## Muscle Force in Motion

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The first step in the analysis of forces acting on a body segment is to draw a free-body diagram of the segment. To this end, the part of the body is considered as distinct from the entire body, and all forces acting on the part of the body are identified. Then the equations of motion are used to gather information about the unknown muscle forces acting on the body part. The following example on the kicking of a soccer ball illustrates this technique.

Example 6.1. Quadriceps Force Before Kicking. Digital analysis of movies capturing the kicking of a soccer ball during a penalty kick showed that the angular acceleration of the lower leg was maximal at the instant the foot struck the ball (Fig. 6.2). The lower leg was vertical at that instant. The angular velocity and angular acceleration just before the foot touched the ball were a = 8 rad/s and a = 400 rad/s2, respectively. The lower leg (including the foot) weighed 7 kg and its mass moment of inertia Io about the center of rotation of the knee was determined to be 0.35 kg-m2. The perpendicular distance d from the patellar tendon to the center of rotation of the knee joint was found to be 4 cm. The distance r from the center of mass of the lower leg to the center of rotation of the knee was 22 cm. Determine the force exerted by the quadriceps muscle before kicking.

Solution: The muscle that actuates the kicking motion is the quadriceps muscle. The hamstring muscle group acts as the antagonist and would prevent the rotation of the lower leg beyond that of extension. We neglect the force exerted by the antagonist. We assume that the center of gravity of the lower leg lies in the vertical line that passes through the center of rotation of the knee. Under these conditions, the only force that creates a moment with respect to the center of rotation is the force Fq that is ex- 