# Cycling Biomechanics and Its Relationship to Performance
## 3 Joint Torque  
Crank power is the result of the powers developed at each joint (ankle, knee and hip) and the power transferred across the hip joint from the upper-body [34]. Joint power is the scalar product of joint torque (N-m) and joint angular velocity (rad/s). Angular velocity is computed by the derivation of the position of the segments, which is obtained directly from a system of cameras (e.g., Vicon, OptiTrack) or using inertial measurement units, whereas joint torque is estimated using inverse dynamic procedures [35]. An example of torque profile at the crank axis, the hip, the knee and the ankle computed at maximal power is provided in Figure 2. Note that joint torque and power can also be assessed for individual joint using isokinetic devices (e.g., Biodex, Contrex [33]). Joint torque represents an estimation of the net muscular efforts around the joints. The imprecision is due to approximate anthropometric tables (segment mass and inertia) and approximate kinematics of the segments (e.g., soft tissue artefact influence). Moreover, joint torque is the result of the actions produced by composite structures combining the activity of several agonist and antagonist muscles crossing a joint and the action of passive tissues such as ligaments or the joint capsule. Despite these methodologic approximations, joint torques and joint power are the usual way in which the work generated by the muscles is quantified and the techniques used by cyclists are compared. Joint power is generally used to assess the contribution of the different joints to the crank power output. Previous studies showed that this distribution is approximately 40%, 40%, 15% and 5% for the hip, knee, ankle and trunk/upper limbs (hip transfer), respectively [36], but it varies with the target power, pedaling rate or position [36; 37]. This distribution is meaningful because crank power is the sum of the joint powers and of the power transferred across the hip when these variables are integrated over an entire cycle (for a time-to-time analysis, the kinetic energy of the system must be taken into account). The distribution of joint powers can be studied for the purpose of identifying which joint contribution is most affected by a modified position or by fatigue, for example [34; 37]. [PERSON] et al. (2009) [34] showed that ankle power decreased more rapidly than hip and knee power during a maximal cycling trial of 30 s, suggesting that the muscles crossing the ankle joint might require specific attention when a cyclist is training for sprint events. Figure 1: Set of feasible forces at different joint configurations. The figure represents different configurations of the lower limb during the cycle, that is, at 0\({}^{o}\), 90\({}^{o}\), 180\({}^{o}\) and 270\({}^{o}\) of the crank arm angle, respectively. The dotted areas represent the feasible static force vectors at the foot level, given the joint configurations and the maximal torque of each joint. Two examples of feasible force vectors (F\({}_{1}\) and F\({}_{2}\)) are drawn in (B). F\({}_{2}\) is purely orthogonal to the crank arm (ME = 1), whereas F1 is directed more forwardly (ME \(<\) 1). However, F\({}_{1}\) will provide a greater orthogonal component than F\({}_{2}\), showing that maximizing effectiveness is not necessarily the best option to maximize performance. At 270\({}^{o}\), a negative effective force is illustrated (ME \(<\) 0). The details of the method used to define the feasible force vector sets can be found in Valero-Cuevas [32] and Kutch and Valero-Cuevas [31]; see text also. On the right, illustration of real forces vectors. BDC: bottom dead center; ME: mechanical effectiveness; TDC: Top Dead Center. There is a less direct relationship between joint torque and crank power output. It is worth noting that joint torques are not necessarily maximized when cycling at maximal power [33], in part because such maximization would not necessarily create forces in the proper direction at the level of the pedal.