The paper aims to solve problems of the mathematical modeling and realization of a cube robot capable of self-bouncing and self-balancing. First, the dynamic model of the cube robot is derived by using the conservation of the angular momentum and the torque equilibrium theory. Furthermore, the controllability of the cube robot is analyzed and the angle of the cube robot is derived from the attitude and heading reference system (AHRS). Then the parallel proportional–integral–derivative (PID) controller is proposed for the balancing control of the self-designed cube robot. As for the bounce control of the cube robot, a braking system triggered by the servo motor is designed for converting the kinetic energy to the potential energy. Finally, the experimental results are included to demonstrate that the cube robot can complete the actions of self-bouncing and self-balancing with good robustness to external disturbances.

A PC-based precision promotion module named “Precimatics” is presented in this study, which uses a spatial error compensation algorithm to modify the G/M code of coordinates of a CNC machine tool. The spatial errors of three axes machine tools were measured by two kinds of laser interferometers (Renishaw Inc. & Optodyne Inc.) According to the American standard (ASME B 5.54) and the laser vector method with sequential step diagonal path (LDDM™), the spatial errors of machine tools, such as linear position error, horizontal straightness error, vertical straightness error, and squareness error, were obtained without time consuming. A spatial error map of machine tools was created and embedded into the “Precimatics” for error compensation. The compensated results were simulated and verified by the coordinates of numerical control (NC) code. Integrating a CAD/CAM system with the “Precimatics”, the position accuracy of micro/meso machine tools (mMTs) can be improved by spatial error compensation without changing the configuration of CNC controller.