Abstract
Human locomotion is similar to the motion of a bouncing ball. Therefore, the term “bouncing gait” has been used to describe locomotion in which the lower limbs perform the role of “springs” responsible for the movement of the general centre of mass. “Spring-mass model” is used to describe a bouncing gait and contains a material point that represents a total body mass and massless lower limb used as a “spring”, which performs the supporting function. An estimation of the stiffness of this spring determines the value of leg stiffness; this stiffness is a ratio of changes in the ground reaction force to the respective change in the “spring length” representing both lower limbs. Leg stiffness is a quantitative measure of elastic properties and determines the ability to accumulate potential elastic energy. The conceptual and methodological confusion regarding the concept of leg stiffness have made it difficult to organize and compare the results obtained by different authors. Due to the substantial roles of inertia and damping on force-displacement relationships, especially during transient states, leg stiffness in terms of human continuous movement should be considered as “quasi-stiffness”.
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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. https://doi.org/10.1123/ijspp.8.2.181
Arampatzis A, Brüggemann G-P, Metzler V (1999) The effect of speed on leg stiffness and joint kinetics in human running. J Biomech 32(12):1349–1353. https://doi.org/10.1016/S0021-9290(99)00133-5
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. https://doi.org/10.1016/S1050-6411(01)00009-8
Blickhan R (1989) The spring-mass model for running and hopping. J Biomech 22(11):1217–1227. https://doi.org/10.1016/0021-9290(89)90224-8
Blum Y, Lipfert SW, Seyfarth A (2009) Effective leg stiffness in running. J Biomech 42(14):2400–2405. https://doi.org/10.1016/j.jbiomech.2009.06.040
Boullosa DA, Tuimil JL, Alegre LM et al (2011) Concurrent fatigue and potentiation in endurance athletes. Int J Sport Physiol 6(1):82–93. https://doi.org/10.1123/ijspp.6.1.82
Brauner T, Sterzing T, Wulf M et al (2014) Leg stiffness comparison between unilateral and bilateral hopping tasks. Hum Movement Sci 33:263–272. https://doi.org/10.1016/j.humov.2013.08.009
Brughelli M, Cronin J (2008) A review of research on the mechanical stiffness in running and jumping: methodology and implications. Scand J Med Sci Spor 18(4):417–426. https://doi.org/10.1111/j.1600-0838.2008.00769.x
Butler RJ, Crowell HP III, McClay Davis I (2003) Lower extremity stiffness: implications for performance and injury. Clin Biomech 18(6):511–517. https://doi.org/10.1016/S0268-0033(03)00071-8
Cavagna GA (1970) Elastic bounce of the body. J Appl Physiol 29(3):279–282. https://doi.org/10.1152/jappl.1970.29.3.279
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. https://doi.org/10.1113/jphysiol.1988.sp017069
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. https://doi.org/10.1055/s-2003-45252
Farley CT, González O (1996) Leg stiffness and stride frequency in human running. J Biomech 29(2):181–186. https://doi.org/10.1016/0021-9290(95)00029-1
Farley CT, Morgenroth DC (1999) Leg stiffness primarily depends on ankle stiffness during human hopping. J Biomech 32(3):267–273. https://doi.org/10.1016/S0021-9290(98)00170-5
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. https://doi.org/10.1152/jappl.1991.71.6.2127
Farley CT, Glasheen J, McMahon TA (1993) Running springs: speed and animal size. J Exp Biol 185(1):71–86
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. https://doi.org/10.1152/jappl.1998.85.3.1044
Ferris DP, Farley CT (1997) Interaction of leg stiffness and surface stiffness during human hopping. J Appl Physiol 82(1):15–22. https://doi.org/10.1152/jappl.1997.82.1.15
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. https://doi.org/10.1016/S1050-6411(02)00003-2
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. https://doi.org/10.1519/14343.1
Hobara H, Kanosue K, Suzuki S (2007) Changes in muscle activity with increase in leg stiffness during hopping. Neurosci Lett 418(1):55–59. https://doi.org/10.1016/j.neulet.2007.02.064
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. https://doi.org/10.1016/j.jbiomech.2009.04.047
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. https://doi.org/10.1016/j.jbiomech.2009.09.040
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. https://doi.org/10.1007/s00421-011-1841-3
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. https://doi.org/10.1007/s00421-011-1853-z
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. https://doi.org/10.1016/j.jbiomech.2012.09.008
Hobara H, Inoue K, Kanosue K (2013) Effect of hopping frequency on bilateral differences in leg stiffness. J Appl Biomech 29(1):55–60. https://doi.org/10.1123/jab.29.1.55
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. https://doi.org/10.1123/jab.2012-0285
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. https://doi.org/10.1016/j.jelekin.2015.02.004
Hunter I (2003) A new approach to modeling vertical stiffness in heel-toe distance runners. J Sport Sci Med 2(4):139–143
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. https://doi.org/10.1242/jeb.033191
Kramer A, Ritzmann R, Gruber M et al (2012) Leg stiffness can be maintained during reactive hopping despite modified acceleration conditions. J Biomech 45(10):1816–1822. https://doi.org/10.1016/j.jbiomech.2012.04.014
Kuitunen S, Ogiso K, Komi PV (2011) Leg and joint stiffness in human hopping. Scand J Med Sci Spor 21(6):e159–e167. https://doi.org/10.1111/j.1600-0838.2010.01202.x
