Geometric constraint-based reconfiguration and self-motions of a four-CRU parallel mechanism

Over the past few years, the concept of multi-directional three-dimensional (3D) printing has been introduced to print complex shapes and overhang geometry. This technique requires the nozzle to constantly change orientation to print the object along its tangential direction. A six-degrees-of-freedom (6-DOF) robotic arm or Stewart platform can be a solution, but these mechanisms use more components and motors. An alternative solution has been proposed in this paper based on a four-CRU (cylindrical, revolute, and universal joints) mechanism. This mechanism can orient the nozzle by switching into different motion types with minimal numbers of motors while keeping the mechanism rigid and agile. Therefore, analyses of the reconfiguration, workspace, singularities, and self-motions of a four-CRU mechanism presented in this paper have become necessities. By using primary decomposition, four geometric constraints have been identified, and the reconfiguration analysis has been carried out in each of these. It reveals that each geometric constraint will have three distinct operation modes, namely Schönflies mode, reversed Schönflies mode, and an additional mode. The additional mode can either be a four-DOF mode or a degenerated three-DOF mode, depending on the type of geometric constraints. By taking into account the actuation and constraint singularities, the workspace of each operation mode has been analyzed and geometrically illustrated. It allows us to determine the regions in which the reconfiguration takes place. Furthermore, the inherent self-motion in the Schönflies mode is revealed and illustrated, which occurs at two specified actuated leg lengths. Demonstration of the reconfiguration process and self-motions is provided through a mock-up prototype.