Leg stiffness and joint stiffness while running to and jumping over an obstacle G. Mauroy, B. Schepens, P.A. Willems n Laboratoire de physiologie et biomécanique de la locomotion, Institute of NeuroScience, Université catholique de Louvain, Place Pierre de Coubertin 1, B-1348 Louvain-la-Neuve, Belgium article info Article history: Accepted 21 October 2013 Keywords: Leg-stiffness Running Obstacle Joint stiffness Jump abstract During running, muscles of the lower limb act like a linear spring bouncing on the ground. When approaching an obstacle, the overall stiffness of this leg-spring system (k leg ) is modified during the two steps preceding the jump to enhance the movement of the center of mass of the body while leaping the obstacle. The aim of the present study is to understand how k leg is modified during the running steps preceding the jump. Since k leg depends on the joint torsional stiffness and on the leg geometry, we analyzed the changes in these two parameters in eight subjects approaching and leaping a 0.65 m-high barrier at 15 km h 1 . Ground reaction force (F) was measured during 5–6 steps preceding the obstacle using force platform and the lower limb movements were recorded by camera. From these data, the net muscular moment (M j ), the angular displacement (θ j ) and the lever arm of F were evaluated at the hip, knee and ankle. At the level of the hip, the M j –θ j relation shows that muscles are not acting like torsional springs. At the level of the knee and ankle, the M j –θ j relation shows that muscles are acting like torsional springs: as compared to steady-state running, the torsional stiffness k j decreases from 1/3 two contacts before the obstacle, and increases from 2/3 during the last contact. These modifications in k j reflect in changes in the magnitude of F but also to changes in the leg geometry, i.e. in the lever arms of F. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction During running, the muscles–tendons units of the lower limb act like a linear spring storing and releasing elastic energy during contact (Alexander, 1992; Blickhan, 1989; Cavagna et al., 1988; McMahon and Cheng, 1990). When the running conditions are changing, the bouncing mechanism is adapted by adjusting the stiffness of the leg-spring system (k leg ) and the angle swept during contact. When the speed of progression increases, k leg does not change but the angle swept increases (Farley et al., 1993; He et al., 1991; Morin et al., 2005). If at a given speed the step frequency is increased, k leg increases and the angle swept decreases (Farley and Gonzalez, 1996); k leg is also adapted when subjects are running on an uneven ground (Seyfarth et al., 2002; Grimmer et al., 2008) or when the softness of the surface is modified (Ferris et al., 1999, 1998). Mauroy et al. (2012) have shown that when approaching an obstacle, k leg and the angle swept are adjusted during the last two contacts before the jump. Two contacts before the obstacle, k leg decreases whereas the angle swept increases slightly, and the COM is lowered and accelerated forwards. Then, during the last contact before the obstacle, k leg increases whereas the angle swept decreases, and the COM is raised and accelerated upwards, while its forward velocity decreases. During running and hopping on place, the lower limb can be assimilated to a multi-jointed system composed of 4 segments – foot, shank, thigh, head-arms-trunk – and 3 torsional springs – ankle, knee, hip (Fig. 1). The overall leg-spring stiffness, k leg , depends (1) on the torsional stiffness, k j , of the joints and (2) on the geometry of the leg at touchdown (Farley et al., 1998; Farley and Morgenroth, 1999). Torsional stiffness of a joint is defined as the slope of the relation between the net muscular moment and the angular displacement at that joint (Stefanyshyn and Nigg, 1998); k j determines how much the joint angle changes in response to a given external moment. It depends on muscle activation, reflexes and joint angle (Agarwal and Gottlieb, 1977; Gottlieb and Agarwal, 1978; Hunter and Kearney, 1982; Nielsen et al., 1994; Sinkjaer et al., 1988; Weiss et al., 1988; Weiss et al., 1986a,b). If the lower limb joints are stiffer, they undergo smaller angular displacements during contact, resulting in less leg com- pression and higher leg-stiffness. A second factor influencing k leg is the touchdown leg geometry (Farley et al., 1998; Farley and Morgenroth, 1999), i.e. the position of the joints relative to the ground force vector when landing. For a given ground reaction force and a given k j , if the joints are more flexed during contact, the lever arms and thus the net external Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jbiomech www.JBiomech.com Journal of Biomechanics 0021-9290/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jbiomech.2013.10.039 n Corresponding author. Tel.: þ32 10 47 44 32; fax: þ32 10 47 31 06. E-mail address: patrick.willems@uclouvain.be (P.A. Willems). Journal of Biomechanics 47 (2014) 526–535