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 motionon 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 ladderA fire-fighteris 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, azibx, 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 Coby a parallel to the axis of therevoluterevolute motor that connects B and A.bz = parallel to the axis of therevolute motor that connects B and Cdirected 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).QuantitySymbol Typeax measure of A, 's velocity in NVAby measure of B's angular velocity in AAngle from by to êx with +c, senseC measure of Q's position from CoUse definitions to form the following quantities:CoF =Cx +●C+Q=B+Q=B₂ =A+Q=AQ =N==Lcx +2x +żexX-6x cax +Cx +ConstantConstant0 Variablex Variableje3Ao=fbyBoSince A is not rotating in N.NA0.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 +XӨ1 (0)0c₂Cx +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 (blinear viscous damping constant) and a linear actuator applies a force Fêx on Q from Co.Resultant (net) force on Qz contactmgby + Fycontact Cy + Fzco(Fr-bi) ex=ma Use the clever method (MG road-maps of Section 21.1) shown below to form an equaticand Fzcontact.motion for a while eliminating unknowns FycontactO.cz0c₂C₂Cz

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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

Section: Chapter Questions

Problem 1.1MA

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