Mobility analysis of single-loop kinematic chains: an algorithmic approach based on displacement groups

Fanghella, Pietro; Galletti, C.

doi:10.1016/0094-114x(94)90009-4

Cited by 32 publications

(24 citation statements)

References 11 publications

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“…(46) to the mobility calculation of the mechanism presented in Fig. 1, we obtain obviously the same erroneous results that were obtained by using Eq.…”

Section: Gronowicz's Contributionmentioning

confidence: 42%

“…(49) extends Eq. (46) proposed by Gronowicz to multiple jointed mechanisms. Agrawal and Rao [43] considered that Eq.…”

Section: Contribution Of Agrawal and Raomentioning

confidence: 99%

“…During the XX century, sustained efforts were made to find general methods for the determination of the mobility of any rigid body mechanism. Various formulas and approaches were derived and presented in the literature by Koenigs [9], Grü bler [10,11], Malytsheff [12], Kutzbach [13], Dobrovolski [14,15], Artobolevski [16], Moroskine [17,18] Voinea and Atanasiu [19], Kolchin [20], Rö ssner [21], Boden [22], Manolescu and Manafu [23], Ozol [24], Hunt and Phillips [25], Waldron [26], Manolescu [27], Bagci [28], Antonescu [29,30], Freudenstein and Alizade [31], Hunt [32], Hervé [33,34], Baker [35,36], Gronowicz [37] , Davies [38][39][40], Agrawal and Rao [41,43], Angeles and Gosselin [44], Dudit ßȃ and Diaconescu [45], Fanghella and Galletti [46,47], Fayet [48][49][50] Tsai [51], McCarthy [52]. Contributions have continued to emerge in the last years: Huang et al [53], Rico and Rava...…”

Section: Introductionmentioning

confidence: 99%

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Mobility of mechanisms: a critical review

Gogu

2005

Mechanism and Machine Theory

287

130

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“…(46) to the mobility calculation of the mechanism presented in Fig. 1, we obtain obviously the same erroneous results that were obtained by using Eq.…”

Section: Gronowicz's Contributionmentioning

confidence: 42%

“…(49) extends Eq. (46) proposed by Gronowicz to multiple jointed mechanisms. Agrawal and Rao [43] considered that Eq.…”

Section: Contribution Of Agrawal and Raomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mobility of mechanisms: a critical review

Gogu

2005

Mechanism and Machine Theory

287

130

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“…The first barrier arises from implementation of matrix groups for affine transformations where finite motions of a rigid body cannot be directly represented by Chasles' axis [17] as well as by the angular and/or linear displacement about the axis, leading to a complicated description of rigid body motion. The second barrier comes from that the finite motion composition cannot be algebraically derived by Baker-Campbell-Hausdorff formula [33]. Consequently, motion patterns of a number of parallel mechanisms cannot precisely be described using the existing matrix group based method since they can no longer be represented by products of several Lie subgroups [34].…”

Section: Introductionmentioning

confidence: 99%

A way of relating instantaneous and finite screws based on the screw triangle product

Sun

Yang

Huang

et al. 2017

Mechanism and Machine Theory

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Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP URL' above for details on accessing the published version and note that access may require a subscription. Abstract: It has been a desire to unify the models for structural and parametric analyses and design in the field of robotic mechanisms.This requires a mathematical tool that enables analytical description, formulation and operation possible for both finite and instantaneous motions. This paper presents a method to investigate the algebraic structures of finite screws represented in a quasivector form and instantaneous screws represented in a vector form. By revisiting algebraic operations of screw compositions, this paper examines associativity and derivative properties of the screw triangle product of finite screws and produces a vigorous proof that a derivative of a screw triangle product can be expressed as a linear combination of instantaneous screws. It is proved that the entire set of finite screws forms an algebraic structure as Lie group under the screw triangle product and its time derivative at the initial pose forms the corresponding Lie algebra under the screw cross product, allowing the algebraic structures of finite screws in quasi-vector form and instantaneous screws in vector form to be revealed.

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“…Agrawal and Rao analyzed and determined the mobility of kinematic chains with fractionated DOFs (Agrawal and Rao, 1987). Based on the SE(3) displacement groups, Fanghella and Galletti analyzed the mobility properties of single-loop kinematic chains by regarding the connectivity between any two links in a chain and the invariant properties of the displacement group of their relative motion (Fanghella and Galletti, 1994). Hwang and Hwang presented a loopdecreasing method for the detection of rigid subchains of rigid planar kinematic chains (Hwang and Hwang, 1991).…”

Section: Introductionmentioning

confidence: 99%

Solving the double-banana rigidity problem: a loop-based approach

2016

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Abstract. Rigidity detection is an important tool for structural synthesis of mechanisms, as it helps to unveil possible sources of inconsistency in Grübler's count of degrees of freedom (DOFs) and thus to generate consistent kinematical models of complex mechanisms. One case that has puzzled researchers over many decades is the famous "double-banana" problem, which is a representative counter-example of Laman's rigidity condition formula for which existing standard DOF counting formulas fail. The reason for this is the body-by-body and joint-by-joint decomposition of the interconnection structure in classical algorithms, which does not unveil structural isotropy groups for example when whole substructures rotate about an "implied hinge" according to Streinu. In this paper, a completely new approach for rigidity detection for cases as the "double-banana" counterexample in which bars are connected by spherical joints is presented. The novelty of the approach consists in regarding the structure not as a set of joint-connected bodies but as a set of interconnected loops. By tracking isolated DOFs such as those arising between pairs of spherical joints, rigidity/mobility subspaces can be easily identified and thus the "double-banana" paradox can be resolved. Although the paper focuses on the solution of the double-banana mechanism as a special case of paradox bar-and-joint frameworks, the procedure is valid for general body-and-joint mechanisms, as is shown by the decomposition of spherical joints into a series of revolute joints and their rigid-link interconnections.

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Mobility analysis of single-loop kinematic chains: an algorithmic approach based on displacement groups

Cited by 32 publications

References 11 publications

Mobility of mechanisms: a critical review

Mobility of mechanisms: a critical review

A way of relating instantaneous and finite screws based on the screw triangle product

Solving the double-banana rigidity problem: a loop-based approach

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