Kinematic Synthesis of Bevel-Gear-Type Robotic Wrist Mechanisms

Abstract

Bevel-gear-type robotic wrist mechanisms are commonly used in industry. The reasons for their popularity are that they are compact, light-weight, and relatively inexpensive. However, there are singularities in their workspace, which substantially degrade their manipulative performance. The objective of this research is to develop an atlas of three-degree-of-freedom bevel- gear-type wrist mechanisms, and through dimensional synthesis to improve their kinematic performance. The dissertation contains two major parts: the first is structural analysis and synthesis, the other is kinematic analysis and dimensional synthesis.<P>To synthesize the kinematic structures of bevel-gear-type wrist mechanisms, the kinematic structures are separated from their functional considerations. All kinematic structures which satisfy the mobility condition are enumerated in an unbiased, systematic manner. Then the bevel-gear-type wrist mechanisms are identified by applying the functional requirements. Structural analysis shows that a three-degree-of-freedom wrist mechanism usually consists of a non-fractionated, two-degree-of-freedom epicyclic gear train jointed with the base link. Therefore, the structural synthesis can be simplified into a problem of examining the atlas of non-fractionated, two-degree-of-freedom epicyclic gear train jointed with the base link. Therefore, the structural synthesis can be simplified into a problem of examining the atlas of non- fractionated, two-degree-of-freedom epicyclic gear trains. The resulting bevel-gear-type wrist mechanisms has been categorized and evaluated. It is shown that three-degree-of-freedom, four- jointed wrist mechanisms are promising for further improving the kinematic performance.<P>It is found that a spherical planetary gear train is necessarily embedded in a three-degree-of-freedom, four-jointed wrist mechanism. Therefore, to study the workspace and singularity problems of three-degree-of-freedom, four-jointed spherical wrist mechanisms, we have to study the trajectories of spherical planetary gear trains. The parametric equations of the trajectories and some useful geometric properties for the analysis and synthesis of workspace are derived. The workspace boundary equations can be derived via both geometric consideration and Jacobian analysis. The workspace is divided by inner and outer boundaries into regions of accessibility of zero, two and four. The design criteria of full workspace and a maximum four-root region are established. Finally, a design is suggested based on its kinematic performance.