Kempe's (focal) linkage generalized, particularly in connection with Hart's second straight-line mechanism☆
TL;DR: In this paper, a geometric approach as well as an algebraic one clears up some of the mystery that hangs around the focal linkage, and the main results that are achieved in the paper are the invention of a new eight-bar linkage containing a bar having rectilinear translation.
About: This article is published in Mechanism and Machine Theory.The article was published on 1975-01-01. It has received 14 citations till now. The article focuses on the topics: Linkage (mechanical) & Straight line mechanism.
Citations
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TL;DR: This paper presents for the first time a novel two degrees of freedom (2-DOF) single-looped dual-plane-symmetric spatial eight-bar linkage with exact straight-line motion applied to the synthesis and construction of a group of deployable Platonic mechanisms with radially reciprocating motion.
Abstract: This paper presents for the first time a novel two degrees of freedom (2-DOF) single-looped dual-plane-symmetric spatial eight-bar linkage with exact straight-line motion. Geometry and kinematics of the eight-bar linkage are investigated and closed-form equations are presented revealing the exact straight-line motion feature of the linkage on the condition that two symmetric inputs are given. In order to secure two symmetric inputs, a geared eight-bar linkage is then proposed converting the linkage into a 1-DOF linkage of exact straight-line motion. The direction of the straight-line motion produced by the proposed eight-bar linkage is changeable and is only dependent on the structure parameters of the two pairs of V-shaped R-R dyads of the linkage. Further, the proposed eight-bar linkage is applied to the synthesis and construction of a group of deployable Platonic mechanisms with radially reciprocating motion. The virtual-center-based (VCB) method is presented for the synthesis and prototypes of the deployable Platonic mechanisms are fabricated verifying the mobility and motion of the proposed mechanisms.
63 citations
01 Jan 2004
TL;DR: In this paper, the focal linkage was used for steering mechanisms for cars or vehicles with symmetrically or eccentrically installed steering-wheels, and a practical design for (un)symmetrical steering mechanisms was presented.
Abstract: It all started with the invention of Peaucellier’s Compound Compass, and a century later with Kempe’s complete compound of which the focal linkage, among other cases, just appeared as a particular case; two conditions for degeneration then being necessary. Mathematical exact straight-line mechanisms came out of it, whereas a special case of the complete compound gave rise to a straight-guided body- motion in any required direction. Kempe’s complete compound lead also to the most generalized inversor of which Peaucellier’s inversor was only a very special case. Application of the focal linkage finally resulted into a practical design for (un)symmetrical steering mechanisms for cars or vehicles with symmetrically or eccentrically installed steering-wheels.
6 citations
Cites background from "Kempe's (focal) linkage generalized..."
...ref.[ 10 ] and figure 16 demonstrating part of the complete bar-linkage.) A further degeneration may finally turn the then conjugated quadrilateral into the already mentioned triple-joint....
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...This may be done by successively stretchrotating each of the inner four-bars, contained in the focal linkage, about the turningjoints of the overall, initial four-bar (ref.[ 10 ].) (The complex multiplication-factor of the first stretch-rotation represents a free choice for its amplitude and its argument, whereas the three remaining stretch-rotations are all dependent on the first....
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01 Jan 1975
TL;DR: The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
6 citations
01 Jan 2010
TL;DR: In this article, the authors presented four overconstrained linkages that are capable of transferring rotations to radially reciprocating motion and analyzed the linkages connected by revolute joints using the screw-loop equation method.
Abstract: Stemming from study of polyhedral and spheroidal linkages and investigation of reciprocating motion of the PRRP chain, this paper presents four overconstrained linkages that are capable of transferring rotations to radially reciprocating motion. The linkages connected by revolute joints are of symmetrical arrangement and mobility one and are analysed by using the screw-loop equation method. The paper further investigates geometry and kinematics of the linkages and reveals their kinematic characteristics, leading to the constraint equation.Copyright © 2010 by ASME
5 citations
TL;DR: In this paper, it was shown that kinematic inversion does not destroy this property, and the symmetry conditions were expressed in terms of the dimensions of the linkage, producing the symmetrical positions of the line.
5 citations
Cites background from "Kempe's (focal) linkage generalized..."
...The symmetry-conditions of the curves, expressed in terms of the dimensions of the generating mechanism, are successively: (1) AoA = BoB, (2) AoE = BoE, (3) <~ AAoF = 4....
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...(3) Choose the angle a and so determine the direction of the symmetry-axis and of the parallel lines AoA and B'B~....
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...Mechanism & Machine Theory, 15(3), 221-228....
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...(3) Stretch-rotate the 4-bar CF"FB~ about C such that F" transforms into the point A"....
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...(1)~ BoAE = BoaAoa = BoaB L (2) J (3) FAAo a 3_ BYE if A, Ao ~ and B y are aligned (or 4( F~Ao~A = ¢....
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References
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34 citations
TL;DR: Developing in a simple and modern manner the essential geometric properties of Burmmester's focal mechanism with applications to the driving of double-rocker linkages and the synthesis of Hart's straight-line mechanism.
19 citations