A Theoretical and Experimental Investigation into the Factors Affecting the Z- Width of a Haptic Display

by J. Michael Brown

A thesis submitted to the faculty of Northwestern University in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering, March 1995.

Abstract:

This thesis addresses some of the issues that come up in the implementation of virtual environments for haptic display. In particular, the concept of "Z-width", or dynamic range of achievable impedances, will be used to evaluate the performance of different device configurations. We suggest that an impedance is achievable if it satisfies a robustness property such as passivity. Several factors affecting Z-Width - sample-and-hold, inherent interface dynamics, displacement sensor quantization, and velocity filtering - are discussed. A set of human subject experiments designed to evaluate these factors are described, and experiemental results are presented. A striking result is that inherent interface damping exerts an overwhelming influence on Z-width. Finally, we discuss the practical difficulties of implementing low impedances with a damped haptic display, introducing the concept of "frequency-dependent damping."

To download the entire thesis: (~70 pages)

Table of Contents

Abstract & Table of Contents (this page)
Acknowledgments

1. Introduction

1.1 Introduction
1.2 The state of the art
1.3. Long term research goals
1.4. Project Goal

2. Theoretical work

2.1. Some important characteristics of tool simulation
2.2. Passivity ensures robust stable behavior
2.3. The effect of inherent mechanism dynamics and sampling on Z-width
2.4. Sensor quantization and filtering

3. Experimental work

3.1. Hardware description
3.2. Experimental Protocol
3.3. Experimental Results
3.4. Discussion of experimental results and limitations

4. Implementing low impedances with a damped haptic display

4.1. Velocity-based damping cancellation
4.2. Torque-based damping cancellation
4.2.1. Damper design
4.2.2. Torque measurement using strain gauges
4.2.3. Pressure buildups in the damper
4.2.4. Unwanted strain gauge signals due to radial forces
4.2.5. Redesign of the damper and damper torque sensor

5. Conclusion

Bibliography
Appendix A. Passivity criterion for 1 DOF with velocity filtering
Appendix B. Experimental results for subjects B and C