A New Metric for Motion Approximation for the Synthesis of Planar Four-Bar Linkages

Huan Liu; Qiaode Jeffrey Ge

doi:10.1007/978-3-031-95489-4_22

A New Metric for Motion Approximation for the Synthesis of Planar Four-Bar Linkages

Huan Liu
, Qiaode Jeffrey Ge

Mechanical Engineering

Stony Brook University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Motion generation or rigid body guidance for planar four-bar linkages is a classical problem in planar kinematics. This paper introduces a novel metric for motion approximation that guides a bounded planar object rather than an infinite plane through a set of given positions. The metric is based on an estimate of an object size using the average squared distance (ASD) among all homologous points of the bounded object. In this way, the motion approximation problem is reduced to that of finding the linkage dimensions that minimizes the sum of ASD distances for all given positions. Numerical examples are provided to compare the proposed metric with three other existing metrics for motion approximation without taking into account the size of the moving object. Also explored is the effect of the object size on the dimensions of the resulting four-bar linkages.

Original language	English
Title of host publication	Proceedings of the 2025 CCToMM Symposium on Mechanisms, Machines, and Mechatronics
Editors	Eric Lanteigne, Scott Nokleby
Publisher	Springer Science and Business Media B.V.
Pages	270-286
Number of pages	17
ISBN (Print)	9783031954887
DOIs	https://doi.org/10.1007/978-3-031-95489-4_22
State	Published - 2025
Event	13th CCToMM Symposium on Mechanisms, Machines, and Mechatronics, CCToMM M3 2025 - Ottawa, Canada Duration: Jun 19 2025 → Jun 20 2025

Publication series

Name	Mechanisms and Machine Science
Volume	184
ISSN (Print)	2211-0984
ISSN (Electronic)	2211-0992

Conference

Conference	13th CCToMM Symposium on Mechanisms, Machines, and Mechatronics, CCToMM M3 2025
Country/Territory	Canada
City	Ottawa
Period	06/19/25 → 06/20/25

Keywords

distance metric
motion synthesis
planar linkage
structural error

Access to Document

10.1007/978-3-031-95489-4_22

Cite this

Liu, H., & Ge, Q. J. (2025). A New Metric for Motion Approximation for the Synthesis of Planar Four-Bar Linkages. In E. Lanteigne, & S. Nokleby (Eds.), Proceedings of the 2025 CCToMM Symposium on Mechanisms, Machines, and Mechatronics (pp. 270-286). (Mechanisms and Machine Science; Vol. 184). Springer Science and Business Media B.V.. https://doi.org/10.1007/978-3-031-95489-4_22

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title = "A New Metric for Motion Approximation for the Synthesis of Planar Four-Bar Linkages",

abstract = "Motion generation or rigid body guidance for planar four-bar linkages is a classical problem in planar kinematics. This paper introduces a novel metric for motion approximation that guides a bounded planar object rather than an infinite plane through a set of given positions. The metric is based on an estimate of an object size using the average squared distance (ASD) among all homologous points of the bounded object. In this way, the motion approximation problem is reduced to that of finding the linkage dimensions that minimizes the sum of ASD distances for all given positions. Numerical examples are provided to compare the proposed metric with three other existing metrics for motion approximation without taking into account the size of the moving object. Also explored is the effect of the object size on the dimensions of the resulting four-bar linkages.",

keywords = "distance metric, motion synthesis, planar linkage, structural error",

author = "Huan Liu and Ge, \{Qiaode Jeffrey\}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; 13th CCToMM Symposium on Mechanisms, Machines, and Mechatronics, CCToMM M3 2025 ; Conference date: 19-06-2025 Through 20-06-2025",

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Liu, H & Ge, QJ 2025, A New Metric for Motion Approximation for the Synthesis of Planar Four-Bar Linkages. in E Lanteigne & S Nokleby (eds), Proceedings of the 2025 CCToMM Symposium on Mechanisms, Machines, and Mechatronics. Mechanisms and Machine Science, vol. 184, Springer Science and Business Media B.V., pp. 270-286, 13th CCToMM Symposium on Mechanisms, Machines, and Mechatronics, CCToMM M3 2025, Ottawa, Canada, 06/19/25. https://doi.org/10.1007/978-3-031-95489-4_22

A New Metric for Motion Approximation for the Synthesis of Planar Four-Bar Linkages. / Liu, Huan; Ge, Qiaode Jeffrey.
Proceedings of the 2025 CCToMM Symposium on Mechanisms, Machines, and Mechatronics. ed. / Eric Lanteigne; Scott Nokleby. Springer Science and Business Media B.V., 2025. p. 270-286 (Mechanisms and Machine Science; Vol. 184).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Motion generation or rigid body guidance for planar four-bar linkages is a classical problem in planar kinematics. This paper introduces a novel metric for motion approximation that guides a bounded planar object rather than an infinite plane through a set of given positions. The metric is based on an estimate of an object size using the average squared distance (ASD) among all homologous points of the bounded object. In this way, the motion approximation problem is reduced to that of finding the linkage dimensions that minimizes the sum of ASD distances for all given positions. Numerical examples are provided to compare the proposed metric with three other existing metrics for motion approximation without taking into account the size of the moving object. Also explored is the effect of the object size on the dimensions of the resulting four-bar linkages.

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