| Hexapod configurations are recently being applied to the machine tool with the hopes of greater rigidity, stability, and accuracy than conventional multi-axis structures allow. The many error analyses available for serial machine tools, however, are not completely applicable to the parallel nature of hexapod structures (also called Stewart Platforms). Therefore, this dissertation presents the foundation for error analysis and accuracy enhancement of hexapod machine tools. A nominal model of the hexapod is presented, and an accurate model is also derived, giving a methodology for modeling all sources of pose error in a hexapod machine tool. As a part of the accurate model, mathematical models are developed to describe the elemental sources of pose error.; To investigate the effect that error sources have on pose error, an error analysis is presented. Two formulations for determining pose errors are derived: one based on differentiation of the kinematic equations, and the other based on a modified Jacobian. These error models confirm that errors can be classified in two groups: joint related errors or leg related errors. Using the error models, a sensitivity analysis is developed, and automated error analysis software is demonstrated that allows viewing of pose errors based on a nominal machine configuration and assumed error parameters.; As a method of improving the accuracy of the hexapod machine tool, a calibration method is derived that uses a ball-bar or other simple length measuring device to act as an 'extra leg,' allowing calibration of the hexapod's true kinematic parameters. This method utilizes a total least squares minimization, does not require any special hexapod configuration or difficult six degree of freedom pose measurements, and is effective with as few as one additional length sensor. Simulations show the potential for this algorithm to significantly reduce errors to the point where pose errors are within 5-10 times the measurement errors. |
