This dissertation presents research into the automation of the configuration analysis of eight-bar linkages based on the known 16 linkage topologies. The eight-bar linkage topologies do not distinguish a ground link or an input link, and this research shows that the selection of a ground link yields 71 unique mechanisms. In addition, the selection of a driving link attached to ground results in 153 eight-bar linkages with distinct sets of loop equations. The research automates the configuration analysis process and has been demonstrated for four-bar and six-bar linkages as well as eight-bar linkages. A check of the process includes example 10-bar linkages.
The automation of linkage analysis begins with an adjacency matrix, which defines how the joints connect the links known as the topology of the linkage. The ground link and driving link are selected by the designer, and the automated analysis process determines the smallest set of independent loops. A naming convention is used to automate the definition of link features, dimensions, and joint angles, which yields a text version of the loop equations for the linkage. These loop equations are solved using the Dixon determinant to find the configuration of the linkage for each value of the driving link angle. This formulation also yields the Jacobian of the loop equations, and factors its determinant which is used to find the singularities of the linkage.
The contribution of this research is an automated analysis of eight-bar linkages that applies to four-bar and six-bar linkages, and has been useful in the analysis of 10-bar linkages. This approach has provided a new classification of the 153 eight-bar linkages by family, link assortment, topology, mechanism, and linkage. The automation process can formulate the loop equations and Jacobian conditions for all 153 cases, as well as for all four-bar and six-bar cases.
Automated configuration analysis for eight-bar linkages provides an important tool for evaluating the range of movement of linkages obtained in mechanism synthesis algorithms, allowing identification of linkages that achieve a required task.