A Unified Approach to Dyad and Triad Synthesis for Planar Mechanisms for Motion Generation

Shrinath Deshpande; Anurag Purwar

doi:10.1007/978-3-030-99826-4_21

A Unified Approach to Dyad and Triad Synthesis for Planar Mechanisms for Motion Generation

Shrinath Deshpande
, Anurag Purwar

Mechanical Engineering

Stony Brook University

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

5 Scopus citations

Abstract

In this paper, we present a unified approach to the synthesis of planar dyads and triads found in planar closed-loop mechanisms for the motion generation problem. By decomposing a planar mechanism in terms of dyads and triads as building blocks, the problem of mechanism synthesis is reduced to the identification of such entities. By using planar quaternions and kinematic mapping, a common algebraic form of the geometric constraints of the dyads and triads is derived and a two-step algorithm then finds the type and dimensions of dyads and triads. The input to the problem is a set of constraints on poses, pivot locations, or other practical constraints, which can be represented in an algebraic form. The two-step algorithm first assembles these constraints as a set of linear equations, uses Singular Value Decomposition to obtain a candidate solution space, which is further subjected to constrained Lagrangian optimization to find the exact or approximate dyads or triads. This algorithm outputs a set of dyads and triads as solutions, which can be combined to obtain four-bar and six-bar mechanisms as well as planar parallel manipulators.

Original language	English
Title of host publication	Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics
Editors	Pierre Larochelle, J. Michael McCarthy
Publisher	Springer Science and Business Media B.V.
Pages	243-261
Number of pages	19
ISBN (Print)	9783030998257
DOIs	https://doi.org/10.1007/978-3-030-99826-4_21
State	Published - 2022
Event	2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022 - Rapid City, United States Duration: May 19 2022 → May 21 2022

Publication series

Name	Mechanisms and Machine Science
Volume	118 MMS
ISSN (Print)	2211-0984
ISSN (Electronic)	2211-0992

Conference

Conference	2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022
Country/Territory	United States
City	Rapid City
Period	05/19/22 → 05/21/22

Keywords

Dyad synthesis
Motion generation
Planar parallel manipulators
Simultaneous type and dimension synthesis
Triad synthesis

Access to Document

10.1007/978-3-030-99826-4_21

Cite this

Deshpande, S., & Purwar, A. (2022). A Unified Approach to Dyad and Triad Synthesis for Planar Mechanisms for Motion Generation. In P. Larochelle, & J. M. McCarthy (Eds.), Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics (pp. 243-261). (Mechanisms and Machine Science; Vol. 118 MMS). Springer Science and Business Media B.V.. https://doi.org/10.1007/978-3-030-99826-4_21

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title = "A Unified Approach to Dyad and Triad Synthesis for Planar Mechanisms for Motion Generation",

abstract = "In this paper, we present a unified approach to the synthesis of planar dyads and triads found in planar closed-loop mechanisms for the motion generation problem. By decomposing a planar mechanism in terms of dyads and triads as building blocks, the problem of mechanism synthesis is reduced to the identification of such entities. By using planar quaternions and kinematic mapping, a common algebraic form of the geometric constraints of the dyads and triads is derived and a two-step algorithm then finds the type and dimensions of dyads and triads. The input to the problem is a set of constraints on poses, pivot locations, or other practical constraints, which can be represented in an algebraic form. The two-step algorithm first assembles these constraints as a set of linear equations, uses Singular Value Decomposition to obtain a candidate solution space, which is further subjected to constrained Lagrangian optimization to find the exact or approximate dyads or triads. This algorithm outputs a set of dyads and triads as solutions, which can be combined to obtain four-bar and six-bar mechanisms as well as planar parallel manipulators.",

keywords = "Dyad synthesis, Motion generation, Planar parallel manipulators, Simultaneous type and dimension synthesis, Triad synthesis",

author = "Shrinath Deshpande and Anurag Purwar",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022 ; Conference date: 19-05-2022 Through 21-05-2022",

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Deshpande, S & Purwar, A 2022, A Unified Approach to Dyad and Triad Synthesis for Planar Mechanisms for Motion Generation. in P Larochelle & JM McCarthy (eds), Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics. Mechanisms and Machine Science, vol. 118 MMS, Springer Science and Business Media B.V., pp. 243-261, 2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022, Rapid City, United States, 05/19/22. https://doi.org/10.1007/978-3-030-99826-4_21

A Unified Approach to Dyad and Triad Synthesis for Planar Mechanisms for Motion Generation. / Deshpande, Shrinath; Purwar, Anurag.
Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics. ed. / Pierre Larochelle; J. Michael McCarthy. Springer Science and Business Media B.V., 2022. p. 243-261 (Mechanisms and Machine Science; Vol. 118 MMS).

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

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N2 - In this paper, we present a unified approach to the synthesis of planar dyads and triads found in planar closed-loop mechanisms for the motion generation problem. By decomposing a planar mechanism in terms of dyads and triads as building blocks, the problem of mechanism synthesis is reduced to the identification of such entities. By using planar quaternions and kinematic mapping, a common algebraic form of the geometric constraints of the dyads and triads is derived and a two-step algorithm then finds the type and dimensions of dyads and triads. The input to the problem is a set of constraints on poses, pivot locations, or other practical constraints, which can be represented in an algebraic form. The two-step algorithm first assembles these constraints as a set of linear equations, uses Singular Value Decomposition to obtain a candidate solution space, which is further subjected to constrained Lagrangian optimization to find the exact or approximate dyads or triads. This algorithm outputs a set of dyads and triads as solutions, which can be combined to obtain four-bar and six-bar mechanisms as well as planar parallel manipulators.

AB - In this paper, we present a unified approach to the synthesis of planar dyads and triads found in planar closed-loop mechanisms for the motion generation problem. By decomposing a planar mechanism in terms of dyads and triads as building blocks, the problem of mechanism synthesis is reduced to the identification of such entities. By using planar quaternions and kinematic mapping, a common algebraic form of the geometric constraints of the dyads and triads is derived and a two-step algorithm then finds the type and dimensions of dyads and triads. The input to the problem is a set of constraints on poses, pivot locations, or other practical constraints, which can be represented in an algebraic form. The two-step algorithm first assembles these constraints as a set of linear equations, uses Singular Value Decomposition to obtain a candidate solution space, which is further subjected to constrained Lagrangian optimization to find the exact or approximate dyads or triads. This algorithm outputs a set of dyads and triads as solutions, which can be combined to obtain four-bar and six-bar mechanisms as well as planar parallel manipulators.

KW - Dyad synthesis

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