Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_49

⚡ Mecademy AIENG정역학 · ch7  Problem Statement The work surface with mass and center of mass is tilted into position by a screw-driven mechanism. The double-thread screw with square threads has a pitch (axial distance between adjacent threads) and controls the horizontal motion of the threaded collar as the motor (not shown) applies a torque . The screw is supported by the fixed bearings and . The uniform support link has mass and length . Find the torque necessary to tilt the work surface for a given value of . Simplify your result for the case where and the mass of the support link is negligible. Problem 7/49 (a) General expression for the torque 1. Formula: We use the principle of virtual work: . The total potential energy of the system is the sum of the gravitational potential energies of the work surface and the support link: where is the height of the center of mass of the work surface and is the height of the midpoint of link . 2. Substitution: Let the horizontal axis of the screw be . The pivot is at a height above this axis, so . From the diagram, the distance from to along the board is , and is at a distance from along the board. The coordinates are: Collar The potential energy is: m 0 G p C MAB CDmbM θd=b M δW=Mδφ−δV=0 V V=m gy + 0G mgy mid y G Gy mid CD y=0O aO=(0,a)OD dG2dO D=(dcosθ,a+dsinθ) G=(2dcosθ,a+2dsinθ) C=(x ,0) C V=m g(a+ 0 2dsinθ)+ m g ( 2 a+dsinθ+0 ) Differentiating with respect to : From geometry, the length of link is : Let be the angle link makes wit