This research presents a new and generic geometric approach that characterizes the kinematic singularity of wheeled mobile robots. First, the kinematic models of all the common wheels are obtained: fixed, centered orientable, castor, and Swedish. Then, a procedure for generating robot kinematic models is presented based on the set of wheel equations and the null space concept. Next, two examples are developed to illustrate the nongeneric singularity characterization. In order to improve that approach, a generic and practical geometric approach is established to characterize the singularity of any kinematic model of a wheeled mobile robot (WMR). Finally, the singular configurations for many types of mobile robots are depicted employing the proposed approach.

This paper concerns the presentation and analysis of a type of three translational degrees of freedom (DoFs) parallel cube-manipulator. The parallel manipulators are the topology architectures of the DELTA robot and Tsai's manipulator, respectively, which have three translational DoFs. In the design, the three actuators are arranged according to the Cartesian coordinate system, which means that the actuating directions are normal to each other, and the joints connecting to the moving platform are located on three sides of a cube, for such reason we call this type of manipulator the parallel cube-manipulator. The kinematics problems, singularity, workspace, compliance characteristic of the manipulator are investigated in the paper. The analysis results show that the manipulators have the advantages of no singularities in the workspace, relatively more simple forward kinematics, and existence of a compliance center. The parallel cube-manipulator can be applied to the fields of micro-motion manipulators, remote center compliance (RCC) devices, assembly, and so on.