Topological synthesis and analysis of geared linkages based on matrix powers

D. G. Olson; A. G. Erdman; D. R. Riley

doi:10.1115/DETC1989-0104

Topological synthesis and analysis of geared linkages based on matrix powers

D. G. Olson, A. G. Erdman, D. R. Riley

Mechanical Engineering

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

1 Scopus citations

Abstract

A new method for transforming pin-jointed kinematic chains into geared linkages is introduced. The method utilizes the graph representation in the form of the adjacency matrix and the 'degree matrix', and the powers of these matrices. The method involves first determining the feasible locations for assigning gear pairs in a kinematic chain, followed by determining which of the choices are distinct, and finally, determining the distinct possible ways of assigning the ground link for each distinct 'geared kinematic chain' so formed. Because the method is based on matrix manipulations and does not rely on visual inspection, it is easily implemented on a digital computer. The method is applied to an example class of geared mechanism, the single-dof geared seven-bar linkages.

Original language	English (US)
Title of host publication	Mechanical Systems Analysis, Design and Simulation
Publisher	American Society of Mechanical Engineers (ASME)
Pages	371-377
Number of pages	7
Volume	19-3
Edition	pt 3
ISBN (Electronic)	9780791803691
DOIs	https://doi.org/10.1115/DETC1989-0104
State	Published - 1989
Event	ASME 1989 Design Technical Conferences, DETC 1989 - Montreal, United States Duration: Sep 17 1989 → Sep 21 1989

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	3

Conference

Conference	ASME 1989 Design Technical Conferences, DETC 1989
Country/Territory	United States
City	Montreal
Period	9/17/89 → 9/21/89

Bibliographical note

Publisher Copyright:
© 1989 American Society of Mechanical Engineers (ASME). All rights reserved.

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10.1115/DETC1989-0104

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Olson, D. G., Erdman, A. G., & Riley, D. R. (1989). Topological synthesis and analysis of geared linkages based on matrix powers. In Mechanical Systems Analysis, Design and Simulation (pt 3 ed., Vol. 19-3, pp. 371-377). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 3). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC1989-0104

Topological synthesis and analysis of geared linkages based on matrix powers. / Olson, D. G.; Erdman, A. G.; Riley, D. R.
Mechanical Systems Analysis, Design and Simulation. Vol. 19-3 pt 3. ed. American Society of Mechanical Engineers (ASME), 1989. p. 371-377 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 3).

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

Olson, DG, Erdman, AG & Riley, DR 1989, Topological synthesis and analysis of geared linkages based on matrix powers. in Mechanical Systems Analysis, Design and Simulation. pt 3 edn, vol. 19-3, Proceedings of the ASME Design Engineering Technical Conference, vol. 3, American Society of Mechanical Engineers (ASME), pp. 371-377, ASME 1989 Design Technical Conferences, DETC 1989, Montreal, United States, 9/17/89. https://doi.org/10.1115/DETC1989-0104

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AB - A new method for transforming pin-jointed kinematic chains into geared linkages is introduced. The method utilizes the graph representation in the form of the adjacency matrix and the 'degree matrix', and the powers of these matrices. The method involves first determining the feasible locations for assigning gear pairs in a kinematic chain, followed by determining which of the choices are distinct, and finally, determining the distinct possible ways of assigning the ground link for each distinct 'geared kinematic chain' so formed. Because the method is based on matrix manipulations and does not rely on visual inspection, it is easily implemented on a digital computer. The method is applied to an example class of geared mechanism, the single-dof geared seven-bar linkages.

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Topological synthesis and analysis of geared linkages based on matrix powers

Abstract

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