Elliptical Rolling Link Toggle Mechanisms for Passive Force Closures with Self-Adjustment

142 Pages·2016·3.39 MB·English

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Theses and Dissertations
2007-07-19
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Jacob Ross Montierth
Brigham Young University - Provo
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Montierth, Jacob Ross, "Elliptical Rolling Link Toggle Mechanisms for Passive Force Closures with Self-
Adjustment" (2007). Theses and Dissertations. 1182.
https://scholarsarchive.byu.edu/etd/1182
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ELLIPTICAL ROLLING LINK TOGGLE MECHANISMS FOR

PASSIVE FORCE CLOSURES WITH SELF-ADJUSTMENT

By

Jacob R. Montierth

A thesis submitted to the faculty of

Brigham Young University

in partial fulfillment of the requirements for the degree of

Master of Science

Department of Mechanical Engineering

Brigham Young University

August 2007
Copyright © 2007 Jacob R. Montierth

All Rights Reserved
BRIGHAM YOUNG UNIVERSITY

GRADUATE COMMITTEE APPROVAL

of a thesis submitted by

Jacob R. Montierth

This thesis has been read by each member of the following graduate committee
and by majority vote has been found to be satisfactory.

___________________________ ______________________________________
Date Robert H. Todd, Chair

___________________________ ______________________________________
Date Larry L. Howell

___________________________ ______________________________________
Date Spencer P. Magleby
BRIGHAM YOUNG UNIVERSITY

As chair of the candidate’s graduate committee, I have read the thesis of Jacob R.
Montierth in its final form and have found that (1) its format, citations, and
bibliographical style are consistent and acceptable and fulfill university and department
style requirements; (2) its illustrative materials including figures, tables, and charts are in
place; and (3) the final manuscript is satisfactory to the graduate committee and is ready
for submission to the university library.

___________________________ ______________________________________
Date Robert H. Todd
Chair, Graduate Committee

Accepted for the Department

______________________________________
Matthew R. Jones
Graduate Coordinator

Accepted for the College

______________________________________
Alan R. Parkinson
Dean, Ira A. Fulton College of
Engineering and Technology
ABSTRACT

ELLIPTICAL ROLLING LINK TOGGLE MECHANISMS FOR

PASSIVE FORCE CLOSURES WITH SELF-ADJUSTMENT

Jacob R. Montierth

Department of Mechanical Engineering

Master of Science

This thesis presents elliptical rolling contact joints as an alternative to circular
rolling contact and conventional revolute joints where high quality force transmission—
low friction and backlash—with variable output are desired. Parameters specific to the
joint and its position are developed in terms of relative link angles and elliptical surface
geometry. These parameters are used to generate the basic forward kinematics for
elliptical rolling link toggle mechanisms with oscillatory motion and high mechanical
advantage. As large compressive loads are characteristic of such mechanisms, stress
conditions are identified and principles for joint stability with variable, precision outputs
are discussed. Finally, application is made to self-adjusting passive force closures with a
case study of the MUSCLE Brake (Multi-toggle Self-adjusting Connecting-Linked
Electromechanical) disc brake caliper.
Elliptical rolling contact joints are shown to offer several benefits over circular
rolling contact, including: reduced Hertz contact stresses and flexure bending stresses,
variable output velocity, maximum use of contact interface by distributing small rotations
across surfaces of small curvature, reduced forces on stabilizing members, increased
mechanical advantage due to eccentricity, and no-slip pure rolling provided exclusively
by connecting links (or flexures) without the need for gear teeth or friction.
ACKNOWLEDGMENTS

This work represents the contribution and sacrifice of many individuals. I
appreciate the guidance, encouragement, and wisdom of my advisor, Dr. Robert Todd.
His faith in my potential never waned, and his example of persistence and determination
continues to motivate me to “do good work”. I also want to thank Dr. Larry Howell for
his expertise in mechanism design and Dr. Spencer Magleby for product insights and
mentoring throughout my graduate career. I count it a privilege to have attended
Brigham Young University and studied under these great professors.
Funding for my research was provided by the Utah Center of Excellence Program
and the Department of Mechanical Engineering at BYU; both are appreciated. I’m grate-
ful for the ideas and input of fellow Compliant Mechanisms Research lab members, in
particular Brian Winder for feedback on early design iterations and prototype generation.
Nick Hawkins is also acknowledged for his technical expertise in manufacturing proto-
type hardware.
I acknowledge the inspiration received from my Father in Heaven, for all that is
light comes from Him. I thank my parents for teaching me how to work and granting me
every opportunity to succeed in whatever I chose to do. Finally, I’m grateful to my
loving wife Laura and three sons Ryan, Caden, and Andrew who are my biggest fans and
have supported me throughout.

T C
ABLE OF ONTENTS
LIST OF TABLES.................................................................................................xi
LIST OF FIGURES ..............................................................................................xii
CHAPTER 1 INTRODUCTION .......................................................................... 1
1.1 Motivation.........................................................................................2
1.2 Thesis Objective...............................................................................4
1.2.1 Research Justification........................................................4
1.2.2 Contributions.....................................................................5
1.3 Thesis Outline...................................................................................6
CHAPTER 2 BACKGROUND AND LITERATURE SEARCH................................... 9
2.1 Constraining Mechanisms.................................................................9
2.2 Self-centering Force-balanced Grasping Mechanisms...................11
2.3 Differential Mechanisms.................................................................12
2.3.1 Planetary and Bevel Gear Differentials...........................13
2.3.2 Fluidic T-pipe..................................................................14
2.3.3 Movable Pulley................................................................15
2.3.4 Seesaw Mechanism..........................................................16
2.4 Self-adjustment...............................................................................17
2.4.1 Discrete............................................................................18
2.4.2 Continuous.......................................................................20
2.5 Joints...............................................................................................28
2.5.1 Rigid-link Mechanisms....................................................28
2.5.2 Compliant Mechanisms...................................................29
2.5.3 Compression vs. Tension.................................................30
2.5.4 Rolling Contact Joints......................................................31
2.6 Pressure Angles and Transmission Angles.....................................47
2.7 Mechanical Advantage...................................................................48
2.8 Elastic Deflections..........................................................................49
CHAPTER 3 ELLIPTICAL ROLLING CONTACT JOINTS .................................. 53
3.1 Connecting Link Angles.................................................................54
3.2 Elliptical Rolling Link Motion.......................................................59
ix