Leg Stiffness Controversies and Interpretations

  • Artur Struzik


The conceptual and methodological confusions around the concept of leg stiffness make it difficult to organize the existing knowledge and compare the results obtained by different authors. There are several computation methods, but they do not necessarily yield the same values of leg stiffness. However, these methods provide a more general estimation of quasi- or apparent stiffness, rather than actual stiffness, consistent with strict definitions originating from mechanics. The substantially different values of leg stiffness are likely to have been caused by calculations inconsistent with force-displacement curve profiles. The leg stiffness examined in this study should be viewed as quasi-stiffness, similar to other studies that have examined human continuous motion, due to the contribution of inertia and damping forces. The vast majority of authors should use the term vertical quasi-stiffness of the human body instead of using the concept of leg stiffness. This study seems to be one of the few reports that actually consider leg quasi-stiffness. Correctly estimated leg stiffness values allow for wider use of these values for various needs, including maximizing sports performance, optimizing human movement and designing man-like robots.


Centre of body mass Computation methods Countermovement Force-displacement relationship Human movement Leg stiffness Locomotion Motion system Quasi-stiffness Sport performance Spring Take-off Vertical jump 


  1. Aboodarda SJ, Yusof A, Osman NAA et al (2013) Enhanced performance with elastic resistance during the eccentric phase of a countermovement jump. Int J Sports Physiol 8(2):181–187. Scholar
  2. Arampatzis A, Schade F, Walsh M et al (2001) Influence of leg stiffness and its effect on myodynamic jumping performance. J Electromyogr Kines 11(5):355–364. Scholar
  3. Blickhan R (1989) The spring-mass model for running and hopping. J Biomech 22(11):1217–1227. Scholar
  4. Blum Y, Lipfert SW, Seyfarth A (2009) Effective leg stiffness in running. J Biomech 42(14):2400–2405. Scholar
  5. Brüggemann G-P, Arampatzis A, Emrich F et al (2008) Biomechanics of double transtibial amputee sprinting using dedicated sprinting prostheses. Sports Technol 1(4–5):220–227. Scholar
  6. Buckley J (2011) Understanding classification: a guide to the classification systems used in paralympic sports. Accessed 10 June 2019
  7. Butler RJ, Crowell HP III, McClay Davis I (2003) Lower extremity stiffness: implications for performance and injury. Clin Biomech 18(6):511–517. Scholar
  8. Cavagna GA, Franzetti P, Heglund NC et al (1988) The determinants of the step frequency in running, trotting and hopping in man and other vertebrates. J Physiol 399(1):81–92. Scholar
  9. Dalleau G, Belli A, Bourdin M et al (1998) The spring-mass model and the energy cost of treadmill running. Eur J Appl Physiol O 77(3):257–263. Scholar
  10. Dalleau G, Belli A, Viale F et al (2004) A simple method for field measurements of leg stiffness in hopping. Int J Sports Med 25(3):170–176. Scholar
  11. Dumke CL, Pfaffenroth CM, McBride JM et al (2010) Relationship between muscle strength, power and stiffness and running economy in trained male runners. Int J Sport Physiol 5(2):249–261. Scholar
  12. Dutto DJ, Smith GA (2002) Changes in spring-mass characteristics during treadmill running to exhaustion. Med Sci Sport Exer 34(8):1324–1331. Scholar
  13. Farley CT, González O (1996) Leg stiffness and stride frequency in human running. J Biomech 29(2):181–186. Scholar
  14. Farley CT, Morgenroth DC (1999) Leg stiffness primarily depends on ankle stiffness during human hopping. J Biomech 32(3):267–273. Scholar
  15. Farley CT, Blickhan R, Saito J et al (1991) Hopping frequency in humans: a test of how springs set frequency in bouncing gaits. J Appl Physiol 71(6):2127–2132. Scholar
  16. Farley CT, Houdijk HHP, van Strien C et al (1998) Mechanism of leg stiffness adjustment for hopping on surfaces of different stiffnesses. J Appl Physiol 85(3):1044–1055. Scholar
  17. Ferris DP, Farley CT (1997) Interaction of leg stiffness and surface stiffness during human hopping. J Appl Physiol 82(1):15–22. Scholar
