Full analysis 'Position, Velocity, Acceleration, Force' for a system

This project is about Design of Machines. a front loader mechanism. 1- Derive a mathematical model that relates the input actuators lengths to the bucket position and orientation. 2- Based on the motion described above and using the vertical position of point A as an independent variable, find the required input values (lengths) of the actuators. Plot these inputs for both actuators O4B and AD for the full range of motion of the bucket. 3- Based on the range of motion of the actuator OaB found in (2) above, program this motion using cycloidal motion and an execution time of 4 seconds. 4- Plot the path of the centroid of the bucket (point G). 5- Plot the velocity and acceleration in the X and Y direction.