A novel geometric approach for planar motion generation based on similarity transformation of pole maps

Burmester theory provide guidance solutions by dyad precise synthesis with up to five given exact poses. But it has little influence on solution mechanism features and not suitable for the rigid body guidance mechanisms without “center- and circle-point” structure or planar motion generation with partly fuzzy positions. This paper proposed a geometric synthesis approach, which is composed of fuzzy position construction, function module selection, fuzzy pole determination and quasi-similarity transformation. Based on quasi-similarity transformation theory, pole maps were built up as unified geometric identification between given positions and guidance mechanisms. Various normalized mechanism function modules were established with full topology information, including dimension ratios. As a bridge, the mapping rules directly revealed the relationship between guidance tasks and guidance mechanisms. Finally, this feature-driven geometric synthesis approach was demonstrated with two examples, a belt mechanism for exact three-position task and a geared linkage mechanism for fuzzy four-position task.