The Art of Making Watch Mainsprings, Repeater Springs and Balance Springs
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The Swinging Spring: Regular and Chaotic Motion
References The Swinging Spring: Regular and Chaotic Motion Leah Ganis May 30th, 2013 Leah Ganis The Swinging Spring: Regular and Chaotic Motion References Outline of Talk I Introduction to Problem I The Basics: Hamiltonian, Equations of Motion, Fixed Points, Stability I Linear Modes I The Progressing Ellipse and Other Regular Motions I Chaotic Motion I References Leah Ganis The Swinging Spring: Regular and Chaotic Motion References Introduction The swinging spring, or elastic pendulum, is a simple mechanical system in which many different types of motion can occur. The system is comprised of a heavy mass, attached to an essentially massless spring which does not deform. The system moves under the force of gravity and in accordance with Hooke's Law. z y r φ x k m Leah Ganis The Swinging Spring: Regular and Chaotic Motion References The Basics We can write down the equations of motion by finding the Lagrangian of the system and using the Euler-Lagrange equations. The Lagrangian, L is given by L = T − V where T is the kinetic energy of the system and V is the potential energy. Leah Ganis The Swinging Spring: Regular and Chaotic Motion References The Basics In Cartesian coordinates, the kinetic energy is given by the following: 1 T = m(_x2 +y _ 2 +z _2) 2 and the potential is given by the sum of gravitational potential and the spring potential: 1 V = mgz + k(r − l )2 2 0 where m is the mass, g is the gravitational constant, k the spring constant, r the stretched length of the spring (px2 + y 2 + z2), and l0 the unstretched length of the spring. -
Floating and Platform Balances an Introduction
Floating and Platform Balances An introduction ©Darrah Artzner 3/2018 Floating and Platform Balances • Introduce main types • Discuss each in some detail including part identification and function • Testing and Inspecting • Cleaning tips • Lubrication • Performing repairs Balance Assembly Type Floating Platform Floating Balance Frame Spring stud Helicoid spring Hollow Tube Mounting Post Regulator Balance wheel Floating Balance cont. Jewel Roller Pin Paired weight Hollow Tube Safety Roller Pivot Wire Floating Balance cont. Example Retaining Hermle screws Safety Roller Note: moving fork Jewel cover Floating Balance cont. Inspecting and Testing (Balance assembly is removed from movement) • Inspect pivot (suspension) wire for distortion, corrosion, breakage. • Balance should appear to float between frame. Top and bottom distance. • Balance spring should be proportional and not distorted in any way. • Inspect jewels for cracks and or breakage. • Roller pin should be centered when viewed from front. (beat) • Rotate balance wheel three quarters of a turn (270°) and release. It should rotate smoothly with no distortion and should oscillate for several (3) minutes. Otherwise it needs attention. Floating Balance cont. Cleaning • Make sure the main spring has been let down before working on movement. • Use non-aqueous watch cleaner and/or rinse. • Agitate in cleaner/rinse by hand or briefly in ultrasonic. • Rinse twice and final in naphtha, Coleman fuel (or similar) or alcohol. • Allow to dry. (heat can be used with caution – ask me how I would do it.) Lubrication • There are two opinions. To lube or not to lube. • Place a vary small amount of watch oil on to the upper and lower jewel where the pivot wire passed through the jewel holes. -
Dynamics of the Elastic Pendulum Qisong Xiao; Shenghao Xia ; Corey Zammit; Nirantha Balagopal; Zijun Li Agenda