  18. Granata KP, Padua DA, Wilson SE (2002) Gender differences in active musculoskeletal stiffness. part II. quantification of leg stiffness during functional hopping tasks. J Electromyogr Kines 12(1):127–135. Scholar
  19. Harrison AJ, Gaffney SD (2004) Effects of muscle damage on stretch-shortening cycle function and muscle stiffness control. J Strength Cond Res 18(4):771–776. Scholar
  20. Heise G, Martin P (1998) “Leg spring” characteristics and the aerobic demand of running. Med Sci Sport Exer 30(5):750–754. Scholar
  21. Hobara H (2014) Running-specific prostheses: the history, mechanics, and controversy. J Soc of Biomech 38(2):105–110. Scholar
  22. Hobara H, Muraoka T, Omuro K et al (2009) Knee stiffness is a major determinant of leg stiffness during maximal hopping. J Biomech 42(3):506–511. Scholar
  23. Hobara H, Inoue K, Muraoka T et al (2010) Leg stiffness adjustment for a range of hopping frequencies in humans. J Biomech 43(11):1768–1771. Scholar
  24. Hobara H, Inoue K, Kato E et al (2011a) Acute effects of static stretching on leg-spring behavior during hopping. Eur J Appl Physiol 111(9):2115–2121. Scholar
  25. Hobara H, Inoue K, Omuro K et al (2011b) Determinant of leg stiffness during hopping is frequency-dependent. Eur J Appl Physiol 111(9):2195–2201. Scholar
  26. Hobara H, Kato E, Kobayashi Y et al (2012) Sex differences in relationship between passive ankle stiffness and leg stiffness during hopping. J Biomech 45(16):2750–2754. Scholar
  27. Hobara H, Inoue K, Kanosue K (2013) Effect of hopping frequency on bilateral differences in leg stiffness. J Appl Biomech 29(1):55–60. Scholar
  28. Hobara H, Inoue K, Kobayashi Y et al (2014) A comparison of computation methods for leg stiffness during hopping. J Appl Biomech 30(1):154–159. Scholar
  29. Hobara H, Kobayashi Y, Yoshida E et al (2015) Leg stiffness of older and younger individuals over a range of hopping frequencies. J Electromyogr Kines 25(2):305–309. Scholar
  30. Hunter I (2003) A new approach to modeling vertical stiffness in heel-toe distance runners. J Sport Sci Med 2(4):139–143Google Scholar
  31. Kim S, Park S (2011) Leg stiffness increases with speed to modulate gait frequency and propulsion energy. J Biomech 44(7):1253–1258. Scholar
  32. Kim S, Son Y (2018) Mechanical work-canceling strategy modulates initial push-off force depending on vertical height. J Mech Sci Technol 32(11):5345–5350. Scholar
  33. Kim S, Wensing PM (2014) Design of dynamic legged robots. Foundations and Trends in Robotics 5(2):117–190. Scholar
  34. Korff T, Horne SL, Cullen SJ et al (2009) Development of lower limb stiffness and its contribution to maximum vertical jumping power during adolescence. J Exp Biol 212(22):3737–3742. Scholar
  35. Kuitunen S, Kyröläinen H, Avela J et al (2007) Leg stiffness modulation during exhaustive stretch-shortening cycle exercise. Scand J Med Sci Spor 17(1):67–75. Scholar
  36. Kuitunen S, Ogiso K, Komi PV (2011) Leg and joint stiffness in human hopping. Scand J Med Sci Spor 21(6):e159–e167. Scholar
  37. Latash ML, Zatsiorsky VM (1993) Joint stiffness: myth or reality? Hum Mov Sci 12(6):653–692. Scholar
  38. Latash ML, Zatsiorsky VM (2016) Biomechanics and motor control: defining central concepts. Academic, AmsterdamGoogle Scholar
  39. Linthorne NP (2001) Analysis of standing vertical jumps using a force platform. Am J Phys 69(11):1198–1204. Scholar
  40. Liu Y, Peng C-H, Wei S-H et al (2006) Active leg stiffness and energy stored in the muscles during maximal counter movement jump in the aged. J Electromyogr Kines 16(4):342–351. Scholar
  41. Luhtanen P, Komi PV (1980) Force-, power-, and elasticity-velocity relationships in walking, running, and jumping. Eur J Appl Physiol O 44(3):279–289. Scholar
  42. Maloney SJ, Fletcher IM, Richards J (2015) A comparison of methods to determine bilateral asymmetries in vertical leg stiffness. J Sport Sci 34(9):829–835. Scholar
  43. Maloney SJ, Richards J, Nixon DGD et al (2017) Vertical stiffness asymmetries during drop jumping are related to ankle stiffness asymmetries. Scand J Med Sci Spor 27(6):661–669. Scholar
  44. McMahon JJ, Comfort P, Pearson S (2012) Lower limb stiffness: effect on performance and training considerations. Strength Cond J 34(6):94–101. Scholar
