In this paper, we introduce a method to design useful four-bar and six-bar linkages that reach more than the five specified task positions used in Burmester synthesis of RR cranks. Similar to existing methods, we minimize the crank-length error in each task position, however our approach does not introduce penalty functions to eliminate defective linkage. Instead, we search user defined tolerance zones around the task positions to find defect-free, or usable, linkage designs. Finally, candidate linkages are ranked by average link length. A numerical example is provided for seven task positions for a four and six-bar linkage.
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