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 αip + αfp < αis + αfs where αs = π − αp. Then the input link is fully rotatable iff αip + αfp < αc + α0, |αip − αfp| > |αc − α0| and αip + αfp + 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.