Grashof-Type Rotatability Criteria of Spherical Five-Bar Linkages

Abstract

In this paper rotatability criteria of spherical five-bar linkages are analytically derived. First an equivalent linkage in which the sum of any two link lengths is less than π is found and then rotatability criteria of spherical five-bar linkages are developed for this linkage. The rotatability criteria developed in this paper are stated as follows: The two input angles are completely revolvable if and only if in the equivalent linkage the sum of the longest and the two shortest links is less than the sum of the remaining two links and there is one and only one long link between each pair of noninput angles (long link being any link excluding the shortest links). It is also shown that an angle θ included by two links αi and αj is completely revolvable if and only if the sum of the longest link and shorter of αi and αj is less than or equal to the sum of the remaining three links.