Automation and mechatronics
AA 2024-2025
Practice 1
EX. 1
Given two vectors 𝑎⃗ = (2; 0; 0) and 𝑏*⃗ = (√3; 1; 0) in the xy plane, it is asked to:
a. Graphically represent them in the Cartesian space
b. Write them in the three different notations (i.e., per components, in the Gauss plane, in polar
form)
c. Calculate their sum
d. Calculate their scalar product
e. Calculate their cross product.
EX. 2
Given arm and forearm lengths equal to a [m] and b [m],
respectively, and given that the orthosis has a fixed angle at elbow
level equals to 90°, determine:
a. The degrees of freedom of the arm-forearm system
b. Position, velocity and acceleration vectors at hand level (H).
EX. 3
In a technological hospital, the delivery of the therapies to the
nurses in the different wards is carried out by a self-guided robot.
Given the route and the velocity profiles in the figures, calculate:
a. The time needed for the robot to get to its delivery point (D)
b. Displacement and acceleration diagrams.