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COMPUTER AIDED DESIGN of HARRISON TWIN PIVOT and TWIN BALANCE GRASSHOPPER ESCAPEMENT GEOMETRIES

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COMPUTER AIDED DESIGN of HARRISON TWIN PIVOT and TWIN BALANCE GRASSHOPPER ESCAPEMENT GEOMETRIES PART ONE - THE TWIN PIVOT GRASSHOPPER ESCAPEMENT COMPUTER AIDED DESIGN of HARRISON TWIN PIVOT and TWIN BALANCE GRASSHOPPER ESCAPEMENT GEOMETRIES 1 © David Heskin. 16th November 2011 PART ONE - THE TWIN PIVOT GRASSHOPPER ESCAPEMENT Computer Aided Design of Harrison Twin Pivot and Twin Balance Grasshopper Escapement Geometries Written in Lancashire, England by David Heskin Produced and published by: Soptera Publications, 3 Purley Rise, Shepshed, Loughborough, Leicestershire. LE12 9JT. England Copied to DVD ROM in England. Copyright © David Heskin 2011 First Edition. 16th November 2011 Published in A4 format (21.0 x 29.7 cm) All rights reserved. No part of this DVD ROM publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, DVD ROM copying, Inter- net transmission, recording, or any information storage and retrieval system, without permission in writing from the author and the publisher. You must not circulate this DVD ROM publication with any other label, or in any other cover, and you must impose the same condition on any acquirer. The author and publisher of this publication accept no responsibility whatsoever, however caused, for any loss, damage, injury, death or any other consequence as a result of the use of this publication, its contents and/or any errors and/or any omissions contained within it. Correct and normal workshop practices and timepiece operation must be observed at all times and the author and publisher of this book accept no liability for any accident, injury or consequence, no matter how caused, by following the procedures presented herein, which are given in good faith. This publication is not intended to be a thorough or complete constructional guide. Information has been supplied, in good faith, in order to assist construction by those with sufficient skills and experi- ence. All explanations, descriptions, observations, calculations, CAD drawings, output, dimensions, fig- ures and diagrams are for explanatory and illustrative purposes only and should not be assumed to be accurate, correct or to scale. British Library Cataloguing in Publication Data: A catalogue record for this publication is available from the British Library. ISBN 978-0-9555875-9-7 2 © David Heskin. 16th November 2011 PART ONE - THE TWIN PIVOT GRASSHOPPER ESCAPEMENT TABLE OF CONTENTS PREFACE...................................................................................................................................................................5 PART ONE THE TWIN PIVOT GRASSHOPPER ESCAPEMENT INTRODUCING THE TWIN PIVOT GRASSHOPPER ESCAPEMENT................................................................7 MECHANICAL ARRANGEMENT...................................................................................................................8 COMPONENT BEHAVIOUR....................................................................................................................................9 KEY TO ILLUSTRATIONS...............................................................................................................................9 STARTING THE GRASSHOPPER.........................................................................................................................15 COMPLETE CYCLE OF OPERATION..................................................................................................................19 TWO MINUTE ESCAPE WHEEL...................................................................................................................24 NO SLIDING FRICTION, NO WEAR, NO LUBRICATION.........................................................................24 ESCAPEMENT MEAN SPAN.........................................................................................................................24 HARRISON'S STIPULATIONS..............................................................................................................................24 WRITTEN STIPULATIONS............................................................................................................................25 ILLUSTRATED STIPULATIONS ..................................................................................................................25 THE 17.5 MEAN SPAN SINGLE PIVOT MS3972/3 GEOMETRY...............................................................27 1 - PALLET ARMS LINES OF ACTION.................................................................................................27 2 - HARRISON’S THREE NUMBERED POINTS..................................................................................29 3 - TORQUE ARM CIRCLES...................................................................................................................29 4 - VARYING FORCES............................................................................................................................29 CONCLUSIONS - STIPULATION SIX...........................................................................................................29 MS3972/3 SINGLE PIVOT GEOMETRIES ESCAPING ARC.......................................................................30 MS3972/3 SINGLE PIVOT GEOMETRIES LINES OF ACTION..................................................................30 CSM, MS3972/3 AND THE TWIN PIVOT GEOMETRY..............................................................................30 GEOMETRICAL REPRESENTATION...................................................................................................................30 SYMMETRICAL ENTRY VERSUS EXIT TORQUE ARMS........................................................................31 COMPUTER AIDED DESIGN OF THE TWIN PIVOT GEOMETRY..................................................................31 COMPUTER HARDWARE AND CAD SOFTWARE....................................................................................31 DRAWING SEQUENCE OVERVIEW............................................................................................................31 DESIGNER CHOICES......................................................................................................................................32 DRAWING CONVENTIONS AND SUGGESTIONS.....................................................................................32 STEP ONE - Figure 35......................................................................................................................................33 STEP TWO - Figure 36.....................................................................................................................................34 STEP THREE - Figure 37.................................................................................................................................35 STEP FOUR - Figure 38....................................................................................................................................36 STEP FIVE - Figure 39.....................................................................................................................................37 STEP SIX - Figure 40........................................................................................................................................38 STEP SEVEN - Figure 41.................................................................................................................................39 BALANCING THE ESCAPING ARCS...................................................................................................................40 BALANCED ESCAPING ARC ADJUSTMENT....................................................................................................41 MEAN TORQUE ARM ADJUSTMENT ................................................................................................................42 DETERMINING INSTANTANEOUS PALLET NIB LOCKING CORNER LIFTS ...........................................42 CHECKING GEOMETRIES....................................................................................................................................43 PART TWO THE TWIN BALANCE GRASSHOPPER ESCAPEMENT INTRODUCING THE TWIN BALANCE GRASSHOPPER ESCAPEMENT.......................................................45 TWO AND FOUR MINUTE ESCAPE WHEELS...........................................................................................46 NO SLIDING FRICTION, NO WEAR, NO LUBRICATION.........................................................................46 HARRISON'S STIPULATIONS..............................................................................................................................46 WRITTEN (CSM) STIPULATIONS................................................................................................................46 ILLUSTRATED STIPULATIONS...................................................................................................................47 ESCAPE WHEEL TOOTH COUNT.........................................................................................................47 MECHANICAL ARRANGEMENTS.......................................................................................................47 MS3972/3 ANALYSIS IN EIGHT PARTS...............................................................................................48 3 © David Heskin. 16th November 2011 PART ONE - THE TWIN PIVOT GRASSHOPPER ESCAPEMENT 1 - PALLET ARMS LINES OF ACTION.........................................................................................48 2 - TORQUE ARM CIRCLES...........................................................................................................50
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