This paper provides examples of a method used to analyze the motion characteristics of single-degree-of-freedom, closed-loop linkages under study a designated input angle and one or two design parameters. The method involves the construction of a singularity trace, which is a plot that reveals changes in the number of geometric inversions, singularities, and changes in the number of branches as a design parameter is varied. This paper applies the method to Watt Ⅱ, Stephenson Ⅲ and double butterfly linkages. For the latter two linkages, instances where the input angle is able to rotate more than one revolution between singularities have been identified. This characteristic demonstrates a net-zero, singularity free, activation sequence that places the mechanism into a different geometric inversion. Additional observations from the examples are given. Instances are shown where the singularity trace for the Watt Ⅱ linkage includes multiple coincident projections of the singularity curve. Cases are shown where subtle changes to two design parameters of a Stephenson Ⅲ linkage drastically alters the motion. Additionally, isolated critical points are found to exist for the double butterfly, where the linkage becomes a structure and looses the freedom to move.
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