Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_39

⚡ Mecademy AIENG정역학 · ch7  Problem Statement One of the critical requirements in the design of an artificial leg for an amputee is to prevent the knee joint from buckling under load when the leg is straight. As a first approximation, simulate the artificial leg by the two light links with a torsion spring at their common joint. The spring develops a torque , which is proportional to the angle of bend at the joint. Determine the minimum value of which will ensure stability of the knee joint for . Problem 7/39 (a) Determination of minimum torsional stiffness for stability 1. Formula: The stability of a mechanical system in equilibrium is analyzed using its total potential energy . For a conservative system, an equilibrium position is stable if the potential energy is at a minimum, which requires the second derivative of the potential energy with respect to the generalized coordinate to be positive: The total potential energy is the sum of gravitational potential energy () and elastic potential energy (): 2. Substitution: Let be the angle each link makes with the vertical. Since the load is constrained to move vertically and the links have equal length , the geometry is symmetric. The bend angle is the relative angle between the links, where . Taking the ground as the datum (), the height of the mass is . Gravitational potential energy: . Elastic potential energy for the torsional spring: . M=k β T β k T β=0 V > dq 2 dV 2 0 V g V e V=V + g V e θm l ββ=2θ y=0mh= 2lcosθ= 2 l cos