Synthesis and Analysis of Parallel Kinematic XY Flexure Mechanisms

Transcription

1 Synthesis and Analysis of Parallel Kinematic XY Flexure Mechanisms By Shorya Awtar B.Tech., Mechanical Engineering, 1998 Indian Institute of Technology, Kanpur, India M.S., Mechanical Engineering, 2000 Rensselaer Polytechnic Institute, Troy, NY Submitted to the Department of Mechanical Engineering in partial fulfillment Of the requirements for the degree of Doctor of Science in Mechanical Engineering at the Massachusetts Institute of Technology February, Massachusetts Institute of Technology All rights reserved Signature of author Department of Mechanical Engineering 19 December 2003 Certified by Alexander H. Slocum Professor of Mechanical Engineering, Mac Vicar Faculty Fellow Accepted by Chairman, Department Committee on Graduate Students

2 2

3 Synthesis and Analysis of Parallel Kinematic XY Flexure Mechanisms by Shorya Awtar submitted to the Department of Mechanical Engineering on December 19, 2003 in partial fulfillment of the requirements for the degree of Doctor of Science in Mechanical Engineering This thesis presents a family of XY flexure mechanisms with large ranges of motion, first-order decoupled degrees of freedom, and small parasitic error motions. Synthesis is based on an systematic and symmetric layout of constraints that are realized by means of common flexure building blocks. An analytical formulation incorporating geometric nonlinearities is used in deriving the characteristics of these flexure building blocks. Of concern are issues related to qualification and quantification of undesirable motions, mobility, stiffness variation within the range of motion, determination of center of stiffness, and sensitivity to manufacturing and assembly tolerances. Based on the properties of the building blocks, the performances characteristics of the resulting XY flexure mechanisms are discussed and the influence of symmetry in reducing error motions is analytically illustrated. To verify the design theory, a 300mm x 300mm prototype stage was fabricated, assembled and tested at the National Institute of Standards and Technology (NIST). Measurements using laser interferometry, autocollimation and capacitance gauges indicate levels of performance much better than the capabilities of the current state of the art of precision flexure stages. The prototype flexure stage has a 5mm x 5mm range of motion, with cross-axis errors of the order of one part in one thousand, and motion stage yaw errors of the order of a few arc seconds. Thesis Supervisor: Alexander H. Slocum Title: Professor of Mechanical Engineering, Mac Vicar Faculty Fellow 3

4 4

5 Acknowledgement Prof. Alex Slocum has mentored, guided and inspired me in my academic as well as personal life, and therefore is my guru. I express my gratitude for the education that I have received from him. I would like to acknowledge the help of my committee members Professors Samir Nayfeh and Martin Culpepper of MIT, and Dr. William Plummer of WTP Optics, during the course of this thesis. I would also like to acknowledge the role of my professors at Rensselaer Polytechnic Institute and the Indian Institute of Technology at Kanpur, in helping me learn the fundamentals of the mechanical engineering discipline. The experimental part of this thesis would have been impossible without the unconditional help offered by Nicholas Dagalakis, Jason Gorman and Kevin Lyons of the Intelligent Systems Division at the National Institute of Standards and Technology, Gaithersburg, MD. Finally, I want to acknowledge several machinists and instrument makers for their contribution to the hardware made for this thesis and to my learning of machine design. These include Gerry Wentworth of the MIT LMP machine shop, Ken Stone of MIT hobby shop, Mike Luparelli of the MIT Central Machine Shop, and Dwight Barry of the NIST Fabrication Division. 5

6 6

7 List of Contents Chapter 1. Introduction Flexures Background Flexure Mechanisms for Motion Control Contributions 18 Chapter 2. Synthesis of Parallel Kinematic XY Flexure Mechanisms Design Requirements and Challenges Proposed Design Principle for a Two Axis Flexure Mechanism XY Flexure Mechanism based on the simple Beam Flexure XY Flexure Mechanism based on the Parallelogram Flexure XY Flexure Mechanism based on the Double Parallelogram Flexure 42 Chapter 3. Non-linear Beam Bending Static Analysis Beam Bending Analysis Engineering Approximations and Simplified Results Observations and Comments on the Simplified Results Mobility of Flexure Mechanisms Error motions in Flexure Mechanisms Energy Methods 80 Chapter 4. Analysis of Basic Flexure Building Blocks Parallelogram Flexure Double Parallelogram Flexure 94 Chapter 5. Static Non-Linear Analysis of Parallel Kinematic XY Flexure Mechanisms Preliminary Discussion XY Flexure Mechanism Design XY Flexure Mechanism Design XY Flexure Mechanism Design

8 5.5 XY Flexure Mechanism Design Concluding Remarks 156 Chapter 6. Fabrication, Assembly and Experimental Test Set-up Metrology Objectives Choice of Material Choice of Manufacturing Process Actuation Methods Sensor Schemes In-plane Capacitance Probe/Actuator Clamping Mechanism Metrology Alignments 176 Chapter 7. Experimental Measurements Primary Motion and Stiffness Cross-axes Coupling Error Parasitic Yaw Error 187 Appendix A: Multiple DOF Flexure Mechanisms 189 References 193 8

9 This page is intentionally left blank 9

10 This page is intentionally left blank 10