Question

Robots with telescoping arms are sometimes used to perform tasks (e.g., welding or placing screws) where access may be difficult for other robotic types. During a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt , where r is in feet, θ is in radians, and t is in seconds. Use a computer program to plot the path of tip A in x and y coordinates for 0 ≤ t ≤ 4s.

Answer 1

Answer:

A code was used to plot the path of of tip A in x and y coordinates for 0 ≤ t ≤ 4s. and the velocity V = 1.25π = 3.925 m/s for acceleration = 4.33 m/s

Solution

Given that:

(a) r = 3 ++ 0.5cos(4θ)

r = dr/dt = - 0.5 xy sin(4θ)

r = - 2 sin (4θ)

(b) t=0:0.01:3;

theta=-(.*t.^2/4)+(π.*t);

r=3+0.5.*cos(4.*theta);

x=r.*cos(theta);

y=r.*sin(theta);

plot(t,x,t,y)

xlabel('time')

ylabel('x & Y')

legend('X','Y')

Note: Kindly find an attached work solution for option A below, with the full complete question to this exercise.

Complete question: Robots with telescoping arms are sometimes used to perform tasks (e.g., welding or placing screws) where access may be difficult for other robotic types. During a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt ,where r is in feet, θ is in radians, and t is in seconds. (a) Determine the velocity and acceleration of the robot tip A at t = 3 s.(b) Use a computer program to plot the path of tip A in x and y coordinates for 0 ≤ t ≤ 4s.