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


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
PublisherPubl by American Soc of Mechanical Engineers (ASME)
Number of pages7
Editionpt 3
StatePublished - Dec 1 1989
EventAdvances in Design Automation - 1989 - Montreal, Que, Can
Duration: Sep 17 1989Sep 21 1989


OtherAdvances in Design Automation - 1989
CityMontreal, Que, Can

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