Consider the two-link arm above that operates in the 2D plane defined by this page. Assuming: • the origin of the global frame is at the arm's anchor point with the table (thicker blue rectangle), with y-axis upwards and x-axis pointing to the right, • the arm has one motor in each joint (indexed by theta one and two as shown), the joint angles have zero angles for their respective theta when the arm is straight upwards, • the joints have limits, o the first link cannot rotate through the table (max 6, = , min 0, =), o the second link cannot rotate through the first link (max 02 = TI, min 02 = -n), collisions are not allowed (the arm cannot poke into or through the table), the tasks all involve the end-effector, that is the orange/yellow ball at the end of the %3D %3D arm, and • each "link" in the arm has length one. Write the: a) state space, b) action space, c) forward kinematics function and, d) inverse kinematics function for this robot. For spaces, use vector notation. For the functions, give the “specs" (return value and function arguments), as well as pseudo-code or some simple equations for the function body.
Consider the two-link arm above that operates in the 2D plane defined by this page. Assuming: • the origin of the global frame is at the arm's anchor point with the table (thicker blue rectangle), with y-axis upwards and x-axis pointing to the right, • the arm has one motor in each joint (indexed by theta one and two as shown), the joint angles have zero angles for their respective theta when the arm is straight upwards, • the joints have limits, o the first link cannot rotate through the table (max 6, = , min 0, =), o the second link cannot rotate through the first link (max 02 = TI, min 02 = -n), collisions are not allowed (the arm cannot poke into or through the table), the tasks all involve the end-effector, that is the orange/yellow ball at the end of the %3D %3D arm, and • each "link" in the arm has length one. Write the: a) state space, b) action space, c) forward kinematics function and, d) inverse kinematics function for this robot. For spaces, use vector notation. For the functions, give the “specs" (return value and function arguments), as well as pseudo-code or some simple equations for the function body.
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:Consider the two-link arm above that operates in the 2D plane defined by this page. Assuming:
• the origin of the global frame is at the arm's anchor point with the table (thicker blue
rectangle), with y-axis upwards and x-axis pointing to the right,
• the arm has one motor in each joint (indexed by theta one and two as shown),
the joint angles have zero angles for their respective theta when the arm is straight
upwards,
• the joints have limits,
o the first link cannot rotate through the table (max 6, = , min 0, =),
o the second link cannot rotate through the first link (max 02 = TI, min 02 = -n),
collisions are not allowed (the arm cannot poke into or through the table),
the tasks all involve the end-effector, that is the orange/yellow ball at the end of the
%3D
%3D
arm, and
• each "link" in the arm has length one.
Write the:
a) state space,
b) action space,
c) forward kinematics function and,
d) inverse kinematics function
for this robot. For spaces, use vector notation. For the functions, give the “specs" (return value
and function arguments), as well as pseudo-code or some simple equations for the function
body.
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