Topological synthesis and analysis of geared linkages based on matrix powers

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


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 languageEnglish (US)
Title of host publicationMechanical Systems Analysis, Design and Simulation
PublisherAmerican Society of Mechanical Engineers (ASME)
Number of pages7
Editionpt 3
ISBN (Electronic)9780791803691
StatePublished - 1989
EventASME 1989 Design Technical Conferences, DETC 1989 - Montreal, United States
Duration: Sep 17 1989Sep 21 1989

Publication series

NameProceedings of the ASME Design Engineering Technical Conference


ConferenceASME 1989 Design Technical Conferences, DETC 1989
Country/TerritoryUnited States

Bibliographical note

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


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