Synthesis of Useful Eight-Bar Linkages as Constrained 6R Loops

This paper formulates a methodology for designing planar eight-bar linkages for five task positions, by adding two RR constraints to a user specified 6R loop. It is known that there are 32 ways in which these constraints can be added, to yield as many as 340 different linkages. The methodology uses a random search within the tolerance zones around the task specifications to increase the number of candidate linkages. These linkages are analyzed using the Dixon determinant approach, to find all possible linkage configurations over the range of motion. These configuration trajectories are sorted into branches. Linkages that have all the five task configurations on one branch, ensure their smooth movement through the five task positions. The result is an array of branch-free useful eight-bar linkage designs. An example is provided to illustrate the results.