Project: Consider a Four bar linkage as shown in Figure 1. The crank is described by the vector R = iP+jQ and the connecting rod lengths are S and T, where P, Q, S and T will correspond to your 8 digits City Tech ID, e.g., P = Average of largest three digits of your student ID, Q = mean of 8 digits, T = (mean + median), and S = (mode + mean + median). Find the connecting rods orientation as described below. Note: All lengths like P and Q MUST be multiplied by 5 and S and T MUST be multiplied by 10 and units should be in mm. R S T Fixed Link Figure 1: A typical Four bar linkage. Project MUST meet the following requirements: Use Grashof Criterion to characterize the above mechanism. Check for all 5 options. Find the range of values for fixed link if the linkage to be crank rocker and considering optimum transmission angle range. Use analytical vector method (cross product) for positional analysis. Use analytical dot product method for positional analysis & compare your result with cross product. Use graphical method (vector polygon method) for positional and velocity analysis. Compare between analytical and graphical methods. Calculate the velocity and relative velocity of the links. Report requirements: You need to submit a comprehensive report that includes, not limited to, cover page, table, abstract, introduction, theory, methodology, procedure, programming, calculation, data, result, discussion & analysis, conclusion, references, etc. Submit all programming scripts. Include all necessary plotting with standard engineering format.