Quaternion Model of Workpieces Orienting Movements in Manufacturing Engineering and Tool Production

One of the most significant requirements in modern mechanical engineering and instrument-making productions is workpieces’ orientation systems productivity and their simulation speed. Workpieces’ orientation systems simulation, in particular their orientation movements, is one of the most challenging and essential pre-production tasks. The complexity of the mathematical model equations, its accuracy, and computational complexity affect simulation effectiveness. The article describes the mathematical model of the workpiece orienting movements, which relies upon the mathematical apparatus of quaternions. Moreover, the article shows the principal properties of quaternions and the rules for working with them. Theoretical and experimental studies of the workpiece orienting movements quaternion model are presented, particularly the sequence and results of determining the geometric parameters of these movements, i.e., rotation angle and direction of the vector, which is collinear to the workpiece’s axis of rotation. The model has been studied for an arbitrary workpiece. The results show that the performed works’ productivity and speed increased by approximately 40%. At the same time, computational costs and intellectual efforts are significantly reduced compared to the traditional methods of the workpiece’s movement description.