Singularity analysis of a novel 4-dof parallel manipulator H4

Recently, it has been shown that a novel parallel manipulator called H4 can be employed to perform high speed motion for semiconductor applications. In this new family of parallel manipulator, singularities are associated with either loss or gain of degrees of freedom (DOF). This paper deals with singularity analysis of H4 utilizing line geometry tools and screw theory. Firstly, the static equilibrium condition of the end effector is derived to obtain the full 6×6 matrix, which is set of governing lines of the manipulator. Based on linear dependency of these lines, the singular configurations of the manipulator can be identified. Moreover, in order to deal with singularities associated with loss of DOFs (serial singularity), the static equilibrium of the actuators is also defined. Secondly, architecture and constraint singularities associated with gain of DOFs (parallel singularity) are defined and analyzed using linear complex approximation algorithm (LCAA), which is employed to obtain the closest linear complex, presented by its screw coordinates, to the set of governing lines. The linear complex axis and pitch provide additional information and a better physical understanding of the manipulator’s self-motion when in or closed to a singular configuration. Lastly, various singularities of an example H4 manipulator are presented and analyzed using the proposed methods.