Classification of higher mobility closed-loop linkages

Abstract

We provide a complete classification of paradoxical closed-loop n-linkages, where \(n\ge 6\), of mobility \(n-4\) or higher, containing revolute, prismatic or helical joints. We also explicitly write down strong necessary conditions for nR-linkages of mobility \(n-5\). Our main new tool is a geometric relation between a linkage L and another linkage \(L'\) resulting from adding equations to the configuration space of L. We then lift known classification results for \(L'\) to L using this relation.