Abstract
This paper provides three representations for the topological structures of mechanisms and chains with variable topologies. The concepts are topology matrices, graphs, and joint codes. Topology matrices and graphs are traditional representations of mechanism topologies, and have the advantage of observation ease. Joint codes are proposed for simplifying the topology matrices and graphs for mechanisms with variable topologies. The push-button mechanical lock is applied as an example to illustrate the proposed three representations. These representations are useful for analyzing the characteristics of topological structures of mechanisms and chains with variable topologies. The result of this work can be extended for synthesizing mechanisms and chains with variable topologies.
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