A Decoupling Method for Successive Robot Rotation Based on Time Domain Instantaneous Euler Angle

In the present study, a novel time domain decoupling method was proposed for the multiple successive rotations of different kinds of robots. This is achieved through the utilization of instantaneous Euler angles. For a general parallel mechanism, the Plücker coordinates of the intersection line of the before and after rotation plane are determined through the reciprocal product principle of screw theory. Additionally, the angle between these two rotation planes is defined as the instantaneous Euler angle. The analysis of the general parallel mechanism was used as an example to illustrate the solution method of the instantaneous Euler angle. To investigate the intrinsic relationship between the instantaneous Euler angle and the conventional Euler angle, the mathematical mapping relationship and the difference between the instantaneous Euler angle and the two kinds of Euler angles (Z-Y-X and Z-Y-Z) were explored, respectively. Simulations of a 3-sps-s parallel mechanism and a robotic arm were employed to illustrate the superiority of the instantaneous Euler angle. The findings showed that the instantaneous Euler angle exhibited enhanced temporal consistency compared to the conventional Euler angle. Further, it is better suited for accurately describing the decoupled rotation of robotic systems. The proposed approach is also generally applicable to robot performance evaluation, mechanism design, and other relevant fields.