I am working on a hydraulic lifting mechanism. I want to do some analysis, so I was trying to correlate the angles of the mechanism as it moves. I realized that the mechanism is essentially a four bar linkage. I did some reading on four bars, but could not find any clear equations correlating the angles. I have included a simplified diagram of my linkage; I would like to find the angles beta and alpha as theta changes.
If you know the distance from one pivot to another on the links, it is a simple triangle problem:
With angle theta and the distance from the two base pivot points and the length of the link that describes theta, you have enough to obtain the distance from the outboard end of the theta link to the base of the alpha link using basic triangle equations.
That distance and the length of the alpha and beta links gives you enough to calculate the rest of the angles. See any kinematics textbook.