A Pose-Matrix Approach to Size-Dependent Approximate Motion Synthesis of Planar Four-Bar Linkages

Huan Liu; Anurag Purwar; Qiaode Jeffrey Ge

doi:10.1007/978-3-032-30384-4_11

A Pose-Matrix Approach to Size-Dependent Approximate Motion Synthesis of Planar Four-Bar Linkages

Huan Liu
, Anurag Purwar
, Qiaode Jeffrey Ge

Mechanical Engineering

Stony Brook University

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

Abstract

This paper extends and refines our previous work on a new class of approximate motion synthesis problems in that the approximation error is defined using the Average Squared Distance (or ASD) of all homologous points between two poses of a bounded object. This leads to a novel synthesis methodology such that the resulting designs of four-bar linkages are also size-dependent. First, N given poses of a planar object are combined to construct the so-called “pose matrix” whose dimension is N×8. The approximate null space of the pose matrix is then used as a feasible design space for exploring linkage designs that minimize the ASD-based approximation error. The result is a unified algorithm for the size-dependent approximate motion synthesis of planar linkages with revolute and/or prismatic joints. A numerical example is provided to illustrate this novel approach.

Original language	English
Title of host publication	Proceedings of the 2026 USCToMM Symposium on Mechanical Systems and Robotics
Editors	J. Michael McCarthy, Pierre Larochelle, Craig P. Lusk, Anurag Purwar, Nina Robson
Publisher	Springer Science and Business Media B.V.
Pages	125-136
Number of pages	12
ISBN (Print)	9783032303837
DOIs	https://doi.org/10.1007/978-3-032-30384-4_11
State	Published - 2027
Event	4th USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2026 - Irvine, United States Duration: May 21 2026 → May 23 2026

Publication series

Name	Mechanisms and Machine Science
Volume	216 MMS
ISSN (Print)	2211-0984
ISSN (Electronic)	2211-0992

Conference

Conference	4th USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2026
Country/Territory	United States
City	Irvine
Period	05/21/26 → 05/23/26

Keywords

Distance metric
Motion synthesis
Structural error

Access to Document

10.1007/978-3-032-30384-4_11

Cite this

Liu, H., Purwar, A., & Ge, Q. J. (2027). A Pose-Matrix Approach to Size-Dependent Approximate Motion Synthesis of Planar Four-Bar Linkages. In J. M. McCarthy, P. Larochelle, C. P. Lusk, A. Purwar, & N. Robson (Eds.), Proceedings of the 2026 USCToMM Symposium on Mechanical Systems and Robotics (pp. 125-136). (Mechanisms and Machine Science; Vol. 216 MMS). Springer Science and Business Media B.V.. https://doi.org/10.1007/978-3-032-30384-4_11

Liu, Huan ; Purwar, Anurag ; Ge, Qiaode Jeffrey. / A Pose-Matrix Approach to Size-Dependent Approximate Motion Synthesis of Planar Four-Bar Linkages. Proceedings of the 2026 USCToMM Symposium on Mechanical Systems and Robotics. editor / J. Michael McCarthy ; Pierre Larochelle ; Craig P. Lusk ; Anurag Purwar ; Nina Robson. Springer Science and Business Media B.V., 2027. pp. 125-136 (Mechanisms and Machine Science).

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title = "A Pose-Matrix Approach to Size-Dependent Approximate Motion Synthesis of Planar Four-Bar Linkages",

abstract = "This paper extends and refines our previous work on a new class of approximate motion synthesis problems in that the approximation error is defined using the Average Squared Distance (or ASD) of all homologous points between two poses of a bounded object. This leads to a novel synthesis methodology such that the resulting designs of four-bar linkages are also size-dependent. First, N given poses of a planar object are combined to construct the so-called {\textquotedblleft}pose matrix{\textquotedblright} whose dimension is N{\texttimes}8. The approximate null space of the pose matrix is then used as a feasible design space for exploring linkage designs that minimize the ASD-based approximation error. The result is a unified algorithm for the size-dependent approximate motion synthesis of planar linkages with revolute and/or prismatic joints. A numerical example is provided to illustrate this novel approach.",

keywords = "Distance metric, Motion synthesis, Structural error",

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

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2027.; 4th USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2026 ; Conference date: 21-05-2026 Through 23-05-2026",

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doi = "10.1007/978-3-032-30384-4\_11",

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Liu, H, Purwar, A & Ge, QJ 2027, A Pose-Matrix Approach to Size-Dependent Approximate Motion Synthesis of Planar Four-Bar Linkages. in JM McCarthy, P Larochelle, CP Lusk, A Purwar & N Robson (eds), Proceedings of the 2026 USCToMM Symposium on Mechanical Systems and Robotics. Mechanisms and Machine Science, vol. 216 MMS, Springer Science and Business Media B.V., pp. 125-136, 4th USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2026, Irvine, United States, 05/21/26. https://doi.org/10.1007/978-3-032-30384-4_11

A Pose-Matrix Approach to Size-Dependent Approximate Motion Synthesis of Planar Four-Bar Linkages. / Liu, Huan; Purwar, Anurag; Ge, Qiaode Jeffrey.
Proceedings of the 2026 USCToMM Symposium on Mechanical Systems and Robotics. ed. / J. Michael McCarthy; Pierre Larochelle; Craig P. Lusk; Anurag Purwar; Nina Robson. Springer Science and Business Media B.V., 2027. p. 125-136 (Mechanisms and Machine Science; Vol. 216 MMS).

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

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N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2027.

PY - 2027

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N2 - This paper extends and refines our previous work on a new class of approximate motion synthesis problems in that the approximation error is defined using the Average Squared Distance (or ASD) of all homologous points between two poses of a bounded object. This leads to a novel synthesis methodology such that the resulting designs of four-bar linkages are also size-dependent. First, N given poses of a planar object are combined to construct the so-called “pose matrix” whose dimension is N×8. The approximate null space of the pose matrix is then used as a feasible design space for exploring linkage designs that minimize the ASD-based approximation error. The result is a unified algorithm for the size-dependent approximate motion synthesis of planar linkages with revolute and/or prismatic joints. A numerical example is provided to illustrate this novel approach.

AB - This paper extends and refines our previous work on a new class of approximate motion synthesis problems in that the approximation error is defined using the Average Squared Distance (or ASD) of all homologous points between two poses of a bounded object. This leads to a novel synthesis methodology such that the resulting designs of four-bar linkages are also size-dependent. First, N given poses of a planar object are combined to construct the so-called “pose matrix” whose dimension is N×8. The approximate null space of the pose matrix is then used as a feasible design space for exploring linkage designs that minimize the ASD-based approximation error. The result is a unified algorithm for the size-dependent approximate motion synthesis of planar linkages with revolute and/or prismatic joints. A numerical example is provided to illustrate this novel approach.

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SN - 9783032303837

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Liu H, Purwar A, Ge QJ. A Pose-Matrix Approach to Size-Dependent Approximate Motion Synthesis of Planar Four-Bar Linkages. In McCarthy JM, Larochelle P, Lusk CP, Purwar A, Robson N, editors, Proceedings of the 2026 USCToMM Symposium on Mechanical Systems and Robotics. Springer Science and Business Media B.V. 2027. p. 125-136. (Mechanisms and Machine Science). doi: 10.1007/978-3-032-30384-4_11