thesis

Static Positional Accuracy and Joint Stiffness Characterization of a Mitsubishi PA-10-6CE Robot Arm : 

Static Positional Accuracy and Joint Stiffness Characterization of a Mitsubishi PA-10-6CE Robot Arm Samuel R. Hamner University of Florida Orthopaedic Biomechanics Laboratory Department of Mechanical & Aerospace Engineering 18 April 2006

The Gator Ray Imaging System: 

The Gator Ray Imaging System Robot-Based Imaging Platform Uses real-time motion capture system to track patient movement Information is passed to robots for automatic tracking of patient Must develop an appropriate control strategy to accurately track patient To develop a good control strategy, the positional and kinematic errors of the robot must be quantified.

The Mitsubishi PA-10-6CE Robot Arm: 

The Mitsubishi PA-10-6CE Robot Arm Six Degree-of-Freedom Robot Arm 3-phase AC Brushless Servo Motors Harmonic Drive Transmissions Manufacturer Specified Positional Repeatability of ±0.1mm Joint Resolver Accuracy of ±0.44 arc min (0.0073º) No Specification of Positional Accuracy

Harmonic Drive Transmissions: 

Harmonic Drive Transmissions Manufactured by Harmonic Drive Systems Inc. 50:1 Gear Ratio for PA-10-6CE Advantages: High Torque Capacity Compact Geometry “Zero” Backlash High Efficiency Disadvantages: Highly Flexible Non-linear Stiffness Hysteresis Loss Resonance Vibration

Research Goals: 

Research Goals To aid in the development of a control strategy for the PA-10 by determining the following: Static positional accuracy & repeatability of the robot A stiffness model for the joints of the robot Hysteresis loss in the joints due to loading & unloading

Methods: Test Setup: 

Methods: Test Setup Constructed “end-effector rig” in order for CMM to measure position and orientation of end-effector Mounted robot on 24” table so end-effector rig could be positioned throughout the CMM working volume CMM Specs Brown & Sharpe MicroVal PFX 454 with a measurement uncertainty of 0.0120mm of its working volume 02/24/05 - ASME B89.4.1-2001b, §5.5

Methods: Calibration: 

Methods: Calibration A transformation from the CMM coordinate system to the robot (BASE) coordinate system was calculated The robot was commanded to move along its X and Y axes. To minimize position error, a Levenberg-Marquardt nonlinear least-squares optimization was used in MATLAB

Methods: Static Positional Accuracy: 

Methods: Static Positional Accuracy Three Loading Scenarios: Unloaded 5-lb Load 10-lb Load Experiment was repeated 10 to 15 times for each loading scenario End-effector position was measured at 27 points evenly distributed in the CMM workspace

Methods: Stiffness & Hysteresis Characterization: 

Methods: Stiffness & Hysteresis Characterization Load at the end-effector was uniformly increased, then decreased in 2.5-lb increments Maximum applied load equaled 20-lb at end-effector CMM measured robot position after each mass was added/removed Tested robot in 5 different configurations Joint deflection calculated from CMM measurements using inverse kinematics Reaction torque at each joint was calculated from known masses, link lengths, and configuration

Results: Static Positional Accuracy: 

Results: Static Positional Accuracy

Results: Joint Stiffness & Hysteresis: 

Results: Joint Stiffness & Hysteresis

Discussion of Results:Static Positional Accuracy: 

Discussion of Results: Static Positional Accuracy Static positional accuracy is a function of the robot configuration / load. Characterized by: Max. Position Error, Avg. Position Error, Stand. Dev. of Position Error Positional repeatability is not sensitive to the robot configuration / load. Characterized by the average of the standard deviation of position error. Average repeatability is ±0.020mm Manufacturer specified repeatability is ±0.1mm

Discussion of Results:Stiffness & Hysteresis: 

Discussion of Results: Stiffness & Hysteresis Consistent stiffness values for each joint Significant variation in deflection angles Average hysteresis in deflection angle translates into approximate position errors of 0.302mm, 0.122mm, and 0.0299mm for joints 2, 3, and 5, respectively. The position errors due hysteresis are less than the average static position error, and can be neglected in the initial model-based control strategy. Hysteresis values may be essential for possible development of a robust control strategy.

Conclusion: 

Conclusion What was accomplished? Characterized Static Positional Accuracy & Repeatability Determined Stiffness & Hysteresis of Joints 2, 3, & 5 Further Research Variations in joint deflection show a need to further examination of the flexibility of the PA-10 Perform Monte Carlo simulation to determine effects of errors in PA-10 geometric model on calculated joint deflection Investigate effects of wave-generator angle Develop & perform experiments to identify accurate geometric parameters of PA-10 Develop full flexibility model of the PA-10, including joints 1, 4, & 6.

THE END: 

THE END THANK YOU QUESTIONS / COMMENTS References: Variable Resolution, Monolithic Resolver-to-Digital Converters, Analog Devices, Inc., Norwood, MA, 1998 Specifications of robot, Mitsubishi Heavy Industries, LTD., Available: http://www.mhi.co.jp/kobe/mhikobe-e/products/mechatronic/qa/qa01/qa01-e.html T.D. Tuttle, “Understanding and modeling the behavior of a harmonic drive gear transmission,” Technical Report 1365, MIT Artificial Intelligence Lab., 1992 Harmonic Drive Gearing: Cup Type Component Sets & Housed Units – CSF & CSG Series, HD Systems, Inc., Hauppauge, NY.

Results: Components of Static Positional Accuracy: 

Results: Components of Static Positional Accuracy RMS of Components of Position Error

Results: R2 Values of Linear Approximations: 

Results: R2 Values of Linear Approximations

Results: Comparison to Manufacturer’s Values: 

Results: Comparison to Manufacturer’s Values Percent Difference: Hysteresis Loss Joint 2: 4% Joint 3: 24% Joint 5: 47% Percent Difference: Stiffness Joint 2: 50-72% Joint 3: 19-54% Joint 5: 5-60% Manufacturer tested harmonic drives in isolation, not on assembled robot. Robot has multiple sources of flexibility beyond the harmonic drive, and which add to the overall compliance like springs in series. Therefore, stiffness values are for robot joints not the harmonic drives.

Sources of Joint Deflection Variation: 

Sources of Joint Deflection Variation Two possible sources: Different of wave generator (WG) angles 2. Errors in the geometric model of the PA-10 Wave Generator Angle: Tuttle reported variations in a stiffness profile of up to 25% due to different WG orientations [ref]. No significant correlation WG orientation & joint deflection Errors in Geometric Model: Transformation for desired position is qualitatively sensitive to small changes in the geometric model. Manufacturing/Assembly tolerances could affect calculated joint deflections.

Optimization Method: 

Optimization Method To minimize position error, a Levenberg-Marquardt nonlinear least-squares optimization was used in MATLAB Design Variables: Three elements of the position of the robot origin in the CMM coordinate system Cost: The vector (2) norm of the position error

End-Effector Rig Deflection Analysis: 

End-Effector Rig Deflection Analysis TOTAL DEFLECTION 0.03010 mm TOTAL DEFLECTION 0.00104 mm Accounted for in calibration