The workspace of three-DOF, four-jointed spherical wrist mechanisms

The orientational workspace of three-DOF (degree-of-freedom), four-jointed spherical wrist mechanisms was investigated. The workspace boundary equations were derived via geometric consideration. It is shown that, for wrist mechanisms with links 2 and 3 coupled, the workspace boundary consists of circles centered at a fixed axis of rotation, while, for mechanisms with links 1 and 2 coupled, the boundary consists of two branches of curves. The workspace is divided by inner and outer boundaries into regions of accessibility zero, two, and four. The criteria for full workspace design as well as for the maximum four-root region have been established