Dynamics of the Elastic Pendulum Qisong Xiao; Shenghao Xia ; Corey Zammit; Nirantha Balagopal; Zijun Li Agenda • Introduction to the elastic pendulum problem • Derivations of the equations of motion • Real-life examples of an elastic pendulum • Trivial cases & equilibrium states • MATLAB models The Elastic Problem (Simple Harmonic Motion) 푑2푥 푑2푥 푘 • 퐹 = 푚 = −푘푥 = − 푥 푛푒푡 푑푡2 푑푡2 푚 • Solve this differential equation to find 푥 푡 = 푐1 cos 휔푡 + 푐2 sin 휔푡 = 퐴푐표푠(휔푡 − 휑) • With velocity and acceleration 푣 푡 = −퐴휔 sin 휔푡 + 휑 푎 푡 = −퐴휔2cos(휔푡 + 휑) • Total energy of the system 퐸 = 퐾 푡 + 푈 푡 1 1 1 = 푚푣푡2 + 푘푥2 = 푘퐴2 2 2 2 The Pendulum Problem (with some assumptions) • With position vector of point mass 푥 = 푙 푠푖푛휃푖 − 푐표푠휃푗 , define 푟 such that 푥 = 푙푟 and 휃 = 푐표푠휃푖 + 푠푖푛휃푗 • Find the first and second derivatives of the position vector: 푑푥 푑휃 = 푙 휃 푑푡 푑푡 2 푑2푥 푑2휃 푑휃 = 푙 휃 − 푙 푟 푑푡2 푑푡2 푑푡 • From Newton’s Law, (neglecting frictional force) 푑2푥 푚 = 퐹 + 퐹 푑푡2 푔 푡 The Pendulum Problem (with some assumptions) Defining force of gravity as 퐹푔 = −푚푔푗 = 푚푔푐표푠휃푟 − 푚푔푠푖푛휃휃 and tension of the string as 퐹푡 = −푇푟 : 2 푑휃 −푚푙 = 푚푔푐표푠휃 − 푇 푑푡 푑2휃 푚푙 = −푚푔푠푖푛휃 푑푡2 Define 휔0 = 푔/푙 to find the solution: 푑2휃 푔 = − 푠푖푛휃 = −휔2푠푖푛휃 푑푡2 푙 0 Derivation of Equations of Motion • m = pendulum mass • mspring = spring mass • l = unstreatched spring length • k = spring constant • g = acceleration due to gravity • Ft = pre-tension of spring 푚푔−퐹 • r = static spring stretch, 푟 = 푡 s 푠 푘 • rd = dynamic spring stretch • r = total spring stretch 푟푠 + 푟푑 Derivation of Equations of Motion -
Chrono Times NAWCC Chapter 190 Newsletter
Chrono Times NAWCC Chapter 190 Newsletter Ventura and Santa Barbara Counties INSIDE THIS ISSUE November/December 2015 President’s Message 1, 5 Tales From The Bench PRESIDENT’S MESSAGE Ferdinand Geitner 2-4 By George Gaglini Meeting Location 2 This Month’s t has been my pleasure to serve as President of Chapter 190 for 2014 Mini Workshop 3 I and 2015. In these years I have seen our chapter continue to grow in Chapter Meeting membership (176 members as of last count) and vigorously pursue its Calendar 3 mission to preserve and encourage interest in and appreciation of the art The Santa Barbara Tower Clock—Breakdown and and science of timekeeping, timepieces and all things horological. Repair Ernie Jensen 6-10 In past mini-workshops and monthly meeting programs, Chapter 190’s Biography: enthusiasts learned how to anneal metal without using flame, and the best Mark Harmeling 11 way to pack precious and delicate clocks for safe shipment by commercial Introduction to Clock carriers. In a recent 2015 meeting program, members and guests discov- Collecting Repair and Maintenance ered the secrets behind “mystery clocks.” In yet another, we marveled at a David Perez 12 –14 series of ingenious homemade tools that help in clock repair and restora- Highlights of September’s tion. Every monthly meeting is packed with information and designed to Meeting 15 raise interest and provide answers to questions attendees may have in the Educational Workshops 16 ever-expanding world of horological knowledge. (Continued on page 5) Chapter Officers 17 Classifieds 18 TALES FROM THE BENCH By Ferdinand Geitner The Weakest Link beautiful triple fusee A English Bracket Clock, chiming on 8 bells came by my shop recently with what the customer thought was a broken spring. -
The Spring-Mass Experiment As a Step from Oscillationsto Waves: Mass and Friction Issues and Their Approaches
The spring-mass experiment as a step from oscillationsto waves: mass and friction issues and their approaches I. Boscolo1, R. Loewenstein2 1Physics Department, Milano University, via Celoria 16, 20133, Italy. 2Istituto Torno, Piazzale Don Milani 1, 20022 Castano Primo Milano, Italy. E-mail: [email protected] (Received 12 February 2011, accepted 29 June 2011) Abstract The spring-mass experiment is a step in a sequence of six increasingly complex practicals from oscillations to waves in which we cover the first year laboratory program. Both free and forced oscillations are investigated. The spring-mass is subsequently loaded with a disk to introduce friction. The succession of steps is: determination of the spring constant both by Hooke’s law and frequency-mass oscillation law, damping time measurement, resonance and phase curve plots. All cross checks among quantities and laws are done applying compatibility rules. The non negligible mass of the spring and the peculiar physical and teaching problems introduced by friction are discussed. The intriguing waveforms generated in the motions are analyzed. We outline the procedures used through the experiment to improve students' ability to handle equipment, to choose apparatus appropriately, to put theory into action critically and to practice treating data with statistical methods. Keywords: Theory-practicals in Spring-Mass Education Experiment, Friction and Resonance, Waveforms. Resumen El experimento resorte-masa es un paso en una secuencia de seis prácticas cada vez más complejas de oscilaciones a ondas en el que cubrimos el programa del primer año del laboratorio. Ambas oscilaciones libres y forzadas son investigadas. El resorte-masa se carga posteriormente con un disco para introducir la fricción. -
