A body is positioned in a moving table. This table is attached to two fixed points A and C by two ropes (Lba and Ldc). The table will then move freely horizontally and vertically.
The question is what is the formulation that gives the position of the point E in relation to its initial position (shown in the second and third drawing attached) as a function of the change in the rope lengths (i.e. r1 and r2 - please see below)?
Note: The formulation should include r1, r2 and use as minimum initial coordinates as possible. In order words, the formulation should only account (at maximum) to r1, r2, xA, yA, xB, xC, xD, yD, xE and yE where:
r1 = LBA - LBA,initial (change in the rope length 1)
r2 = LDC - LDC,initial (change in the rope length 2)
(xA,yA) = Initial coordinates of point A
(xB,yB) = Initial coordinates of point B
(xC,yC) = Initial coordinates of point C
(xD,yD) = Initial coordinates of point D
(xE,yE) = Initial coordinates of point E
The question is also described in the sketch attached. All the points mentioned (A to E) are shown in the first drawing.
Really appreciate your help! :)
Try looking at the mechanism problem where $ ADBC $ is an idealized/modeled 4-bar mechanism with point $E$ rigidly attached to the connecting rod $ BD.$ You are looking at a rotating triangle $BDE.$
Hrones & Nelson "4 Bar Atlas " is a good reference.