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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.