A Numerically Robust Algorithm to Solve the Five-Pose Burmester Problem

Al-Widyan, Khalid; Ángeles, Jorge; ́nchez, J. Jesu ́s Cervantes-Sa

doi:10.1115/detc2002/mech-34270

Cited by 15 publications

(10 citation statements)

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“…In a similar procedure vector a can be computed. It is shown in [42] that the four equations of any of the two sets reduce to a quartic polynomial. According to the proposed algorithm, a four-bar linkage can be designed by considering the following design specifications: the point P is required to have the support phase of length b, with height h to overpass obstacles.…”

Section: Synthesis Of the Leg-mechanismmentioning

confidence: 98%

“…Several authors have addressed the Burmester problem, it can be solved by intersecting two curves representing the loci of the centre points for two four-pose subsets out of the given five-pose set, as reported in [26,38,39], by applying complex numbers [40] and using kinematic mapping. [41] In the following, we have used the method proposed in [42] based on dyalitic elimination method, which leads to a numerically robust algorithm that can be successfully used for the case understudy. In particular, joint centres can be found through the intersections of the four possible contours of the four-pose problem.…”

Section: Synthesis Of the Leg-mechanismmentioning

confidence: 99%

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THROO: a Tracked Hybrid Rover to Overpass Obstacles

2014

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In this paper, the design, simulation and experimental tests are presented for THROO: a Tracked Hybrid Rover, which has been developed to Overpass Obstacles. The proposed mobile robot has 3-DOFs and it is capable of straight motion, turning ability and two operations, namely rover-like motion with tracks on flat terrain and walking-like motion with track and legs to overpass obstacles to move on uneven terrain. The leg mechanism is composed of a four-bar linkage, which has been synthesized according to the desired features. In particular, the Burmester problem, which aims at finding the geometric parameters of a four-bar linkage required for a prescribed set of finitely separated poses are solved for the case understudy. Dynamic simulations have been carried out and a prototype has been built. The proposed results show the hybrid rover ability to overpass obstacles, for which size is comparable or greater than the track high.

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Section: Synthesis Of the Leg-mechanismmentioning

confidence: 98%

Section: Synthesis Of the Leg-mechanismmentioning

confidence: 99%

THROO: a Tracked Hybrid Rover to Overpass Obstacles

2014

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“…Consider the rigid body guidance problem proposed by J. Michael McCarthy, U.C. Irvine for the 2002 ASME International Design Engineering Technical Conferences held in Montreal, Quebec and listed in [18]. The 11 planar locations are listed in Table 1 and the origins of the coordinate frames with the respect to the fixed reference frame F are shown in Figure 3 [PF] =   1.0000 0.0067 0.0094 -0.0067 1.0000 0.6199 0.0000 0.0000 1.0000…”

Section: Example: Eleven Planar Locationsmentioning

confidence: 99%

A Displacement Metric for Finite Sets of Rigid Body Displacements

Venkataramanujam

Larochelle

2008

Volume 2: 32nd Mechanisms and Robotics Conference, Parts a and B

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There are various useful metrics for finding the distance between two points in Euclidean space. Metrics for finding the distance between two rigid body locations in Euclidean space depend on both the coordinate frame and units used. A metric independent of these choices is desirable. This paper presents a metric for a finite set of rigid body displacements. The methodology uses the principal frame (PF) associated with the finite set of displacements and the polar decomposition to map the homogenous transform representation of elements of the special Euclidean group SE(N-1) onto the special orthogonal group SO(N). Once the elements are mapped to SO(N) a bi-invariant metric can then be used. The metric obtained is thus independent of the choice of fixed coordinate frame i.e. it is left invariant. This metric has potential applications in motion synthesis, motion generation and interpolation. Three examples are presented to illustrate the usefulness of this methodology.

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“…Lin et al [35] have presented pole curve transformation-based approach for motion synthesis of planar mechanisms. Al-Widyan et al [36] have presented a numerically robust algorithm to solve the classic Burmester problem. Bourrelle et al [37] presented a graphical user interface that uses the algorithm developed in Ref.…”

Section: Introductionmentioning

confidence: 99%

A Task-Driven Approach to Optimal Synthesis of Planar Four-Bar Linkages for Extended Burmester Problem

Deshpande

Purwar

2017

Journal of Mechanisms and Robotics

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The classic Burmester problem is concerned with computing dimensions of planar four-bar linkages consisting of all revolute joints for five-pose problems. We define extended Burmester problem as the one where all types of planar four-bars consisting of dyads of type RR, PR, RP, or PP (R: revolute, P: prismatic) and their dimensions need to be computed for n-geometric constraints, where a geometric constraint is an algebraically expressed constraint on the pose, pivots, or something equivalent. In addition, we extend it to linear, nonlinear, exact, and approximate constraints. This extension also includes the problems when there is no solution to the classic Burmester problem, but designers would still like to design a four-bar that may come closest to capturing their intent. Machine designers often grapple with such problems while designing linkage systems where the constraints are of different varieties and usually imprecise. In this paper, we present (1) a unified approach for solving the extended Burmester problem by showing that all linear and nonlinear constraints can be handled in a unified way without resorting to special cases, (2) in the event of no or unsatisfactory solutions to the synthesis problem, certain constraints can be relaxed, and (3) such constraints can be approximately satisfied by minimizing the algebraic fitting error using Lagrange multiplier method. We present a new algorithm, which solves new problems including optimal approximate synthesis of Burmester problem with no exact solutions.

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A Numerically Robust Algorithm to Solve the Five-Pose Burmester Problem

Cited by 15 publications

References 0 publications

THROO: a Tracked Hybrid Rover to Overpass Obstacles

THROO: a Tracked Hybrid Rover to Overpass Obstacles

A Displacement Metric for Finite Sets of Rigid Body Displacements

A Task-Driven Approach to Optimal Synthesis of Planar Four-Bar Linkages for Extended Burmester Problem

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