An important question facing a designer is wether a certain machine system will have a stable operating condition. In this paper, the distributions of the critical running speeds of flexible linkage mechanisms are investigated theoretically by utlizing the Floquet theory. The explicit relationships between the critical running speeds and the average frequencies of the linkage mechanisms in a period are presented. The relationships are suitable for the linkage mechanisms with all links considered as elastic members and having large number of elastic degrees of freedom. Numerical verifications for the relationships are provided.

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