A novel motion synthesis approach with expandable solution space for planar linkages based on kinematic-mapping

Burmester theory states that up to 4 exact solutions can be found for dyad synthesis problem with five prescribed poses. Many cases have shown that five given poses could result in no exact solution. For more than five poses, what designers obtained are usually mathematically optimal approximated solution, which might not be suitable under practical conditions. In those situations, designers usually want to gradually lower the accuracy requirement so as to bring more approximated solution into consideration. This paper proposed an N-pose motion synthesis approach with expandable solution space for planar linkages. Based on kinematic mapping theory, the optimal joint type and linkage dimensions for planar dyads can be simultaneously obtained. The proposed work mainly focused on the situation that no exact solution exists for five given poses, or that mathematical optimal solution cannot satisfy practical requirements. In those two cases, our approach showed that the solution space can be expanded by introducing or gradually increasing error tolerance, and hereby we could obtain more approximate solutions to determine the best-suited dyads subject to various practical constraints. Finally, four-bar linkages or parallel linkage systems can be constructed to approximate the N-pose given motion and satisfy practical constraints as well.