Question

At time ? = 0 link OA of the mechanism shown below has an initial angular velocity of ?_?? = 9? ???/? and is at a position of ? = −30^? . Suddenly, a brake is applied which provides a time-dependent deceleration of link OA of ?_?? = (−1 − ?)? ???/?² . Use kinematic relationships to find expressions for the angular velocity of link OA (?_??(?)) as well as the angular position of point A (?(?)) on the link as a function of time. Assume the mechanism comes to a complete stop when the angular velocity of link OA first becomes zero. If so, determine the amount of time required for link OA to come to a stop. Determine the angular position of link OA when the system comes to a stop. Use geometry and the time dependent expression of ?(?) to determine a time dependent expression of the angle ?(?).

100 mm 9 rad/s VO 80 mm A AB = 200 mm

Answer 1

. AB 2200 O For On linki * WO = Ñ..000)=-30° (0)=-30° X(+) = (-1-4) Rzadle2 det . Now x= das L'act) @CH) - - Ha= ladt Woo ito (wszy every 5c-1-2) dt W.C%)= 9-*=) Ans

For that WoAct) = 0 9-- -0 L it+2-18=0 Jiits -24/4 + 4C19) + -21 871779 2 Not possible | = 3.358895] - 08 -5.358 Ans. Pistop = 3.35389] ③ Now for oa link for degsoe to radian i Olzaid= 0°x TT مله = لن . It pot) 0-0, tot OC) - 860) = 88-+-$3dt OCH -OCCO 94 - *- at t= 3.35669 sec OCH) - (-30, mens Jaad = 9(3.35359) - (3.35359) * 6.33% Olt) + 0.523598 - 16.2730 O(A) = 17.7494727 and -Octstop) = 1016.976° Conticlockwise) 2 revolution + 296.967°,

- from figner 100 + OA sino - AB sin r 100+ so sino = 200 sing : siny - 0.5+0.4 sino YE+) = sint 10.5+ 0.4 Sin O(+) where ott) & Yl) is in zad.