Workspace atlases for the design of spherical 3-DOF serial wrists

In this paper, the physical model of the solution space of spherical 3-DOF serial wrists is established. The reachable workspaces are classified. The dexterous workspaces for such wrists are investigated based on the rotatability conditions for the spherical 4-bar mechanism. Using the theory of conformal transformation, we obtain plane figures of the reachable and dexterous workspaces. The atlases of the workspaces in the physical model of the solution space are plotted. These results are useful not only for designer overall to understand the relationship between the workspaces and link lengths of spherical 3-DOF serial wrists, but also for the design of the wrists.