Consider the manipulator provided in the figure. Given the Position vector P w.r.t. to the base frame, derive the Analytical Jacobian for the position. Write your answer as J = [dpx/dq1 dpx/dq2 dpx/dq3; dpy/dq1 dpy/dq2 dpy/dq3; dpz/dq1 dpz/dq2 dpz/dq3]

Consider the manipulator provided in the figure. Given the Position vector P w.r.t. to the base frame, derive the Analytical Jacobian for the position. Write your answer as J = [dpx/dq1 dpx/dq2 dpx/dq3; dpy/dq1 dpy/dq2 dpy/dq3; dpz/dq1 dpz/dq2 dpz/dq3]

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

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works on a structure comes under the categories of loading. The external load generates its effects as stress and strain in the structure.

Question

Consider the manipulator provided in the
figure. Given the Position vector P w.r.t. to
the base frame, derive the Analytical
Jacobian for the position. Write your answer
as
J = [dpx/dq1 dpx/dq2 dpx/dq3; dpy/dq1
dpy/dq2 dpy/dq3; dpz/dq1 dpz/dq2 dpz/dq3]
%3D
Z3, Z4
Z1, Y,
b,s, +b;C;82
-b,c +b3S152
-b;C2
X4
YA
#3
b2
b3
O2, 02
P =
#2
Z, Y3
#0

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