A simplified dynamic model of the hind leg of a beetle during step initiation Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/2b88qg94g

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  • This thesis investigates a simple dynamic model of the hind leg of a beetle during initiation of a step. The primary assumption was that the full load of the body was carried on the hind leg during this time. That is, the only forces on the body were that of the hind leg and gravity and their resultant produced forward acceleration. Only two dimensional models were used in this study. This was justified since the beetle is bilaterally symmetrical. However, it required the assumption that hind legs were positioned symmetrically and it limited the investigation to forward acceleration in a straight line. Models with two and three links were tested. The two link model assumed the body has no motion relative to the upper legs; that is the muscles were strong enough to prevent movement at the joint between body and leg. The three link model assumed only friction prevented movement at the joint between body and leg. Dynamic equations were developed using Lagrangian mechanics. These equations were integrated using the 4th order Runge-Kutta algorithm. Both models were driven by applying a constant torque at the joint between upper and lower segments. Driving torque was adjusted to minimize verical movement of body center of mass. Initial position of body center of mass relative to foot was varied to examine it's influence on both horizontal travel of body, center of mass and driving torque required for this travel. For both models horizontal travel was less dependent on initial height of body center-of-mass than on initial horizontal position. For both models required driving torque increased with decrease in initial height of body center-of-mass and with increase of initial horizontal distance from foot to body center-of-mass. For both models maximum horizontal travel was attained with minimum initial height of body center-of-mass and minimum initial horizontal distance between foot and body center-of-mass. For the two link model, maximum horizontal travel was approximately half of the total leg length while for the three link model the equivalent number was approximately one quarter, of total leg length.
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