A mechanism consists of the linkage of three rods AB, BC and CD, as shown in Figure 2.112, where AB = CD (= a, say), BC = AD = a√2, and M is the midpoint. The rods are freely jointed at B and C, and are free to rotate about A and D. Using polar coordinates with their pole O at the midpoint of AD and initial line OD, show that the curve described by M as CD rotates about D is r² = a² cos 2θ. Draw a careful graph of this curve, the ‘lemniscate’ of Bernoulli. Show that

(a) The cartesian coordinates of M satisfy

(b) AM × DM = 1/2 a².

Transcribed Image Text:

(x + y) = a(x - y)