Isotropic Design of Spatial Parallel Manipulators

Fattah, Abbas; Ghasemi, Ali

doi:10.1177/027836402128964666

Cited by 18 publications

(33 citation statements)

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“…For C F , C d the ordering is respected although the changes in the index are relatively small for C F . On the other hand there is a surprisingly decrease of C 3 2 , C 3 F between P 2 and P 1 while there is a significant increase between P 1 and P 3 . Hence none of this condition numbers exhibits a completely coherent behavior with respect to the accuracy of this robot.…”

Section: Condition Numbermentioning

confidence: 83%

Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots

Merlet

2005

Journal of Mechanical Design

626

159

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Although the concepts of Jacobian matrix, manipulability, and condition number have existed since the very early beginning of robotics their real significance is not always well understood. In this paper we revisit these concepts for parallel robots as accuracy indices in view of optimal design. We first show that the usual Jacobian matrix derived from the input-output velocities equations may not be sufficient to analyze the positioning errors of the platform. We then examine the concept of manipulability and show that its classical interpretation is erroneous. We then consider various common local dexterity indices, most of which are based on the condition number of the Jacobian matrix. It is emphasized that even for a given robot in a particular pose there are a variety of condition numbers and that their values are not coherent between themselves but also with what we may expect from an accuracy index. Global conditioning indices are then examined. Apart from the problem of being based on the local accuracy indices that are questionable, there is a computational problem in their calculation that is neglected most of the time. Finally, we examine what other indices may be used for optimal design and show that their calculation is most challenging.

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Section: Condition Numbermentioning

confidence: 83%

Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots

Merlet

2005

Journal of Mechanical Design

626

159

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“…The condition number of the Jacobian matrix was first used by Salisbury and Craig (1982) to design mechanical fingers and developed by as a kinetostatic performance index of the robotic mechanical systems. The isotropic design aims at ideal kinematic and dynamic performance of the manipulator (Fattah and Ghasemi 2002). In an isotropic configuration, the sensitivity of a manipulator is minimal with regard to both velocity and force errors and the manipulator can be controlled equally well in all directions.…”

Section: Types Of Parallel Robots With Respect To Motion Couplingmentioning

confidence: 99%

Structural Synthesis of Parallel Robots

Gogu¹

2009

Solid Mechanics and Its Applications

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The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids.The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design.The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity.For other titles published in this series, go to

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“…where ρ > 0 and in general ρ = 1. This choice is motivated by the 3-way symmetry inherent in the manipulator architecture, and the set of configurations is more general than those studied in [10,11,3,1].…”

Section: Architecture Configuration Constraintsmentioning

confidence: 99%

“…A consequence of this approach is the concurrence of kinematic and static isotropy, where the later implies the ability of the manipulator endeffector to resist forces and moments equally well in all spatial directions. Among the spatial parallel manipulators, the Stewart platform manipulator (SPM) has been studied by several researchers for isotropy [1,2,3,4]. However, to the best of our knowledge, no mechanically feasible, non-singular isotropic configuration has been obtained for a manipulator of this class.…”

Section: Introductionmentioning

confidence: 99%

An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

Bandyopadhyay

Ghosal

2009

Mechanism and Machine Theory

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In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions. We use the force and moment transformation matrices separately, and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation is applied to a class of Stewart platform manipulator, and a multi-parameter family of isotropic manipulator is identified analytically.We show that it is impossible to obtain a spatially isotropic configuration within this family. We also compute the isotropic configurations of an existing manipulator and demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

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Isotropic Design of Spatial Parallel Manipulators

Cited by 18 publications

References 0 publications

Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots

Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots

Structural Synthesis of Parallel Robots

An algebraic formulation of static isotropy and design of statically isotropic 6–6 Stewart platform manipulators

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