Manual air pump calculation for machine dynamics

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JamesBennettBeta
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mentor note: moved from ME forum hence no HW template.

Summary:: I am stuck into this problem for almost a week now. I think I solved it, but it seems something is wrong. Can someone point me, what is wrong here. It'll be so much helpful.

I am stuck into this problem for almost a week now. I think I solved it, but it seems something is wrong. Can someone point me, what is wrong here. It'll be so much helpful.
Schematic of a manually operated air pump mechanism with links OA, AC and DP, a cylinder with piston P, and labelled angles 75°, 30° and 30°, with dimensions OA = 6.0 cm, AC = 12.0 cm, OC = 17.456 cm, not to scale.


Handwritten linkage diagram with points A, B, C, D and O, and a velocity diagram below it with points o, p, c and p', plus notes giving linear velocity at C as 20.0 cm/s, scale 1:4, and angular velocity 5 rad/s.
 
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Discussion

Should we assume that the mentioned steady velocity of point C is a vector always perpendicular to CO?
 
Lnewqban said:
Should we assume that the mentioned steady velocity of point C is a vector always perpendicular to CO?
I assumed it meant a steady tangential speed, not linear velocity.
I haven't come across this velocity diagram technique before. As far as I can make out, the solution is obtained by measurements from a scale drawing, not by algebra.