$**$please help me :( $***$ i will fail if you dont

We consider the robot show $n$ in Figure $1$ in any configuration.

Consider the RPPR robot with $4$ degrees of freedom described schematically in the figure below.

This robot is made up of $5$ solid bodies denoted $S0,S1,S2,S3$ and $S4$ articulated together as

follows:

the connection between the bodies $S0$ and $SI$ is a pivot connection with a vertical axis,

parameterized by the angle ql$,$

the connection between the bodies $S1$ and $S2$ is a slide connection with a horizontal axis

perpendicular to the axis of the previous connection; parameterized by the distance $q2,$

the connection between the bodies $S2$ and $S3$ is a slide connection with a horizontal axis

perpendicular to the axis of the previous connection; parameterized by the distance $q3,$

the connection between the bodies $S3$ and $S4$ is a pivot connection with a vertical axis

perpendicular to the axis of the previous connection, parameterized by the angle $q4.$

The body $S4$ is a rod whose end, denoted $P,$ is located at the distance $14$ from the axis of the

connection S$3-$ S$4$

The frames $R0$ to $R4$ being given. Complete the other frames $R1,R2$ and $R3$ in Figure $2$

in accordance with the Denavit$-$Hartenberg convention.

Give the associated Denavit and Hartenberg parameters in the following table.

Explain without explicitly doing the calculation how to obtain OT$4($q$)$ taking care to give

each transformation.

How many operational parameters can be controlled? Which?

$5$ We now delete the last connection $S3-$ S$4.$ Calculate the transformation $0T3(q)$ as a

function of $q1,q2,q3$ and deduce the position of point D$3$ in the frame R$0.$

$($Bonus$)$ Find these relationships with a geometric method $($Chasles$).$ What operational

components can be controlled?