Construction of Overconstrained Linkages by Factorization of Rational Motions

Hegedüs, Gábor; Schicho, Josef; Schröcker, Hans-Peter

doi:10.1007/978-94-007-4620-6_27

Cited by 10 publications

(22 citation statements)

References 7 publications

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“…We give a brief sketch of the construction in [8,9]. Linear motion polynomials of the form (t − a − bh), a, b ∈ R, b = 0, h ∈ DH, h 2 = −1 parametrize revolutions.…”

Section: Linkages With Rank 2 Andmentioning

confidence: 99%

Classification of angle-symmetric 6R linkages

Schicho

2013

Mechanism and Machine Theory

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In this paper, we consider a special kind of overconstrained 6R closed linkage which we call angle-symmetric 6R linkage. These are linkages with the property that the rotation angles are equal for each of the three pairs of opposite joints. We give a classification of these linkages. It turns out that there are three types. First, we have the linkages with line symmetry. The second type is new. The third type is related to cubic motion polynomials.

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“…We give a brief sketch of the construction in [8,9]. Linear motion polynomials of the form (t − a − bh), a, b ∈ R, b = 0, h ∈ DH, h 2 = −1 parametrize revolutions.…”

Section: Linkages With Rank 2 Andmentioning

confidence: 99%

Classification of angle-symmetric 6R linkages

Schicho

2013

Mechanism and Machine Theory

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“…Different approaches have been proposed for the kinematic analysis of the 6R overconstrained mechanisms [2][3][4][5][6][7][8][9][10][11][12][13][14]17]. A matrix based method (see [17] for example) will be used in this paper for the analysis of 6R overconstrained mechanisms.…”

Section: Kinematic Equations Of a 6r Overconstrained Mechanismmentioning

confidence: 99%

“…The research on single DOF single-loop overconstrained mechanisms started from 1853 when the Sarrus mechanism appeared. Since then, a number of single-loop overconstrained spatial mechanisms [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] have been proposed. Meanwhile, different approaches, such as construction approaches [1,5,9,16], geometric methods [12], algebraic approaches [3,8,10,11,14,15,17,19,21,22] and numerical methods [4,13,23], have been developed to the synthesis and analysis of overconstrained mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Kinematic analysis of a 6R single-loop overconstrained spatial mechanism for circular translation

Kong

2015

Mechanism and Machine Theory

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“…The procedure described in this section is crucial for the construction of linkages with mobility one. It is inspired by similar techniques -involving the interchange of factors in a factorization of a quadratic motion polynomial -used in [9] and [10]. Lemma 6.1.…”

Section: The Flip Proceduresmentioning

confidence: 99%

Planar linkages following a prescribed motion

Gallet

Koutschan

et al. 2016

Math. Comp.

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Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also computer scientists. Already in 1876, Kempe proposed a procedure for solving the problem in full generality, but his constructions tend to be extremely complicated. We provide a novel algorithm that produces much simpler linkages, but works only for parametric curves. Our approach is to transform the problem into a factorization task over some noncommutative algebra. We show how to compute such a factorization, and how to use it to construct a linkage tracing a given curve.

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Construction of Overconstrained Linkages by Factorization of Rational Motions

Cited by 10 publications

References 7 publications

Classification of angle-symmetric 6R linkages

Classification of angle-symmetric 6R linkages

Kinematic analysis of a 6R single-loop overconstrained spatial mechanism for circular translation

Planar linkages following a prescribed motion

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