Movability conditions for a spatial 4RUR mechanism under joint-limit constraints

Movability conditions are derived for a spatial 4RUR (U for universal joint) mechanism with and without joint-limit constraints. The conditions for the existence of fully rotatable cranks and drag link type mechanisms are derived for each of the eight configurations of the mechanism. With no joint-limit constraints or with similar ranges of joint angle limitations, the conditions are identical for pairs of configurations. Changeover possibilities, partial movability and numerical synthesis are discussed.