Question

The figures below show the two snapshots of a rotation to linear motion conversion mechanism. In this mechanism, the locus of the point P from position Pl to P2 is of interest. As a designer, your task is to analytically synthesize the mechanism required to achieve this movement. The lengths of all the links are unknown. The position vectors of Pi and P2 are known; hence P.Pı is a known vector in this scenario. P, B1 B2 Assume: (all with respect to positivex-axis) c Initial position of 02A: e2 A-B: 03 04-B: 04 A, 0 lo, Angular displacement of 02 02-A: φ2 A-B: ф3 04-B: φ4 Ground lengths d A2 Fig 2. Final position of P Fig 1. Initial position of P (dotted lines represent the final position) (a) Using Fig. 1 as a template, draw the vector loop for the "left side dyad (a dyad to find the lengths of Or-Ai and the position of P on the coupler) for determining the lengths of the crank and coupler. Clearly label all the vectors and show your coordinate system clearly. (3 points) (b) Write the vector loop equation for the loop you drew for part (a). (2 points)

Please help.

Answer 1

$\vec{\Theta 2}=\vec{a}+\vec{b},\vec{Q4}=\vec{b}+\vec{c}$