A number of theorems interrelating certain properties of the algebraic loci traced by some mechanisms are presented. The properties discussed are the algebraic-geometric concepts of order, class, and rank, which are here shown to be related to one another by some new theorems based entirely on the kinematic geometry of the mechanisms. These theorems lead to a better understanding of the geometric relationships both within a mechanism and between different mechanisms. The theorems are also useful in some cases for determining these algebraic-geometric properties.

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