What Is Hooke's Law? 16 February 2015, by Matt Williams
What is Hooke's Law? 16 February 2015, by Matt Williams Like so many other devices invented over the centuries, a basic understanding of the mechanics is required before it can so widely used. In terms of springs, this means understanding the laws of elasticity, torsion and force that come into play – which together are known as Hooke's Law. Hooke's Law is a principle of physics that states that the that the force needed to extend or compress a spring by some distance is proportional to that distance. The law is named after 17th century British physicist Robert Hooke, who sought to demonstrate the relationship between the forces applied to a spring and its elasticity. He first stated the law in 1660 as a Latin anagram, and then published the solution in 1678 as ut tensio, sic vis – which translated, means "as the extension, so the force" or "the extension is proportional to the force"). This can be expressed mathematically as F= -kX, where F is the force applied to the spring (either in the form of strain or stress); X is the displacement A historical reconstruction of what Robert Hooke looked of the spring, with a negative value demonstrating like, painted in 2004 by Rita Greer. Credit: that the displacement of the spring once it is Wikipedia/Rita Greer/FAL stretched; and k is the spring constant and details just how stiff it is. Hooke's law is the first classical example of an The spring is a marvel of human engineering and explanation of elasticity – which is the property of creativity. -
Pioneers in Optics: Christiaan Huygens
Downloaded from Microscopy Pioneers https://www.cambridge.org/core Pioneers in Optics: Christiaan Huygens Eric Clark From the website Molecular Expressions created by the late Michael Davidson and now maintained by Eric Clark, National Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32306 . IP address: [email protected] 170.106.33.22 Christiaan Huygens reliability and accuracy. The first watch using this principle (1629–1695) was finished in 1675, whereupon it was promptly presented , on Christiaan Huygens was a to his sponsor, King Louis XIV. 29 Sep 2021 at 16:11:10 brilliant Dutch mathematician, In 1681, Huygens returned to Holland where he began physicist, and astronomer who lived to construct optical lenses with extremely large focal lengths, during the seventeenth century, a which were eventually presented to the Royal Society of period sometimes referred to as the London, where they remain today. Continuing along this line Scientific Revolution. Huygens, a of work, Huygens perfected his skills in lens grinding and highly gifted theoretical and experi- subsequently invented the achromatic eyepiece that bears his , subject to the Cambridge Core terms of use, available at mental scientist, is best known name and is still in widespread use today. for his work on the theories of Huygens left Holland in 1689, and ventured to London centrifugal force, the wave theory of where he became acquainted with Sir Isaac Newton and began light, and the pendulum clock. to study Newton’s theories on classical physics. Although it At an early age, Huygens began seems Huygens was duly impressed with Newton’s work, he work in advanced mathematics was still very skeptical about any theory that did not explain by attempting to disprove several theories established by gravitation by mechanical means. -
Collectable POCKET Watches 1750-1920
