250 N force acts on the robot on point C Find applied result

250 N force acts on the robot on point C. Find applied resultant force and moment on point O. The robot is massless,.

AB makes - 60 deg with horizontal ( x - axis) .

BC makes 90 + 20 = 110 deg with AB.

so angle made by BC with x axis = -60 + 110 = 40 deg

now angle made by 250N with BC is 90 deg .

hence force 250N makes 90+40 = 130 deg with x axis.

so vector F = 250(cos130i + sin130j) = -160.70i + 191.51j N .....this is force.

now we have to find vector r.

vector r = OC = 500j + ( 400sin60i - 400cos60j) + (300cos40i + 300sin40j) mm

r = 576.22i + 492.84j mm = (576.22i + 492.84j )*10^-3 m

moment = r x F = [ ((576.22i + 492.84j ) x (-160.70i + 191.51j)] x 10^-3

= 110.35k + 79.20k Nm

= 189.55 Nm .....Ans