ECE 470: Introduction to Robotics Homework 5
Question 1.
Consider the single-link manipulator arm in Figure 1(a) as shown also in Figure 10.4
(Craig, Introduction to Robotics 3rd Ed.).
a) Given that the revolute joint moves the link over 2 cubic segments in 6s from
an initial angle ๐ฝ๐ = ๐๐ ๐๐๐ to rest at a final position ๐ฝ๐ = ๐๐ ๐๐๐ through
a via point ๐ฝ๐ = ๐๐ ๐๐๐ at ๐๐ = ๐๐ with a velocity of ๐ฝฬ
๐ = ๐๐ ๐๐๐ /๐ฌ,
obtain the 8 parameters of the 2-segment cubic polynomial. (10 Points)
Figure 1
b) Imagine you decided to create a prismatic-revolute (PR) 2-dof robotic
manipulator and mounted the single-link on a horizontally moving cart as
shown in Figure 1(b),
I. Illustrate the configuration space of this PR manipulator with a sketch
given that the joint limits are ๐ฅ ⊂ [−๐, ๐] and ๐ ⊂ [−๐, ๐].
(2 Points)
II. Describe a possible path in the configuration space if a vertical straight
path is desired from point (0, −๐) to (0,๐) in the workspace
(Hint: circular motion projects to orthogonal axes as sinusoidal motion)
(3 Points)
III. Assuming the motor at ๐๐ rotates at a constant speed of ๐, suggest a
trajectory for ๐๐ (2 Points)
IV. Suggest a control scheme if the manipulator is tasked to performance
ultrasound imaging over a region by sliding the probe along the ๐
direction at a vertically downward controlled contact force with the
surface. You may assume an additional joint ๐๐ to orientate the
ultrasound transducer as shown.in Figure 2 (3 Points)
Figure 2
Question 2 (Optional Bonus Question)
Find the new equation of motion relating ๐ and ๐ to ๐ฬ, ๐ฬ, ๐,๐ฝฬ, ๐ฝฬ and ๐ฝ if the singlelink manipulator is mounted on a horizontally moving cart as shown in Figure 1(b).
(10 Points)
