ME 115(a): Solution to Homework #1
(Winter 2009/2010)
Solution to Problem 1: (10 points).
T
T
Let the 2 1 vectors 1 v = 1 v1 1 v2 and 2 v = 2 v1 2 v2 have associated complex representations 1 v = 1 v1 + i 1 v2 and 2 v = 2 v1 + i 2 v2 respectively (where i
ME 115(a): Solution to Homework #2
(Winter 2009/2010)
Problem 1: (15 points). To nd the geometry of the moving centrode of the elliptical
trammel, place a body xed reference frame on the moving link so that its origin lies at the
mid-point of Points A and
ME 115(a): Solution to Homework #3
(Winter, 2009/2010)
Problem 1:
Part (a): Elements of SU (2) have the form:
z
w
(a + ib) (c + id)
=
w z
(c id) (a ib)
where zz + ww = a2 + b2 + c2 + d2 = 1. To show that the matrices
10
01
i0
0 i
01
1 0
0i
i0
form a basis
ME 115(a): Solution to Homework #4
(Winter 2009/2010)
Problem 1: (10 points)
The Euler-Angle representation of the moving bodys orientation is
R = R R R
where R SO(3) represents rotation by angle about the body xed z -axis, R SO(3)
represents rotation by
ME 115(a): Solution to Homework #5
(Winter 2009/2010)
Problem 1:
Each nger applies a wrench to the disk object due to its contact with the disk. Since
we are assuming a frictionless contact, the nger can only apply forces to the disk that are
normal to th
ME 115(a): Homework #6 Solution
Problem 1: (15 points) Find the Denavit-Hartenberg parameters for manipulators (ii) and
(iv) in Figure 3.23 of the MLS text.
Manipulator (ii): The choice of the stationary frame is abitrary. Place its origin along
joint axi