Using the principle of minimum potential energy find the MEC

Using the principle of minimum potential energy, find the “MECHANICAL ADVANTAGE”, which is defined as the ratio between the force F at the actuator in the figure and the weight W on the lift as a function of x

W/F=___

Solution

solution: potential energy is sum of strain energy and external work done,if we consider just external work done then it is minimum potential energy.

2) here if we consider system stationary then moment around any point is zero

3) here weight is supported at two side of platform ,hence load at each platform

f1=W/2

it is divided into two component along bar and perpendicular to bar as here moment is zero is perpendicular forces has no use to mechanical advantage

4) component of force along each bar till cross point is

F1=W/2*sin(phi)

5) again at cross point forces ressolve along horizontal and vertical direction,here again horizontal component cut each other and vertical component add toghether,hence

F2=2*(W/2*sin(phi)sin(phi))

6) here component again devided along bar connected to fulcrum and bar connected to actuator,angle between vertical force and bar is 90-phi

hence force along rod connected actuator as F3=F2cos(90-phi)=F2sin(phi)

putting value we get

F3=F2sin^3(phi)=Wsin^3(phi)

4) here F3 is acting at actuator at angle phi to horizontal,it is again divided in two component

1-along horizontal direction of required F

2-along vertical direction and create normal reaction

hence required force F as

F=F3cos(phi)=Wsin^3(phi)cos(phi)

5) mechanical advantage is

F/W=sin^3(phi)*cos(phi)