Problem 1 Mechatronics students have developed a robotic arm programmed to an angular position in polar coordinates with the relationship = (2/) sin(ät), 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 (ê, 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)
Problem 1 Mechatronics students have developed a robotic arm programmed to an angular position in polar coordinates with the relationship = (2/) sin(ät), 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 (ê, 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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 1
O Mechatronics students have developed a robotic arm
programmed to an angular position in polar coordinates with the
relationship 0 = (2/л) sin(t), 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 (ê, 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)
B
A
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