|Ph.D Student||Simaan Nabil|
|Subject||Task Based Design and Synthesis of Variable Geometry|
|Department||Department of Mechanical Engineering||Supervisor||Professor Moshe Shoham|
The performance of a non-redundant robot is determined by its architecture and inverse kinematics rather than the complete task demands. However, when, e.g., task stiffness is also considered, the use of redundancy is called for. This work addresses the analysis and synthesis of a category of redundant parallel robot termed VGPR (Variable Geometry Parallel Robots). These robots are capable of changing their geometry for improving their performance per a given task. Since the stiffness of parallel robots is a crucial performance index, it is chosen as a driving criterion for the geometry change of VGPR.
The work considers two modes for stiffness modification of VGPR by utilizing actuation and kinematic redundancies. These two modes are termed stiffness modulation and stiffness synthesis.
Previously reported “higher-order singularities” in which the stiffness modulation problem is singular are investigated and connected with the derivatives of the inverse kinematics Jacobian. Then, these derivatives are associated with 36 lines in space. Consequently, the applicability of line geometry methods for stiffness modulation singularity analysis is shown. This geometric interpretation is the first known line-based interpretation to these stiffness modulation singularities.
In stiffness synthesis, the work investigates VGPR with kinematic redundancy in their branches providing a limited set of free geometric parameters - as is the case for a physical robot. Using Gröbner basis computations the solvability of the stiffness synthesis problems are characterized and then transformed to an associated eigenvalue problem using multiplication tables based on quotient ring algebra. The proposed method is implemented on a planar three DOF (Degrees of Freedom) and double planar six DOF VGPR.