Error Analysis of Hexapod Machine Tools with Inclusion of System Dynamics
By Craig W. Walker
August 1997
Chairman: Dr. Gloria J. Wiens
Major Department: Mechanical Engineering
ABSTRACT
Parallel robotic manipulators have been in use in industry for many years. For machine tool applications the overall tool tip error in position and orientation is of most concern. Currently, the characterization of error propagation to the tool tip has been investigated only by looking at the kinematics of the platform at various points in its workspace. These error investigations typically assume errors are constant and focus on joint mislocation and constant leg length errors.
The objective of this research is to determine the effect of various sources of error on overall positioning error from both a kinematic and dynamic point of view. A comprehensive model for the NIST (National Institute of Standards and Technology)/Ingersoll Octahedral Hexapod milling machine is developed. Two sets of dynamic equations of motion for the platform machine tool are derived using Kanes method, one modeled with joint stiffness and the other without. A full dynamic computer simulation with feedback control is developed to implement emulation algorithms for error sources. The errors were emulated in three ways: by modifying kinematics, by modifying the feedback, and by including a stiffness model for the ball joints.
The error analysis methodology presented in this thesis provides insight into how error sources play a role in platform positioning errors. The average positioning error of the platform was found to be the least sensitive to the cutting load applied to the tool. The case that included the joint stiffness models had the next lowest average error introduced, however little information is available on joint stiffness properties.
Of the thermal expansion errors, the case where the platform is expanded has the lead effect on positioning accuracy. The cases of leg expansion contribute more to the positioning error. The effect of thermal expansion of the base has the greatest effect on positioning accuracy of all of the thermal expansion errors. It should be noted here that the expansion of the moving tube in not considered and would contribute a constant leg length error proportional to its temperature. The case where all thermal expansion errors are included simultaneously shows that the average error is less than the case where only the base is expanded. This is due to the fact that the expansion of the platform cancels out some of the error due to the base expanding. In this case the entire mechanism is 'scaled' equally which contributes less error than when only individual sources of thermal expansion error are present.
The joint dislocation errors represent errors in manufacturing or assembly of the machine tool. From the results it can be concluded that the overall positioning error is much more sensitive to errors in platform joint location than base joint location errors of equal magnitude.