ASSIGNMENT 4 (100 POINTS)
Assigned: 11/19/22 Due: 12/08/22
Problem 1 (20 Points)
Compute the motion of the system (an expression for x(t)) in Fig. 9.2 if parameter values are m = 2,
b = 6, and k = 4 and the block (initially at rest) is released from the position x = 2.
Problem 2 (25 Points)
A single-link robot with a rotary joint is motionless at θ = ?5deg. It is desired to move the joint
in a smooth manner to θ = 80deg in 5 seconds. Find the coefficients of a cubic which accomplishes
this motion and brings the arm to rest at the goal. Plot the position, velocity, and acceleration of
the joint as a function of time.
Problem 3 (35 Points)
A single-link robot with a rotary joint is motionless at θ = 5deg. It is desired to move the joint
in a smooth manner to θ = 80deg in 5 seconds and stop smoothly. Compute the corresponding
parameters of a linear trajectory with parabolic blends. Plot the position, velocity, and acceleration
of the joint as a function of time.
Problem 4 (20 Points)
This problem examines the relationship between distance and disparity. Let the length of the
baseline, the line connecting two camera stations, be 2d. Suppose that an object can be seen from
both station points and that the lines of the left and right cameras to the object make angles θr and
θl, respectively, with the baseline (see Figure 1).
Show that the perpendicular distance to the object from the baseline (or its extension, if needed) is
given by:
h = 2d sinθrsinθl
sin(θrθl) .
Please upload the homework on canvas by midnight at the due date.
Figure 1: Simple stereo camera geometry.