MMAE 350
D. Rempfer
Problem Set IV
Page 1 of 4
Due Date: October 11, 2006
1.
We consider a robotarm problem similar to the
one discussed in class (see picture). A robot arm
consisting of two segments of length
r
and
l
is con
trolled by adjusting the length of the two actuators
a
1
and
a
2
such that a desired position (
p
x
, p
y
) of
the tip of the arm is obtained.
Write the M
AT

LAB
code that is necessary to find the actuator
lengths
s
1
,
s
2
of actuator
a
1
and
a
2
, respectively,
given the position of the endpoint of the robot
arm, (
p
x
, p
y
), and the lengths of the two segments
of the arm,
r
and
l
. You can do this by following
these steps:
l
r
d
a
2
a
1
y
x
r/2
r/2
a.
Write a M
ATLAB
mfile
rpos
that computes the position of the robot arm given the input
parameters
r
,
l
, and a vector containing
s
1
and
s
2
.
As its output, the function should
return a single vectorvalued variable containing the
x
 and
y
position of the robot arm
as its components. You may want to make sure the input lengths
s
1
and
s
2
are restricted
appropriately (both must be positive, there are obvious restrictions on the allowed lengths
for actuator
a
2
, and you may assume that the first robot arm (of length
r
) only moves within
the first quadrant of the coordinate system shown).
b.
Write a M
ATLAB
mfile
drpos
that computes the Jacobian matrix of the function
rpos
,
given the same input parameters as for
rpos
. As its output, this function should return a
single matrixvalued variable containing the 4 elements of the Jacobian.
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 Spring '05
 rempher
 Numerical Analysis, Triangular matrix, robot arm

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