ECE 455/655, Fall 2009, Assignment 5
Due: in class, Thursday 10/29/09
1. For the planar three degree of freedom (RRP) manipulator considered in Assignment 2,
problem 2, find the Jacobian Segment [ ]
v
J relating the joint velocities 12 3
[, , ]
T
d
θθ
=q
to
the end effector linear velocities [ , ]T
x
y=x
(note: find [ ]
v
J and not [ ]J
ω
) by the
following methods:
(a) by direct differentiation of ()
f
=
xqin solutions 2;
(b) from the forward kinematics information in solutions 2, using the formulae
derived in class for the columns of [ ]
v
J.
2. For the planar three degree of freedom (PRP) manipulator considered in Assignment 2,
problem 3, find the Jacobian Segment [ ]
v
J relating the joint velocities 12 3
[, , ]
T
dd
θ
=q
to
the end effector linear velocities [ , ]T
x
y=x
(note: find [ ]
v
J and not [ ]J
ω
) by the
following methods:
(c) by direct differentiation of ( )
f
=
xqin solutions 2;
(d) from the forward kinematics information in solutions 2, using the formulae
derived in class for the columns of [ ]
v
J.
3. For the six degree of freedom (PPPRRR) manipulator considered in Assignment 3
problem 2, find the Jacobian Segment [ ]
v
J relating the joint velocities
12 3456
[, , , , ,]
T
ddd
θ
θθ
=q
to the end effector linear velocities [ , , ]T
x
yz=x
(note: find [ ]
v
J
and not [ ]J
ω
).
