Static forces and moments generated in the insect leg: comparison of a three-dimensional musculo-skeletal computer model with experimental measurements

As a first step towards the integration of information on neural control, biomechanics and isolated muscle function, we constructed a three-dimensional musculo-skeletal model of the hind leg of the death-head cockroach Blaberus discoidalis. We tested the model by measuring the maximum force generated in vivo by the hind leg of the cockroach, the coxa­femur joint angle and the position of this leg during a behavior, wedging, that was likely to require maximum torque or moment production. The product of the maximum force of the leg and its moment arm yielded a measured coxa­femur joint moment for wedging behavior. The maximum musculo-apodeme moment predicted by summing all extensor muscle moments in the model was adequate to explain the magnitude of the coxa­femur joint moment produced in vivo by the cockroach and occurred at the same joint angle measured during wedging. Active isometric muscle forces predicted from our model varied by 3.5-fold among muscles and by as much as 70 % with joint angle. Sums of active and passive forces varied by less than 3.5 % over the entire range of possible joint angles (0­125 °). Maximum musculo-apodeme moment arms varied nearly twofold among muscles. Moment arm lengths decreased to zero and switched to the opposite side of the center of rotation at joint angles within the normal range of motion. At large joint angles (>100 °), extensors acted as flexors. The effective mechanical advantage (musculo-apodeme moment arm/leg moment arm = 0.10) resulted in the six femoral extensor muscles of the model developing a summed force (1.4 N) equal to over 50 times the body weight. The model's three major force-producing extensor muscles attained 95 % of their maximum force, moment arm and moment at the joint angle used by the animal during wedging.