Orientation capability of planar manipulators using virtual joint angle analysis

This paper investigates the orientation capability of a serial manipulator by examining the rotatability of its equivalent mechanism and by proposing the workspace region decomposition, based on the polynomial discriminant derived from the virtual angle analysis of the end-effector link of the equivalent mechanism. The range of real number solutions and that of complex number solutions of the virtual angle are characterised using the analysis of the virtual adjustable ground link. The orientation capability is then characterised in a graphical representation which is then mapped onto a new orientation capability map where the partial dexterous workspace and its orientation range with respect to a workspace position are presented in polar coordinates. The study presents a new way of analysing the orientation capability of planar manipulators in terms of orientation boundary loci and orientation maps.