Kinematics of the 3-UPU wrist

Recently, it has been shown that a parallel mechanism architecture, called 3-UPU and used for translational manipulators, can be employed to obtain manipulators able to make the end effector perform infinitesimal spherical motions. The possibility of performing infinitesimal spherical motions is a necessary but not sufficient condition to guarantee that the end effector performs a finite spherical motion, i.e., the manipulator is a parallel wrist. In this paper it is demonstrated that the 3-UPU architecture, can be employed to obtain parallel wrists, named 3-UPU wrists. Moreover, it is shown that the 3-UPU wrists may reach singular configurations in which the spherical constraint between the end effector and the frame fails. Finally, the singularity condition, that makes it possible to find all the 3-UPU wrist's singular configurations, is written in explicit form and is geometrically interpreted. © 2003 Elsevier Science Ltd. All rights reserved.