cOLLECTABLE POCKET watches 1750-1920 Ian Beilby Clocks Magazine Beginner’s Guide Series No 5 cOLLECTABLE POCKET watches 1750-1920 Ian Beilby Clocks Magazine Beginner’s Guide Series No 5 Published by Splat Publishing Ltd. 141b Lower Granton Road Edinburgh EH5 1EX United Kingdom www.clocksmagazine.com © 2017 Ian Beilby World copyright reserved ISBN: 978-0-9562732-4-6 The right of Ian Beilby to be identified as author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. 2 4 6 8 10 9 7 5 3 1 Printed by CBF Cheltenham Business Forms Ltd, 67 Hatherley Road, Cheltenham GL51 6EG CONTENTS Introduction 7 Chapter 1. The eighteenth century verge watch 13 Chapter 2. The nineteenth century verge watch 22 Chapter 3. The English cylinder and rack lever watch 36 Chapter 4. The English lever watch 42 Chapter 5. The Swiss lever watch 54 Chapter 6. The American lever watch 62 Chapter 7. The Swiss cylinder ladies’ fob watch 72 Chapter 8. Advice on collecting and maintenance 77 Appendix 1. Glossary 82 Appendix 2. Further reading 86 CLOCKS MAGAZINE BEGINNER’S GUIDE SERIES No. 1. Clock Repair, A Beginner’s Guide No. 2. Beginner’s Guide to Pocket Watches No. 3. American Clocks, An Introduction No. 4. What’s it Worth, Price Guide to Clocks 2014 No. -
Computer-Aided Design and Kinematic Simulation of Huygens's
applied sciences Article Computer-Aided Design and Kinematic Simulation of Huygens’s Pendulum Clock Gloria Del Río-Cidoncha 1, José Ignacio Rojas-Sola 2,* and Francisco Javier González-Cabanes 3 1 Department of Engineering Graphics, University of Seville, 41092 Seville, Spain; [email protected] 2 Department of Engineering Graphics, Design, and Projects, University of Jaen, 23071 Jaen, Spain 3 University of Seville, 41092 Seville, Spain; [email protected] * Correspondence: [email protected]; Tel.: +34-953-212452 Received: 25 November 2019; Accepted: 9 January 2020; Published: 10 January 2020 Abstract: This article presents both the three-dimensional modelling of the isochronous pendulum clock and the simulation of its movement, as designed by the Dutch physicist, mathematician, and astronomer Christiaan Huygens, and published in 1673. This invention was chosen for this research not only due to the major technological advance that it represented as the first reliable meter of time, but also for its historical interest, since this timepiece embodied the theory of pendular movement enunciated by Huygens, which remains in force today. This 3D modelling is based on the information provided in the only plan of assembly found as an illustration in the book Horologium Oscillatorium, whereby each of its pieces has been sized and modelled, its final assembly has been carried out, and its operation has been correctly verified by means of CATIA V5 software. Likewise, the kinematic simulation of the pendulum has been carried out, following the approximation of the string by a simple chain of seven links as a composite pendulum. The results have demonstrated the exactitude of the clock. -
A Royal 'Haagseklok'
THE SPLIT (Going and Strike) BARREL (top) p.16 Overview Pendulum Applications. The Going-wheel The Strike-wheel Ratchet-work Stop-work German Origins Hidden Stop Work English Variants WIND-ME MECHANISM? p.19 An "Up-Down" Indicator (Hypothetical Project) OOSTERWIJCK'S UNIQUE BOX CASE p.20 Overview Show Wood Carcass Construction Damage Control Mortised Hinges A Royal 'Haagse Klok' Reviewed by Keith Piggott FIRST ASSESSMENTS p.22 APPENDIX ONE - Technical, Dimensions, Tables with Comparable Coster Trains - (Dr Plomp's 'Chronology' D3 and D8) 25/7/1 0 Contents (Horological Foundation) APPENDIX TWO - Conservation of Unique Case General Conservation Issues - Oosterwijck‟s Kingwood and Ebony Box INTRODUCTION First Impressions. APPENDIX SIX - RH Provenance, Sir John Shaw Bt. Genealogy HUYGENS AUTHORITIES p.1 Collections and Exhibitions Didactic Scholarship PART II. „OSCILLATORIUM‟ p.24 Who was Severijn Oosterwijck? Perspectives, Hypotheses, Open Research GENERAL OBSERVATIONS p.2 The Inspection Author's Foreword - Catalyst and Conundrums Originality 1. Coster‟s Other Contracts? p.24 Unique Features 2. Coster‟s Clockmakers? p.24 Plomp‟s Characteristic Properties 3. Fromanteel Connections? p.25 Comparables 4. „Secreet‟ Constructions? p.25 Unknown Originator : German Antecedents : Application to Galilei's Pendulum : Foreknowledge of Burgi : The Secret Outed? : Derivatives : Whose Secret? PART I. „HOROLOGIUM‟ p.3 5. Personal Associations? p.29 6. The Seconds‟ Hiatus? p.29 The Clock Treffler's Copy : Later Seconds‟ Clocks : Oosterwijck‟s Options. 7. Claims to Priority? p.33 THE VELVET DIALPLATE p.3 8. Valuation? p.34 Overview Signature Plate APPENDIX THREE - Open Research Projects, Significant Makers Chapter Ring User-Access Data Comparable Pendulum Trains, Dimensions. -
