On the optimum design of Stewart platform type parallel manipulators

SUMMARYIn this paper the problem of determining a manipulator design so that its workspace corresponds to a prescribed workspace is considered. Two di erent strategies, resulting in two di erent types of optimization problem are considered. The ÿrst strategy attempts to obtain a good overall approximation to the prescribed workspace and results in an unconstrained optimization problem. The second strategy entails designing a manipulator so that its workspace fully encloses the prescribed workspace and results in a constrained optimization problem. Two speciÿc formulations of the constrained problem are proposed. The ÿrst constrained problem simply aims to ÿt the manipulator workspace as exactly as possible to the prescribed workspace, while still ensuring that the prescribed workspace is fully enclosed. The second constrained optimization formulation is used to design a manipulator, the workspace of which fully encloses the prescribed workspace, but which is also well-conditioned throughout the workspace with respect to some performance measure. The particular manipulator used to illustrate and evaluate these formulations is a simple 2-dof planar parallel manipulator, and the ÿnal formulation is also applied to a 3-dof planar parallel manipulator. Although the manipulators studied here are simple, the objective of this study is to obtain a robust numerical methodology which can be extended to more practical and complex manipulators.

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“…The boundary of the prescribed workspace is deÿned in polar co-ordinates relative to a local co-ordinate system centered at q p = [0; 3] T :…”

Section: Unconstrained Problem Test Resultsmentioning

confidence: 99%

Methodologies for the optimal design of parallel manipulators

Hay

Snyman

2003

Numerical Meth Engineering

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“…Examples of this approach include Atlas approach [1], [2], the cost function approach [3], [4], dual expansion [5], compromise programming methodology [6], physical programming methodology [7] among others [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Performance analysis and design of parallel kinematic machines using interval analysis

Viegas

Daney

Tavakoli

et al. 2017

Mechanism and Machine Theory

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. Performance analysis and design of parallel kinematic machines using interval analysis. Mechanism and Machine Theory, Elsevier, 2017, 115, pp.218 -236 Abstract-Some design methodologies for Parallel Kinematic Machines (PKM) have been proposed but with limitations regarding two main problems: how to improve multiple properties of different nature such as accuracy, force or singularity poses, and how to check these properties for all poses inside the PKM workspace. To address these problems, this work proposes to formulate the design problem as a feasibility problem and use a data representation which takes into account the uncertainty or variation of the involved parameters. This method, based on interval analysis, allows to evaluate several performance indexes of a PKM design. For validation purposes, this methodology is applied to a PKM, obtaining a continuous set of possible kinematic parameters values for its architecture which is capable of fulfilling several performance requirements over a desired workspace.

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“…), in this case, one can remark that the initial solution influences considerably the speed of convergence towards the optimal solution (if it exists) and one can obtain at the end only one solution (only one vector of geometrical parameters). In literature, one can find several works [7][8][9][10] which use the approach of single-objective optimization for solving the problem of dimensional design of parallel robots. All these works deal with the problem by taking only one goal into account among several objectives such as workspace, kinematic performance, stiffness, and dynamic performance.…”

Section: Introductionmentioning

confidence: 99%

Some investigations into the optimal dimensional synthesis of parallel robots

Kelaiaia

Zaatri

Chikh³

2015

Int J Adv Manuf Technol

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In this paper, we will perform a comparison between two approaches of dimensional synthesis of parallel robots. The first one concerns the single-objective optimization approach; in this case, the dimensional synthesis is expressed by taking into account only one performance criterion but enables to get a final solution if it exists. The second one concerns the multi-objective optimization approach; it enables to simultaneously take into account several performance criteria. However, thisRidha Kelaiaia approach appears to provide a set of solutions instead of a single expected final solution which should directly enable to carry out the structural synthesis. In fact, the search of a single final solution is postponed to a further step where the designers have to impose and/or restrict certain parameters. And we will establish if it is really necessary to make a multi-objective optimization approach or if a singleobjective is sufficient to reach the objectives set in the specifications (user requirements). A discussion is proposed concerning the arising questions related to each approach and leading to the optimal dimensional synthesis. The PAR2 robot with two degree-of-freedom is used to exemplify the analysis and the comparison of the two approaches. The proposed comparison can be applied to any classes of parallel robots.

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On the optimum design of Stewart platform type parallel manipulators

Cited by 86 publications

References 12 publications

Methodologies for the optimal design of parallel manipulators

Methodologies for the optimal design of parallel manipulators

Performance analysis and design of parallel kinematic machines using interval analysis

Some investigations into the optimal dimensional synthesis of parallel robots

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