Statics and singularity loci of the 3-UPU wrist

The static analysis of a parallel wrist, known as 3-UPU wrist, is presented and the 3-UPU wrist singularity conditions are interpreted from the static point of view. An equation (singularity equation) that enables one to find the 3-UPU wrist singular configurations is written in an explicit form. Moreover, the use of the Rodrigues parameters to parameterize the 3-UPU wrist platform orientation allows the singularity equation to become a fourth degree polynomial equation in three unknowns. Finally, a numerical example is presented