Mechanical Parts of Clocks Or Watches in General
G04B CPC COOPERATIVE PATENT CLASSIFICATION G PHYSICS (NOTES omitted) INSTRUMENTS G04 HOROLOGY G04B MECHANICALLY-DRIVEN CLOCKS OR WATCHES; MECHANICAL PARTS OF CLOCKS OR WATCHES IN GENERAL; TIME PIECES USING THE POSITION OF THE SUN, MOON OR STARS (spring- or weight-driven mechanisms in general F03G; electromechanical clocks or watches G04C; electromechanical clocks with attached or built- in means operating any device at pre-selected times or after predetermined time intervals G04C 23/00; clocks or watches with stop devices G04F 7/08) NOTE This subclass covers mechanically-driven clocks or clockwork calendars, and the mechanical part of such clocks or calendars. WARNING In this subclass non-limiting references (in the sense of paragraph 39 of the Guide to the IPC) may still be displayed in the scheme. Driving mechanisms 1/145 . {Composition and manufacture of the springs (compositions and manufacture of 1/00 Driving mechanisms {(driving mechanisms for components, wheels, spindles, pivots, or the Turkish time G04B 19/22; driving mechanisms like G04B 13/026; compositions of component in the hands G04B 45/043; driving mechanisms escapements G04B 15/14; composition and for phonographic apparatus G11B 19/00; springs, manufacture or hairsprings G04B 17/066; driving weight engines F03G; driving mechanisms compensation for the effects of variations of for cinematography G03B 1/00; driving mechnisms; temperature of springs using alloys, especially driving mechanisms for time fuses for missiles F42C; for hairsprings G04B 17/227; materials for driving mechnisms for toys A63H 29/00)} bearings of clockworks G04B 31/00; iron and 1/02 . with driving weight steel alloys C22C; heat treatment and chemical 1/04 . -
Pierre-François Leroy: the Lesser-Known Brother of Julien Leroy by Robert St-Louis (CAN)
© 2020 National Association of Watch and Clock Collectors, Inc. Reproduction prohibited without written permission. Pierre-François LeRoy: The Lesser-Known Brother of Julien LeRoy By Robert St-Louis (CAN) “It’s not enough that a watch should give good service importantly will try to shed some light on the life and and work regularly during six to twelve months; it must times of its maker, based on considerable documentary do so during seven or eight years, if possible.” evidence the author has uncovered and, in most cases, —Pierre-François LeRoy (April 1754) translated from the original French. Thus, the largely forgotten Pierre-François will step out from the shadows Introduction of his famous brother and nephew and be given some deserved attention as an innovator and accomplished n France, and particularly in Paris, the name “LeRoy”1 horological craftsman in his own right. in clockmaking and watchmaking is synonymous with quality, prestige, and desirability. At least since the early The early part of the 18th century was a time of great I 6 part of the 18th century, many horlogers (horloger is the innovation and discoveries in horology. Horlogers French term for watchmaker and/or clockmaker) named in France (as in England and other countries) were LeRoy have plied their trade and produced great numbers constantly trying to find better ways to design and of timepieces through the many decades that followed. build clocks and watches so that they would become Not all LeRoys have direct family lines, so it is sometimes more reliable and accurate timepieces.7 The search difficult to determine the connections between them, if to accurately measure longitude, of fundamental any.2 The story in this article deals with an older LeRoy importance to seafaring nations like France, England, family whose importance in the early days of watchmaking Spain, and others, caused great attention and effort to and clockmaking in the 18th century is undeniable.