Section 8.1). Motion of a firefighter on a robotic ladder. (understanding definitions The following figure shows a fire truck chassis A traveling a constant speed) in straight-line motion on Earth (A does not rotate relative to Earth). Earth is a Newtonian reference frame N. A rigid hub B is connected to fire truck A by a revolute motor at point/B, of B. is connected to hub B by a revolute motor at point/C. of C (modeled as a particle of mass m climbs ladder C. A rigid ladder A fire-fighter Right-handed orthogonal unit vectors âx, ây, azi bx, by, bz: êx, cy, C; are fixed in A, B, C, with: a pointing forward on the fire truck a vertically-upward and from Bo to Co by a parallel to the axis of the revolute motor that connects B and A C parallel to the axis of the revolute motor that connects B and C = directed from Co to Q (along the ladder) • b₂ Ao âx by X 0 bx rulor)
Section 8.1). Motion of a firefighter on a robotic ladder. (understanding definitions The following figure shows a fire truck chassis A traveling a constant speed) in straight-line motion on Earth (A does not rotate relative to Earth). Earth is a Newtonian reference frame N. A rigid hub B is connected to fire truck A by a revolute motor at point/B, of B. is connected to hub B by a revolute motor at point/C. of C (modeled as a particle of mass m climbs ladder C. A rigid ladder A fire-fighter Right-handed orthogonal unit vectors âx, ây, azi bx, by, bz: êx, cy, C; are fixed in A, B, C, with: a pointing forward on the fire truck a vertically-upward and from Bo to Co by a parallel to the axis of the revolute motor that connects B and A C parallel to the axis of the revolute motor that connects B and C = directed from Co to Q (along the ladder) • b₂ Ao âx by X 0 bx rulor)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Problem 1.1MA
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![7.20 Motion of a firefighter on a robotic ladder. (understanding definitions - Section 8.1).
The following figure shows a fire truck chassis A traveling at constant speed) in straight-line motion
on Earth (A does not rotate relative to Earth). Earth is a Newtonian reference frame N.
A rigid hub B is connected to fire truck A by a revolute motor at point B, of B.
A rigid ladder
A fire-fighter
is connected to hub B by a revolute motor at point/Co of C
(modeled as a particle of mass my climbs ladder C.
Right-handed orthogonal unit vectors ax, ay, azi
bx, by, bz: êx, Cy, Cz; are fixed in A, B, C, with:
• a pointing forward on the fire truck
●
a vertically-upward and from Bo to Co
by a parallel to the axis of the
revolute
revolute motor that connects B and A
.bz = parallel to the axis of the
revolute motor that connects B and C
directed from Co to Q (along the ladder)
Note: Visualize C's "Body yz" (or Space zy) rotation sequence in N (e.g., physically demonstrate with a ruler).
Quantity
Symbol Type
ax measure of A, 's velocity in N
VA
by measure of B's angular velocity in A
Angle from by to êx with +c, sense
C measure of Q's position from Co
Use definitions to form the following quantities:
CoF =
Cx +
●
C+Q=
B+Q=
B₂ =
A+Q=
AQ =
N==
Lcx +
2x +
żex
X-6x c
ax +
Cx +
Constant
Constant
0 Variable
x Variable
je
3
Ao
=
fby
Bo
Since A is not rotating in N.NA
0.
Since A = VA ay is constant in N. a = 0.
Hence, every point of A has 0 acceleration in N.
Thus, A is also a Newtonian reference frame.
0cy +
0cy +
(Note: Rotational kinematics are in Homework 6.12).
0 ĉy +
r0cy +
[20i+x0y +
Cx +
xocy +
Cx+ [wr sin(0) cos(0) +20+x]cy +
X
Ө
1 (0)
0c₂
Cx +
xocy +
Cx+ [wx sin(0) cos(0) +20+x0]êcy +
Consider the situation when resistance to Q's motion on the wet ladder is modeled -bicx (b
linear viscous damping constant) and a linear actuator applies a force Fêx on Q from Co.
Resultant (net) force on Q
z contact
mgby + Fycontact Cy + Fzco
(Fr-bi) ex
=ma Use the clever method (MG road-maps of Section 21.1) shown below to form an equatic
and Fzcontact.
motion for a while eliminating unknowns Fycontact
O.cz
0c₂
C₂
Cz](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd30ea730-ba6b-4d49-90df-80ffc6e77ea4%2F59e784a4-347b-462d-85da-ffacc7a3db02%2Fwsmlk3j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.20 Motion of a firefighter on a robotic ladder. (understanding definitions - Section 8.1).
The following figure shows a fire truck chassis A traveling at constant speed) in straight-line motion
on Earth (A does not rotate relative to Earth). Earth is a Newtonian reference frame N.
A rigid hub B is connected to fire truck A by a revolute motor at point B, of B.
A rigid ladder
A fire-fighter
is connected to hub B by a revolute motor at point/Co of C
(modeled as a particle of mass my climbs ladder C.
Right-handed orthogonal unit vectors ax, ay, azi
bx, by, bz: êx, Cy, Cz; are fixed in A, B, C, with:
• a pointing forward on the fire truck
●
a vertically-upward and from Bo to Co
by a parallel to the axis of the
revolute
revolute motor that connects B and A
.bz = parallel to the axis of the
revolute motor that connects B and C
directed from Co to Q (along the ladder)
Note: Visualize C's "Body yz" (or Space zy) rotation sequence in N (e.g., physically demonstrate with a ruler).
Quantity
Symbol Type
ax measure of A, 's velocity in N
VA
by measure of B's angular velocity in A
Angle from by to êx with +c, sense
C measure of Q's position from Co
Use definitions to form the following quantities:
CoF =
Cx +
●
C+Q=
B+Q=
B₂ =
A+Q=
AQ =
N==
Lcx +
2x +
żex
X-6x c
ax +
Cx +
Constant
Constant
0 Variable
x Variable
je
3
Ao
=
fby
Bo
Since A is not rotating in N.NA
0.
Since A = VA ay is constant in N. a = 0.
Hence, every point of A has 0 acceleration in N.
Thus, A is also a Newtonian reference frame.
0cy +
0cy +
(Note: Rotational kinematics are in Homework 6.12).
0 ĉy +
r0cy +
[20i+x0y +
Cx +
xocy +
Cx+ [wr sin(0) cos(0) +20+x]cy +
X
Ө
1 (0)
0c₂
Cx +
xocy +
Cx+ [wx sin(0) cos(0) +20+x0]êcy +
Consider the situation when resistance to Q's motion on the wet ladder is modeled -bicx (b
linear viscous damping constant) and a linear actuator applies a force Fêx on Q from Co.
Resultant (net) force on Q
z contact
mgby + Fycontact Cy + Fzco
(Fr-bi) ex
=ma Use the clever method (MG road-maps of Section 21.1) shown below to form an equatic
and Fzcontact.
motion for a while eliminating unknowns Fycontact
O.cz
0c₂
C₂
Cz
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