In a similar fashion as going from position to velocity, to calculate the accelerations of the point on the mechanism we simply take the time derivative of the result from the velocity analysis. Separating the mechanism into its two component parts we get the following two vector loops.
Part 1:
Part 2:
Now the solutions to these equations are quite long and a bit of a handful, but they will be shown nonetheless. These expressions were derived using MATLAB's symbolic solver to generate symbolic expressions, which were then directly implemented into the umbrella code.