Theoretical Analysis of Workspace of a Hybrid Offset Joint

Abstract Offset joints are widely used in robotics, and literature has demonstrated that axial offset joints can expand the workspace. However, the hybrid offset joint, which incorporates offsets in three orthogonal directions (x, y, and z axes), provides a more flexible and comprehensive range of motion compared to traditional axial offset joints. Therefore, a comprehensive understanding of the workspace of hybrid offset joints with three-directional offsets is essential. Firstly, through a parameter model, the interference motion of hybrid offset joints is studied, considering three different directional offsets and obtaining analytical expressions. Next, based on coordinate transformations, the workspace of this joint is investigated, resulting in corresponding theoretical formulas. In addition, the influence of offset amounts in various directions on the joint's workspace is examined. Finally, the application of hybrid offset joints in parallel manipulators (PMs) is introduced, highlighting their practical engineering value. Through comparative analysis, it is found that lateral offsets on the x and y axes adjust the maximum rotation angles, while the z-axis offset expands the rotational range of these joints. Moreover, by increasing the limit rotation angle of the passive joint in a specific direction, the application of hybrid offset joints in PMs can impact the workspace. These findings offer valuable insights for the design of hybrid offset joints and their applications in robotics.