Analysis of the degrees-of-freedom of spatial parallel manipulators in regular and singular configurations

• A general formulation for the analysis of DoF of manipulators is presented.
• The same is applied to five different three-DoF spatial parallel manipulators.
• Gained DoF at singular configurations are analysed within the same framework.

This paper presents a study of the nature of the degrees-of-freedom of spatial manipulators based on the concept of partition of degrees-of-freedom. In particular, the partitioning of degrees-of-freedom is studied in five lower-mobility spatial parallel manipulators possessing different combinations of degrees-of-freedom. An extension of the existing theory is introduced so as to analyse the nature of the gained degree(s)-of-freedom at a gain-type singularity. The gain of one- and two-degrees-of-freedom is analysed in several well-studied, as well as newly developed manipulators. The formulations also present a basis for the analysis of the velocity kinematics of manipulators of any architecture.