An improved design algorithm based on interval analysis for spatial parallel manipulator with specified workspace
21 May 2001-Vol. 2, pp 1289-1294
TL;DR: This algorithm is based on an interval analysis approach and its result is a set of ranges for the design parameters such that the workspace of any robot whose geometry is defined by values within the ranges will include the specified poses.
Abstract: We propose an algorithm that enable one to determine almost all the geometries of a simplified Gough platform whose workspace must include an arbitrary set of poses. Five design parameters have been identified and we assume that the stroke of the linear actuator is known. This algorithm is based on an interval analysis approach and its result is a set of ranges for the design parameters such that the workspace of any robot whose geometry is defined by values within the ranges will include the specified poses.
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TL;DR: This paper proposes and illustrates on an example of parallel robots an approach based on interval analysis that allows to determine almost all possible mechanism geometries such that all compulsory requirements will be satisfied simultaneously.
190 citations
Cites methods from "An improved design algorithm based ..."
...The algorithm that determines the FPBs for the workspace requirement is based on Fw(Q, P) and is similar to the algorithm presented in [25]....
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TL;DR: In this paper, the authors propose a design approach utilizing a performance chart, which has been applied to most industrial designs, to identify an optimum region, which represents a domain of the normalized parameters, with respect to specified indices.
83 citations
05 Dec 2005
TL;DR: Kinematic design of parallel manipulators is addressed in this paper, and the controlled random search (CRS) technique is applied to numerically solve the problem.
Abstract: Kinematic design of parallel manipulators is addressed in this paper. By observation that regular (e.g., hyper-rectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects both requirements on the workspace shape and quality. Dexterity index is utilized to characterize the effectiveness of the workspace. The optimal design problem is then formulated to find a manipulator geometry that maximizes the effective regular workspace. Since the optimal design problem is a constrained nonlinear optimization problem without explicit analytical expressions, the controlled random search (CRS) technique, which was reported robust and reliable, is applied to numerically solve the problem. The commonly-used Stewart-Gough platform is employed as an example to demonstrate the design procedure.
71 citations
Cites background from "An improved design algorithm based ..."
...One is to generate a manipulator whose workspace contains a prescribed workspace [1][2][3] [4]....
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TL;DR: This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators under a unified framework, and proposes the concept of effective regular workspace, which reflects simultaneously requirements on the workspace shape and quality.
Abstract: This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators under a unified framework. Observing that regular (e.g., hyper-rectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects simultaneously requirements on the workspace shape and quality. The effectiveness of a workspace is characterized by the dexterity of the mechanism over every point in the workspace. Other performance indices, such as manipulability and stiffness, provide alternatives of dexterity characterization of workspace effectiveness. An optimal design problem, including constraints on actuated/passive joint limits and link interference, is then formulated to find the manipulator geometry that maximizes the effective regular workspace. This problem is a constrained nonlinear optimization problem without explicitly analytical expression. Traditional gradient based approaches may have difficulty in searching the global optimum. The controlled random search technique, as reported robust and reliable, is used to obtain an numerical solution. The design procedure is demonstrated through examples of a Delta robot and a Gough-Stewart platform.
61 citations
TL;DR: The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespective of whether the linkage is rigid or mobile.
Abstract: This paper presents a new method to isolate all configurations that a multiloop linkage can adopt. The problem is tackled by means of formulation and resolution techniques that fit particularly well together. The adopted formulation yields a system of simple equations (only containing linear, bilinear, and quadratic monomials, and trivial trigonometric terms for the helical pair only) whose structure is later exploited by a branch-and-prune method based on linear relaxations. The method is general, as it can be applied to linkages with single or multiple loops with arbitrary topology, involving lower pairs of any kind, and complete, as all possible solutions get accurately bounded, irrespective of whether the linkage is rigid or mobile.
57 citations
References
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Book•
01 Jan 1987
TL;DR: Finite representations Finite evaluation Finite convergence Computable sufficient conditions for existence and convergence Safe starting regions for iterative methods.
Abstract: Finite representations Finite evaluation Finite convergence Computable sufficient conditions for existence and convergence Safe starting regions for iterative methods Applications to mathematical programming Applications to operator equations An application in finance Internal rates-of-return.
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TL;DR: Optimisation de la cinematique d'un manipulateur utilisant un mecanisme parallele spherique a trois degres de liberte.
Abstract: Optimisation de la cinematique d'un manipulateur utilisant un mecanisme parallele spherique a trois degres de liberte
812 citations
TL;DR: This article makes use of the special structure of these Jacobians to define a set of conditions under which a parallel manipulator can be rendered isotropic, and proposes a systematic method for the optimum kinematic design of parallel manipulators.
Abstract: The differential kinematic equations (DKE) of parallel manip ulators usually involve two Jacobian matrices that, depending on the role they play in the kinetostatic transformation between the joint and Cartesian variables, are commonly referred to as the forward and the inverse Jacobians. In this article, we make use of the special structure of these Jacobians to define a set of conditions under which a parallel manipulator can be rendered isotropic. These conditions are general, and pro vide a systematic method for the optimum kinematic design of parallel manipulators, with or without introducing structural constraints. The application of the proposed conditions is illus trated in detail through a few examples, one of which pertains to the design of a 6-DOF isotropic parallel manipulator.
234 citations
TL;DR: A portable software package for finding all real roots of a system of nonlinear equations within a region defined by bounds on the variables based on interval Newton methods, which allows various control and output options and does not require programming if the equations are polynomials.
Abstract: We present a portable software package for finding all real roots of a system of nonlinear equations within a region defined by bounds on the variables. Where practical, the package should find all roots with mathematical certainty. Though based on interval Newton methods, it is self-contained. It allows various control and output options and does not require programming if the equations are polynomials; it is structured for further algorithmic research. Its practicality does not depend in a simple way on the dimension of the system or on the degree of nonlinearity.
176 citations
DOI•
01 Jan 1991
TL;DR: These Ecole polytechnique federale de Lausanne EPFL, n° 925 (1991)Laboratoire de systemes robotiques 2 Reference doi:10.5075/epflthesis-925Print copy in library catalog Record created on 2005-03-16, modified on 2017-05-10
Abstract: These Ecole polytechnique federale de Lausanne EPFL, n° 925 (1991)Laboratoire de systemes robotiques 2 Reference doi:10.5075/epfl-thesis-925Print copy in library catalog Record created on 2005-03-16, modified on 2017-05-10
167 citations
"An improved design algorithm based ..." refers background in this paper
...Design with respect of a workspace has been considered when the orientation is constant [4] or for planar robot [5] or other specific robots [6],[7],[8]: but in these works only one solution was sought while we will be interested here in finding almost all the possible geometries that include a given workspace....
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