Laffaye G, Choukou MA (2010) Gender bias in the effect of dropping height on jumping performance in volleyball players. J Strength Cond Res 24(8):2143–2148. https://doi.org/10.1519/JSC.0b013e3181aeb140
Laffaye G, Bardy BG, Durey A (2005) Leg stiffness and expertise in men jumping. Med Sci Sport Exer 37(4):536–543. https://doi.org/10.1249/01.MSS.0000158991.17211.13
Latash ML, Zatsiorsky VM (1993) Joint stiffness: myth or reality? Hum Movement Sci 12(6):653–692. https://doi.org/10.1016/0167-9457(93)90010-M
Latash ML, Zatsiorsky VM (2016) Biomechanics and motor control: defining central concepts. Academic, Amsterdam
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. https://doi.org/10.1016/j.jelekin.2005.08.001
Lloyd RS, Oliver JL, Hughes MG et al (2011) The influence of chronological age on periods of accelerated adaptation of stretch-shortening cycle performance in pre and postpubescent boys. J Strength Cond Res 25(7):1889–1897. https://doi.org/10.1519/JSC.0b013e3181e7faa8
Lloyd RS, Oliver JL, Hughes MG et al (2012) The effects of 4-weeks of plyometric training on reactive strength index and leg stiffness in male youths. J Strength Cond Res 26(10):2812–2819. https://doi.org/10.1519/JSC.0b013e318242d2ec
Lockie RG, Murphy AJ, Knight TJ et al (2011) Factors that differentiate acceleration ability in field sport athletes. J Strength Cond Res 25(10):2704–2714. https://doi.org/10.1519/JSC.0b013e31820d9f17
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. https://doi.org/10.1080/02640414.2015.1075055
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. https://doi.org/10.1111/sms.12682
Markou S, Vagenas G (2006) Multivariate isokinetic asymmetry of the knee and shoulder in elite volleyball players. Eur J Sport Sci 6(1):71–80. https://doi.org/10.1080/17461390500533147
Márquez G, Aguado X, Alegre LM et al (2010) The trampoline aftereffect: the motor and sensory modulations associated with jumping on an elastic surface. Exp Brain Res 204(4):575–584. https://doi.org/10.2478/v10078-011-0045-6
McMahon TA (1985) The role of compliance in mammalian running gaits. J Exp Biol 115(1):263–282
McMahon TA, Cheng GC (1990) The mechanics of running: how does stiffness couple with speed? J Biomech 23(suppl. 1):65–78. https://doi.org/10.1016/0021-9290(90)90042-2
McMahon JJ, Comfort P, Pearson S (2012) Lower limb stiffness: effect on performance and training considerations. Strength Cond J 34(6):94–101. https://doi.org/10.1519/SSC.0b013e3182781b4e
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. https://doi.org/10.1123/jab.21.2.167
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. https://doi.org/10.1098/rspb.2003.2435
Moritz CT, Farley CT (2004) Passive dynamics change leg mechanics for an unexpected surface during human hopping. J Appl Physiol 97(4):1313–1322. https://doi.org/10.1152/japplphysiol.00393.2004
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. https://doi.org/10.5277/abb140308
Oliver JL, Smith PM (2010) Neural control of leg stiffness during hopping in boys and men. J Electromyogr Kines 20(5):973–979. https://doi.org/10.1016/j.jelekin.2010.03.011
Pearson SJ, McMahon J (2012) Lower limb mechanical properties: determining factors and implications for performance. Sports Med 42(11):929–940. https://doi.org/10.1007/BF03262304
Pietraszewski B, Struzik A (2013) Evaluation of selected biomechanical parameters in female team sports players. Acta Bioeng Biomech 15(4):103–108. https://doi.org/10.5277/abb130413
Pruyn EC, Watsford ML, Murphy AJ et al (2012) Relationship between leg stiffness and lower body injuries in professional Australian football. J Sport Sci 30(1):71–78. https://doi.org/10.1080/02640414.2011.624540
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. https://doi.org/10.1007/s00421-008-0679-9
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. https://doi.org/10.1115/1.1590358
Schiltz M, Lehance C, Maquet D et al (2009) Explosive strength imbalances in professional basketball players. J Athl Training 44(1):39–47. https://doi.org/10.4085/1062-6050-44.1.39
Serpell BG, Ball NB, Scarvell JM et al (2012) A review of models of vertical, leg, and knee stiffness in adults for running, jumping or hopping tasks. J Sport Sci 30(13):1347–1363. https://doi.org/10.1080/02640414.2012.710755
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. https://doi.org/10.1515/humo-2015-0039
Struzik A, Zawadzki J (2013) Leg stiffness during phases of countermovement and take-off in vertical jump. Acta Bioeng Biomech 15(2):113–118. https://doi.org/10.5277/abb130213
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. https://doi.org/10.5277/ABB-00401-2015-02
Struzik A, Zawadzki J, Rokita A (2016b) Leg stiffness and potential energy in the countermovement phase and CMJ jump height. Biomed Hum Kinet 8:39–44. https://doi.org/10.1515/bhk-2016-0006
Struzik A, Zawadzki J, Rokita A (2016c) Different views on stiffness during a hopping task. In: VII Sympozjum Współczesna Myśl Techniczna w Naukach Medycznych i Biologicznych, Wrocław, 24–25 czerwca 2016: materiały konferencyjne. Oddział Polskiej Akademii Nauk we Wrocławiu, Wrocław, pp 87–88
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):379–386
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. https://doi.org/10.1080/14763141.2015.1062129
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. https://doi.org/10.1519/JSC.0b013e31817ae4a7
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Struzik, A. (2019). Leg Stiffness and Quasi-Stiffness. In: Measuring Leg Stiffness During Vertical Jumps . Springer, Cham. https://doi.org/10.1007/978-3-030-31794-2_3
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