1. Introduction.- 2. Friction in Machines.- 2.1. The Contemporary Model of Machine Friction.- 2.2. Boundary Lubricants: a Domain of Many Choices.- 2.3. Relaxation Oscillations.- 2.4. Friction Modeling in the Controls Literature.- 2.5. An Integrated Friction Model.- 3. Experiment Design.- 4. Repeatability.- 5. Break-Away Experiments.- 5.1. Experimental Issues in Measuring Break-Away Torque.- 5.2. Building the Compensation Table.- 6. Friction as a Function of Velocity.- 6.1. Analysis of Variance in the Motion Friction Data.- 6.2. Friction at Low Velocities.- 6.3. Friction During Compliant Motion.- 6.4. The Dahl Effect.- 6.5. The Stribeck Effect.- 6.6. Temporal Effects in the Rise and Decay of Friction.- 6.7. Variance in Friction as Process Noise.- 7. Analysis of Stick-Slip.- 7.1. Dimensional Analysis.- 7.2. Perturbation Analysis.- 7.3. The Impact of Static Friction Rising as a Function of Dwell Time.- 7.4. Integral Control.- 8. Demonstrations of Friction Compensation.- 8.1. Open-Loop Motion of One Joint.- 8.2. Open-Loop Motion of Three Joints.- 8.3. Friction Compensated Force Control.- 9. Suggestions Toward Friction Modeling and Compensation.- 9.1. Suggestions on Experimental Technique.- 9.2. Suggestions on Control.- 9.3. Conclusion.- Appendix A: Small Studies.- A.1 Friction as a Function of Motor Angle.- A.2 Joint 2 Motor Alone and Joint 2 Link Alone.- A.3 Trials with Dither.- A.4 Friction as a Function of Load.- A.5 Creep.- A.6 Effects that were not Observed.

It is my ambition in writing this book to bring tribology to the study of control of machines with friction. Tribology, from the greek for study of rubbing, is the discipline that concerns itself with friction, wear and lubrication. Tribology spans a great range of disciplines, from surface physics to lubrication chemistry and engineering, and comprises investigators in diverse specialities. The English language tribology literature now grows at a rate of some 700 articles per year. But for all of this activity, in the three years that I have been concerned with the control of machines with friction, I have but once met a fellow controls engineer who was aware that the field existed, this including many who were concerned with friction. In this vein I must confess that, before undertaking these investigations, I too was unaware that an active discipline of friction existed. The experience stands out as a mark of the specialization of our time. Within tribology, experimental and theoretical understanding of friction in lubricated machines is well developed. The controls engineer's interest is in dynamics, which is not the central interest of the tribologist. The tribologist is more often concerned with wear, with respect to which there has been enormous progress - witness the many mechanisms which we buy today that are lubricated once only, and that at the factory. Though a secondary interest, frictional dynamics are note forgotten by tribology.