Determine the manipulator linear and angular velocity for the 3-DOF articulated armusing Jacobian modelling °T,(0₁)=[G 0 S 07S₁ 0-₁ 001 0 0000 12T,(0₂) =[C₂-S₂ 0 42₂C₂]S₂ C₂0L₂S₂0 1 00 0 1'T(8₂) 00[C, -S, 0 LC₁]S₁ C₂ 0 LS00 1 000019.Z₁0₂.02Xo°T₁ = °T₁¹T₂²T₁ =Zo1₁0₁L₂228PYoL3OriZ3WE[C₁C23 -C₁S23 S₁ C₁ (L₂C₂3 +4₂C₂)]S₁C23 S₁ S23 -C₁S₁ (LC₂3 +4₂C₂)S23C23000L3S₂ + L2₂S₂pa satelyAL-X3

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Mechanical Engineering

Determine the manipulator linear and angular velocity for the 3-DOF articulated arm using Jacobian modelling

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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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

Determine the manipulator linear and angular velocity for the 3-DOF articulated arm
using Jacobian modelling

°T,(0₁)=
[G 0 S 07
S₁ 0-₁ 0
01 0 0
00
0 1
2T,(0₂) =
[C₂-S₂ 0 42₂C₂]
S₂ C₂0L₂S₂
0 1 0
0 0 1
'T(8₂) 0
0
[C, -S, 0 LC₁]
S₁ C₂ 0 LS
00 1 0
0
001
9.
Z₁
0₂.
02
Xo
°T₁ = °T₁¹T₂²T₁ =
Zo
1₁
0₁
L₂
22
8P
Yo
L3
Ori
Z3
WE
[C₁C23 -C₁S23 S₁ C₁ (L₂C₂3 +4₂C₂)]
S₁C23 S₁ S23 -C₁
S₁ (LC₂3 +4₂C₂)
S23
C230
0
0
L3S₂ + L2₂S₂
pa sately
AL
-X3

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