Problem 1 = UHart Mechatronics students have developed a robotic arm programmed to an angular position in polar coordinates with the relationship (2/л) sin(лt), where and t are expressed in radians and seconds, respectively. Simultaneously, the arm is pro- grammed to extend so that the distance to A follows the relationship r = 4 + 3e-1.4t, where r and t are expressed in feet and seconds, respectively. When t = 2.65 s, Determine: (a) the velocity of point A in polar coordinates (êr and ê), (b) the velocity of point A in rectangular coordinates, (î and ĵ) (setup and use a transformation matrix) (c) the acceleration of point A in polar coordinates (ê, and êŋ) (d) the acceleration of point A rectangular coordinates (î and ĵ)
Problem 1 = UHart Mechatronics students have developed a robotic arm programmed to an angular position in polar coordinates with the relationship (2/л) sin(лt), where and t are expressed in radians and seconds, respectively. Simultaneously, the arm is pro- grammed to extend so that the distance to A follows the relationship r = 4 + 3e-1.4t, where r and t are expressed in feet and seconds, respectively. When t = 2.65 s, Determine: (a) the velocity of point A in polar coordinates (êr and ê), (b) the velocity of point A in rectangular coordinates, (î and ĵ) (setup and use a transformation matrix) (c) the acceleration of point A in polar coordinates (ê, and êŋ) (d) the acceleration of point A rectangular coordinates (î and ĵ)
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![Problem 1
UHart Mechatronics students have developed a robotic arm
programmed to an angular position in polar coordinates with the
relationship = (2/à) sin(πt), where and t are expressed in
radians and seconds, respectively. Simultaneously, the arm is pro-
grammed to extend so that the distance to A follows the relationship
r = 4 + 3e-1.4t, where r and t are expressed in feet and seconds,
respectively. When t = 2.65 s,
Determine:
(a) the velocity of point A in polar coordinates (êr and êŋ),
(b) the velocity of point A in rectangular coordinates, (î and ĵ)
(setup and use a transformation matrix)
(c) the acceleration of point A in polar coordinates (ê, and êŋ)
(d) the acceleration of point A rectangular coordinates (î and ĵ)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9708b71-abb5-451c-8fe8-5ddd0427a311%2F25876e4f-0e86-4e5d-a7ee-3f536f9cdb56%2F40bgh1j_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 1
UHart Mechatronics students have developed a robotic arm
programmed to an angular position in polar coordinates with the
relationship = (2/à) sin(πt), where and t are expressed in
radians and seconds, respectively. Simultaneously, the arm is pro-
grammed to extend so that the distance to A follows the relationship
r = 4 + 3e-1.4t, where r and t are expressed in feet and seconds,
respectively. When t = 2.65 s,
Determine:
(a) the velocity of point A in polar coordinates (êr and êŋ),
(b) the velocity of point A in rectangular coordinates, (î and ĵ)
(setup and use a transformation matrix)
(c) the acceleration of point A in polar coordinates (ê, and êŋ)
(d) the acceleration of point A rectangular coordinates (î and ĵ)
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