Rotatability Considerations for Spherical Four-Bar Linkages With Applications to Robot Wrist Design

Abstract

The following result for spherical four-bar mechanisms is proved: Let all links of a spherical four-bar linkage be in the range [0, π]. Consider two linkages—one primary (p) and another secondary (s) according to the condition αi p + αf p < αi s + αf s where αs = π − αp . Then the input link is fully rotatable iff αi p + αf p < αc + α0 , |αi p − αf p | > |αc − α0 | and αi p + αf p + αc + α0 < 2π. An alternate form of this result also is developed. Applications of these results in determining full or partial rotatability of grippers in spherical robot wrists are discussed.