ECE 194D
Homework 4 – Extra Credit Quiz Review
Due in class, Tues. May 24
Page 1 of 5
Homework 4 – Extra Credit
Problem 1
This problem involves the standard, 2-link, planar robot arm we’ve discussed several
times in class.
Figure 1 shows a cartoon of an arm, where
θ
1
is the absolute angle of link 1, with
respect to the
x
axis, and where
θ
2
is the relative angle of link 1, with respect to
θ
1
. (Both angles
are measured in the counter-clockwise direction.) Lengths are intentionally NOT drawn to scale!
Fig. 1:
Link lengths, L
1
and L
2
, are
not
drawn to scale, and angles do not correspond to the solution configuration!
Say you have a 2-link arm that is in a geometric configuration such that the Jacobian is:
ܬ ൌ ቂ
െ3.5
െ1.5
2
3
ቃ
a) Sketch the 2-link arm corresponding to this Jacobian (to scale). Label the coordinates of the
elbow (x
m
, y
m
) and of the end effector (x
e
, y
e
). Recall:
ߦ
ሶ
ൌ ܬݍ
ሶ
. Here,
ߦ ൌ ቂ
ݔ
ݕ
ቃ
and
ݍ ൌ
ߠ
ଵ
ߠ
ଶ
൨
.

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ECE 194D
Problem
a) For th
are requi
b) Derive
are no ap
Also assu
Fig. 2 – Th
Defini

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