PART A

1) DRAW THE GEOMETRIC FORM OF THE ROBOT WORKSPACE WITH ITS MAIN DIMENSIONS AND CLASSIFY IT ACCORDINGLY.

2) CALCULATE THE DEGREE OF MOBILITY OF THE ROBOT,APPLYING A) THE GERMAN METHOD AND B) THE RUSSIAN METHOD,WHEN:

- THE JOINT R4 IS INACTIVE

- JOINT R4 IS ACTIVE

3) TO FORMULATE THE COORDINATE SYSTEMS AND THE CHARACTERISTIC QUANTITIES OF THE PARTS OF THE ROBOT, BASED ON THE DENAVIT-HARTENBERG METHODOLOGY.

4) DEVELOP THE PARTIAL HOMOGENEOUS TRANSFORMATION MATRICES AND THE GLOBAL HOMOGENEOUS TRANSFORMATION MATRIX OF THE MECHANISM FOR THE FORMULATION OF THE DIRECT PROBLEM.

5) TO FORMULATE THE MATHEMATICAL MODEL OF THE INVERSE KINEMATIC PROBLEM.

6) DETERMINE THE VARIATION OF THE TRANSFERS OF THE RATES (1,d2,d3,4) FOR THE SOLUTION OF THE FOLLOWING POSITIONS A,B, AND

7) CALCULATE THE MINIMUM TOTAL MOVEMENT TIME OF THE ARM BETWEEN THE POSITIONS ABGD, WHEN THE TRANSITION IN THE RATES OF THE LEVELS IS DONE LINEAR AND THE MAXIMUM REQUIRED SPEEDS ARE (R: 1 rad/s, P: 0. 5m/s), WHEN THE MOVEMENTS OF THE ARTICLES ARE ACTUATED:

- SUCCESSIVELY, ONE AFTER THE OTHER AND

- AT THE SAME TIME WITH THE START AND END OF MOVEMENT. IN THIS CASE THE MAXIMUM SPEED ACHIEVED BY EACH JOINT MUST ALSO BE CALCULATED.

8) CALCULATE THE MINIMUM TOTAL TIME OF MOVEMENT OF THE ARM BETWEEN THE ABGD POSITIONS WHEN THE VARIATION OF THE VALUES OF THE JOINTS IS CARRIED OUT POLYNOMIALLY WITH A POLYNOMIAL OF DEGREE 6 AT MAXIMUM, WITH PARALLEL MOVEMENT OF ALL THE JOINTS AND WITH SIMULTANEOUS START AND END OF MOVEMENT. THE CONSTRAINTS TO BE APPLIED ARE:

- FOR MOVEMENT SPEEDS (R: 1rad/s, P:0,5 m/s) AND

- FOR SPEEDS (R: 1 rad/s^2 , P:1 m/s^2)