Question

# The robot arm is elevating and extending simultaneously. At a given instant. theta = 30 degree, theta with dot = 10 deg/s = constant, l = 0.5 m, i = 0.2 m/s, and l with dieresis = -0.3 m/s2. Compute: express v right words arrow and a right words arrow in terms of unit vectors I with Hat and j with Hat. the magnitudes of the velocity v and acceleration a of the gripped part P.

Answer

{'velocity': '(-0.150i + 0.433j) m/s', 'acceleration': '(-0.479i - 0.057j) m/s^2', 'magnitude of velocity': '0.475 m/s', 'magnitude of acceleration': '0.483 m/s^2'}

- Express the position vector r of point P on the robot arm. r = l(cos(theta)i + sin(theta)j).
- Differentiate r with respect to time to get the velocity v. v = r with dieresis + l with dot(-sin(theta)i + cos(theta)j) + l(theta with dot)(-cos(theta)i - sin(theta)j).
- Substitute the given values into v to get the numerical value. v = (-0.150i + 0.433j) m/s.
- Differentiate v with respect to time to get the acceleration a. a = r with double dieresis + 2l with dot(theta with dot)(-sin(theta)i + cos(theta)j) + l(theta with dieresis)(-cos(theta)i - sin(theta)j) + l(theta with dot) with dieresis(sin(theta)i - cos(theta)j).
- Substitute the given values into a to get the numerical value. a = (-0.479i - 0.057j) m/s^2.