  45. Morgan DL, Proske U, Warren D (1978) Measurements of muscle stiffness and the mechanism of elastic storage of energy in hopping kangaroos. J Physiol 282(1):253–261. Scholar
  46. Morin J-B, Dalleau G, Kyröläinen H et al (2005) A simple method for measuring stiffness during running. J Appl Biomech 21(2):167–180. Scholar
  47. Moritz CT, Farley CT (2003) Human hopping on damped surfaces: strategies for adjusting leg mechanics. P Roy Soc B-Biol Sci 270(1525):1741–1746. Scholar
  48. Moritz CT, Farley CT (2004) Passive dynamics change leg mechanics for an unexpected surface during human hopping. J Appl Physiol 97(4):1313–1322. Scholar
  49. Mrdakovic V, Ilic D, Vulovic R et al (2014) Leg stiffness adjustment during hopping at different intensities and frequencies. Acta Bioeng Biomech 16(3):69–76. Scholar
  50. Poulakakis I, Venkadesan M, Mandre S et al (2017) Legged robots with bioinspired morphology. In: Sharbafi MA, Seyfarth A (eds) Bioinspired legged locomotion models: concepts, control and applications. Elsevier, pp 457–561. Scholar
  51. Rabita G, Couturier A, Lambertz D (2008) Influence of training background on the relationships between plantarflexor intrinsic stiffness and overall musculoskeletal stiffness during hopping. Eur J Appl Physiol 103(2):163–171. Scholar
  52. Rack PMH, Westbury DR (1974) The short range stiffness of active mammalian muscle and its effect on mechanical properties. J Physiol 240(2):331–350. Scholar
  53. Rapoport S, Mizrahi J, Kimmel E et al (2003) Constant and variable stiffness and damping of the leg joints in human hopping. J Biomech Eng 125(4):507–514. Scholar
  54. Sinclair J, Shore HF, Taylor PJ et al (2015) Sex differences in limb and joint stiffness in recreational runners. Hum Mov 16(3):137–141. Scholar
  55. Stefanyshyn DJ, Nigg BM (1998) Dynamic angular stiffness of the ankle joint during running and sprinting. J Appl Biomech 14(3):292–299. Scholar
  56. Struzik A, Zawadzki J (2013) Leg stiffness during phases of countermovement and take-off in vertical jump. Acta Bioeng Biomech 15(2):113–118. Scholar
  57. Struzik A, Zawadzki J (2016) Application of force-length curve for determination of leg stiffness during a vertical jump. Acta Bioeng Biomech 18(2):163–171. Scholar
  58. Struzik A, Zawadzki J (2019) Estimation of potential elastic energy during the countermovement phase of a vertical jump based on the force-displacement curve. Acta Bioeng Biomech 21(1):153–160. Scholar
  59. Struzik A, Zawadzki J, Rokita A (2016) Leg stiffness and potential energy in the countermovement phase and CMJ jump height. Biomed Hum Kinet 8:39–44. Scholar
  60. Trojnacki MT, Zielińska T (2011) Motion synthesis and force distribution analysis for a biped robot. Acta Bioeng Biomech 13(2):45–56PubMedGoogle Scholar
  61. Wade L, Lichtwark G, Farris DJ (2018) Movement strategies for countermovement jumping are potentially influenced by elastic energy stored and released from tendons. Sci Rep 8(1):2300. Scholar
  62. Wang L-I (2008) The kinetics and stiffness characteristics of the lower extremity in older adults during vertical jumping. J Sport Sci Med 7(3):379–386Google Scholar
  63. Wang I-L, Wang S-Y, Wang L-I (2015) Sex differences in lower extremity stiffness and kinematics alterations during double-legged drop landings with changes in drop height. Sport Biomech 14(4):404–412. Scholar
  64. Willwacher S, Funken J, Heinrich K et al (2017) Elite long jumpers with below the knee prostheses approach the board slower, but take-off more effectively than non-amputee athletes. Sci Rep 7:16058. Scholar
  65. Wilson JM, Flanagan EP (2008) The role of elastic energy in activities with high force and power requirements: a brief review. J Strength Cond Res 22(5):1705–1715. Scholar
  66. Winters J, Stark L, Seif-Naraghi A-H (1988) An analysis of the sources of musculoskeletal system impedance. J Biomech 21(12):1011–1025. Scholar
  67. Zatsiorsky VM (1997) On muscle and joint viscosity. Mot Control 1(4):299–309. Scholar
  68. Zawadzki J (2005) Muscle drive strategy in intense cyclic movements of the forearm. Studia i Monografie Akademii Wychowania Fizycznego we Wrocławiu, no 78. Wydawnictwo Akademii Wychowania Fizycznego, WrocławGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Artur Struzik
    • 1
  1. 1.University School of Physical EducationWrocławPoland

Personalised recommendations