In analytical dyadic linkage synthesis, a four bar linkage is modeled as two dyads, joined at the coupler link. Each of the two dyads must satisfy the task requirements, for example position and orientation of a body. A general four-bar linkage model consists of two sets of dyads, each representing the right and left sides of the linkage.
Z r are the vectors forming the right-hand dyad.
Equation 2 is often called the standard-form equation for dyadic linkage synthesis. The problems of interest in this table are the cases of three and four positions. With three positions, the free choices can be made such that the resulting equations are linear, and thus easily solved. This leads to two infinities of solutions based on the two free choices. The difficulty here is the need to select values for the free choices, generally a non-intuitive task.