Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints

Jingzhou Yang; Karim Abdel-Malek

doi:10.1115/detc2005-84180

Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints

Jingzhou Yang, Karim Abdel-Malek

Mechanical Engineering

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

Abstract

An analytical method is presented to obtain all surfaces enveloping the workspace of a general n degree-of-freedom mechanism with non-unilateral constraints. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation method for serial manipulators. The method introduced in this paper is based upon analytical criteria for determining singular behavior of the mechanism. A perturbation approach is implemented to determine the interior and exterior of the workspace. The complete mathematical formulation is presented and illustrated using 3 and 4 DOF spatial manipulators. The paper present a rigorous analysis of the sub-Jacobians to determine a classification of singularities: Type I sets are position Jacobian singularities; Type II sets are instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III sets are domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV sets are coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one submatrix due to either of two occurrences: a Type II or Type III singularities. The paper presents a general formulation for determining the workspace.

Original language	English
Title of host publication	Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005
Subtitle of host publication	29th Mechanisms and Robotics Conference
Publisher	American Society of Mechanical Engineers
Pages	717-726
Number of pages	10
ISBN (Print)	0791847446, 9780791847442
DOIs	https://doi.org/10.1115/detc2005-84180
State	Published - 2005
Event	DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Long Beach, CA, United States Duration: Sep 24 2005 → Sep 28 2005

Publication series

Name	Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005
Volume	7 B

Conference

Conference	DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Country/Territory	United States
City	Long Beach, CA
Period	09/24/05 → 09/28/05

Keywords

Jacobian row-rank deficiency
Non-unilateral
Singularity

Access to Document

10.1115/detc2005-84180

Cite this

Yang, J., & Abdel-Malek, K. (2005). Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints. In Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005: 29th Mechanisms and Robotics Conference (pp. 717-726). (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005; Vol. 7 B). American Society of Mechanical Engineers. https://doi.org/10.1115/detc2005-84180

Yang, Jingzhou ; Abdel-Malek, Karim. / Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005: 29th Mechanisms and Robotics Conference. American Society of Mechanical Engineers, 2005. pp. 717-726 (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005).

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title = "Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints",

abstract = "An analytical method is presented to obtain all surfaces enveloping the workspace of a general n degree-of-freedom mechanism with non-unilateral constraints. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation method for serial manipulators. The method introduced in this paper is based upon analytical criteria for determining singular behavior of the mechanism. A perturbation approach is implemented to determine the interior and exterior of the workspace. The complete mathematical formulation is presented and illustrated using 3 and 4 DOF spatial manipulators. The paper present a rigorous analysis of the sub-Jacobians to determine a classification of singularities: Type I sets are position Jacobian singularities; Type II sets are instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III sets are domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV sets are coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one submatrix due to either of two occurrences: a Type II or Type III singularities. The paper presents a general formulation for determining the workspace.",

keywords = "Jacobian row-rank deficiency, Non-unilateral, Singularity",

author = "Jingzhou Yang and Karim Abdel-Malek",

year = "2005",

doi = "10.1115/detc2005-84180",

language = "English",

isbn = "0791847446",

series = "Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005",

publisher = "American Society of Mechanical Engineers",

pages = "717--726",

booktitle = "Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005",

note = "DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference ; Conference date: 24-09-2005 Through 28-09-2005",

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Yang, J & Abdel-Malek, K 2005, Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints. in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005: 29th Mechanisms and Robotics Conference. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005, vol. 7 B, American Society of Mechanical Engineers, pp. 717-726, DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, United States, 09/24/05. https://doi.org/10.1115/detc2005-84180

Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints. / Yang, Jingzhou; Abdel-Malek, Karim.
Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005: 29th Mechanisms and Robotics Conference. American Society of Mechanical Engineers, 2005. p. 717-726 (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005; Vol. 7 B).

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

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AU - Yang, Jingzhou

AU - Abdel-Malek, Karim

PY - 2005

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N2 - An analytical method is presented to obtain all surfaces enveloping the workspace of a general n degree-of-freedom mechanism with non-unilateral constraints. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation method for serial manipulators. The method introduced in this paper is based upon analytical criteria for determining singular behavior of the mechanism. A perturbation approach is implemented to determine the interior and exterior of the workspace. The complete mathematical formulation is presented and illustrated using 3 and 4 DOF spatial manipulators. The paper present a rigorous analysis of the sub-Jacobians to determine a classification of singularities: Type I sets are position Jacobian singularities; Type II sets are instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III sets are domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV sets are coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one submatrix due to either of two occurrences: a Type II or Type III singularities. The paper presents a general formulation for determining the workspace.

AB - An analytical method is presented to obtain all surfaces enveloping the workspace of a general n degree-of-freedom mechanism with non-unilateral constraints. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation method for serial manipulators. The method introduced in this paper is based upon analytical criteria for determining singular behavior of the mechanism. A perturbation approach is implemented to determine the interior and exterior of the workspace. The complete mathematical formulation is presented and illustrated using 3 and 4 DOF spatial manipulators. The paper present a rigorous analysis of the sub-Jacobians to determine a classification of singularities: Type I sets are position Jacobian singularities; Type II sets are instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III sets are domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV sets are coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one submatrix due to either of two occurrences: a Type II or Type III singularities. The paper presents a general formulation for determining the workspace.

KW - Jacobian row-rank deficiency

KW - Non-unilateral

KW - Singularity

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M3 - Conference contribution

AN - SCOPUS:33244476272

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SN - 9780791847442

T3 - Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005

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BT - Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005

PB - American Society of Mechanical Engineers

T2 - DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

Y2 - 24 September 2005 through 28 September 2005

ER -

Yang J, Abdel-Malek K. Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints. In Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005: 29th Mechanisms and Robotics Conference. American Society of Mechanical Engineers. 2005. p. 717-726. (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005). doi: 10.1115/detc2005-84180

Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints

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Keywords

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