by 26 publications

References 0 publications

Structural synthesis of serial platform manipulators

Structural synthesis of serial platform manipulators

A comparison of methods for the control of redundantly-actuated robotic systems

Flexible multibody modelling for exact constraint design of compliant mechanisms

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