Abstract
When working with the English watch master Thomas Thompin in 1678, Robert Hook (1635–1703) observed that when an elastic body is subjected to stress, its dimension or shape changes in proportion to the applied stress over a range of stresses. On the basis of his experiments with springs, stretching wires and coils, he discovered a relationship between the force and the extension of the spring. This is the so-called Hooke’s law, which we learnt in high school. Using the Hooke's law, in this chapter, we studied the hairspring of the mechanical watch movement. The study also extends to include the case of Tourbillon.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Fu BL (1985) On the modified Castigliano’s theorem. Appl Math Mech 5(2):1263–1272. doi:10.1007/BF01895122
Cai X (2001) Dynamic modeling of helical springs with design parameters defined by functions. Ph.D Thesis, University of Missouri, Columbia
Donkin WT, Clark HH (1929) The electric telemeter and valve-spring surge. Trans SAE 24:185–196
Jehle F, Spiller WR (1929) Idiosyncrasies of valve mechanisms and their causes. Trans SAE 24:197–212
Le L, LinY (1994) Stress analysis and optimal cross-section design of noncircular spring wire. Mach Elem Mach Dyn ASME 71
Lin Y, Hodges PH Pisano AP (1993) Optimal design of resonance suppression helical springs. Trans ASME, J Mech Des 115:380–384
Lin Y, Pisano AP (1987) General dynamics equations of helical springs with static solution and experimental verification. J Appl Mech 54:910–917
Lin Y, Pisano AP (1988) The differential geometry of the general helix as applied to mechanical springs. J Appl Mech 55:831–836
Lin Y, Pisano AP (1990) Three-dimensional dynamic simulations of helical compression springs. Trans ASME, J Mech Des 112:529–537
Love EH (1944) Treaties on the mathematical theory of elasticity, 4th edn. Dover, New York
Pearson D (1982) The transfer matrix method for the vibration of compressed helical springs. J Mech Eng Sci 24(4):163–171
SAE (1997) Manual on design and application of helical and spiral. HS-79548-51
Shimoseki M, Hamano T, Imaizumi T (2003) FEM for springs. Springer, New York
Spring Manufacturers Institute (2002) Handbook of spring design.
Tai KK, Lin Y, Wolansky EB (1997) Derivation and experimental verification of design formulae for barrel-shaped helical springs. Springs 36(1)
Wikipedia (2005) Castigliano’s method. http://en.wikipedia.org/wiki/Castigliano%27s_method. Accessed 12 Dec 2011
Wittrick WH (1966) On elastic wave propagation in helical springs. Int J Mech Sci 8:25–47
Xu G, Ko P. H, Du R (2011) A study on the precision of mechanical watch movement with tourbillon. Sound Vib 330(26):6287–6544
Zhang YH, Liu HH (1997) Spring handbook (in Chinese), Chinese Mechanical Engineering Press, Ningbo pp 407–418
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Du, R., Xie, L. (2013). The Mechanics of the Spiral Spring . In: The Mechanics of Mechanical Watches and Clocks. History of Mechanism and Machine Science, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29308-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-29308-5_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29307-8
Online ISBN: 978-3-642-29308-5
eBook Packages: EngineeringEngineering (R0)