A two-link mechanism (AB and BC) makes contact with a disk of radius R = 0.1 m at point C (a distance R from the center axle around which it rotates). The arm causes the disk to move at an angular rate of p about point D. Suppose the links have length L = 0.2 m and a servomotor rotates link AB at a known rate of = AB= -30 rad /s (CW). At the instant shown, link BC is horizontal and link AB makes an angle = 60 deg with the horizontal. L L 0 ΙΩΑΒ Define the following reference frames: 0 'B SAB b₁ R L d3 аз Од 1. What is the speed vc of point C and the angular rate Iw at which link BC is rotating? Hint: The inertial velocity of point C at the instal shown is Ivc/o = vci1 SD and can be related to the velocity and position observed in frame B via Ivc/o = IUB/0+ I wB x TC/B and we can further expand IvB/O in terms of the observations from frame A as: INC/O = IVA/O + I wA XrB/A + I wB xrC/B Equate the first and last form of Ivc/o by expressing both using vectors of the I frame. 2. How fast is the disk is rotating? (1) (2) (3) Hint: Express the velocity Ivc/o again, but from the perspective of a frame D that rotates with point C. Express Ivc/o using vectors of the I frame and equate to your previous expression from the first part.
A two-link mechanism (AB and BC) makes contact with a disk of radius R = 0.1 m at point C (a distance R from the center axle around which it rotates). The arm causes the disk to move at an angular rate of p about point D. Suppose the links have length L = 0.2 m and a servomotor rotates link AB at a known rate of = AB= -30 rad /s (CW). At the instant shown, link BC is horizontal and link AB makes an angle = 60 deg with the horizontal. L L 0 ΙΩΑΒ Define the following reference frames: 0 'B SAB b₁ R L d3 аз Од 1. What is the speed vc of point C and the angular rate Iw at which link BC is rotating? Hint: The inertial velocity of point C at the instal shown is Ivc/o = vci1 SD and can be related to the velocity and position observed in frame B via Ivc/o = IUB/0+ I wB x TC/B and we can further expand IvB/O in terms of the observations from frame A as: INC/O = IVA/O + I wA XrB/A + I wB xrC/B Equate the first and last form of Ivc/o by expressing both using vectors of the I frame. 2. How fast is the disk is rotating? (1) (2) (3) Hint: Express the velocity Ivc/o again, but from the perspective of a frame D that rotates with point C. Express Ivc/o using vectors of the I frame and equate to your previous expression from the first part.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:A two-link mechanism (AB and BC) makes contact with a disk of radius R = 0.1 m at point C (a
distance R from the center axle around which it rotates). The arm causes the disk to move at an
angular rate of p about point D. Suppose the links have length L = 0.2 m and a servomotor
rotates link AB at a known rate of 0 =AB= -30 rad /s (CW). At the instant shown, link BC is
horizontal and link AB makes an angle 0 = 60 deg with the horizontal.
L
a3
L
0
Define the following reference frames:
SAB
b3
2022
16₂
'B
NAB
R
b₁
L
d₂
d₁
d3
SD
1. What is the speed vc of point C and the angular rate Iw at which link BC is rotating?
Hint: The inertial velocity of point C at the instal shown is
Ivc/o = vci1
and can be related to the velocity and position observed in frame B via
INC/O = ¹VB/O+ IWB X TC/B
and we can further expand IVB/O in terms of the observations from frame A as:
Ivc/o = IVA/O+ I w₁A XrB/A + Iw³ x rc/B
Equate the first and last form of Ivc/o by expressing both using vectors of the I frame.
2. How fast is the disk is rotating?
(1)
(2)
(3)
Hint: Express the velocity Ivc/o again, but from the perspective of a frame D that rotates with
point C. Express Ivc/o using vectors of the I frame and equate to your previous expression from
the first part.
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