Quick Return

The mechanism O-A-B has two links and ground. The input, Bar-OA, oscillates through small angles, α ± Δα. Bar-AB, slot-connected to Bar-OA at A, has a changing, active length, X(t). Figure 1. is the basic configuration with notation. Write a general "specification" for all positions of this planar mechanism. Use a math/physics approach that leads to a solution statement readily expressible in computer code.

♦ A vector description of the mechanism is:

(1)

Eqn-1 represents the mechanism implicitly. More detailed description requires, further notation, specification of unit vectors. Figure 2 shows the unit vectors needed along with "assumed positive" directions of angle, angular velocities, and such.

Disregarding other information of Figure 2,(for the moment)For the moment recognize that it shows a trace of the mechanism. We see by the trace the validity of a vector equation for the mechanism.

(2)

Next we write three sets of unit-vectors-pairs. One set to the "ground" and one to each of the moving members. Our perspective is that the mechanism operates in a vetrtical, say an X-Z plane. In description of this space we afix the vector-pair, I (directed horizontal-right), and K (directed upward). These unit vectors are constant.

The first unit vectors of a "moving" member, a "normal" vector is aligned directed from one pin of the member to another. The second unit vector is defined to be perpendicular the the first "normal" vector. More will be stated as we go.

The unit vector pair, n_A/O and t_A/O are imagined "scribed onto link OA.
• n_A/O is a unit vector directed toward A. Thus it directs normal to A