Kinematic Equation for 4-Bar Linkage

There are some good books regarding mechanisms that have the derivative equations for what you need. Take a quick search on one in a library near you. It is a basic academic calculation development that we usually see in mechanical engineering courses. Serves to understand the system and to be consulted when needed - not really to be known by hard, unless you work with it every day.

To obtain the equations you need make a projection of the thick polygon on the 2 axis.

O1 is the oscillating center for the cylinder and O2 the one of the arm.

Because of the 90° angle between the piston centreline and the radius to the oscillating centre the angle "α" is also the angle between piston centreline and horizontal axis.

The angles with an "*" are those corresponding to the extreme position of the piston when its centreline makes 90° with "R".