PME 52600
HW#5
Out:4/29/14
Due:5/12/14
1. A ring of mass M and radius R is pivoted without friction at O so that it can
swing like a pendulum in the plane of the sketch. A small bead of mass m slides
on the ring without friction. It is desire to obtain l
PME 5260
HW#2
Out:3/17/14
Due:3/31/14
1. Shown in Figure 1 is a humanoid robot Nao. Let X bYb Z b , X uYu Z u , and X lYl Z l
be the coordinate frames attached to the robot torso with X bYb Z b in the middle of
the chest, X uYu Z u in the middle of the l
PME 5260
HW#3
Out:3/31/14
Due:4/14/14
1. Fig. 1 depicts a spherical manipulator. Use both the mathematical and the
physical approaches to derive the 6 3 Jacobian matrix which relates the joint
velocity ( 3 1 ) vector to the endpoint velocity ( 6 1 ) vect
Lagrangian
Newton-Euler
2
Newton-Euler
f = ma
(moment)cfw_C
IC
cfw_CIC
&
n = I C + I C
ICcfw_C
&
ICcfw_C
n
3
Newton-Euler
&
k = k 1 + k qk z k 1
kcfw_k
k-1cfw_k-1
k= 0k= 1