ME 482/582
Chapter 2 HW
August 24, 2011
Chapter 2 HW Hints
Problem 2.1 Get the rotation matrices from text equation (2.77)-(2.79) and make sure to apply them in the correct
order. Note that rst rotation should be the rst R matrix to act on position vector
ME 482/582
Chapter 7 HW
November 23, 2011
Chapter 7 HW Hints
NOTE: The MATLAB function
Y = polyval(P,X)
is useful for evaluating polynomials like the ones used in this homework.
Parameter P is the vector of polynomial coecients, but it is arranged from h
ME 482/582
Chapter 6 HW
November 21, 2011
Chapter 6 HW Solution
Starr Problem. The gure below shows the RR manipulator with attached link frames. There are also frames cfw_C1
and cfw_C2 at the center of the links (with the same orientation as frames cfw
ME 482/582
Chapter 6 HW
November 14, 2011
Chapter 6 HW Problems and Hints
Starr Problem. Consider the 2-DOF RR manipulator shown in Figure 1 below. All link frames are indicated in
Figure 1. Angle 1 is shown in the gure, and positive angle 2 moves link 2
ME 482/582
Chapter 5 HW
November 7, 2011
Chapter 5 HW Solution
Problem 5.1. If you take the Jacobian in frame cfw_0 from (5.67), then set its determinant to zero, you will obtain the
same singular positions as in frame cfw_3. This must be true because sin
ME 482/582
Chapter 5 HW
October 26, 2011
Chapter 5 HW Hints
5.1. This problem refers to Example 5.4, not 5.3. Basically its asking whether the singularities of 0 J are the same as
those of 3 J. Think about whether the existence of singularities is depende
ME 482/582
Chapter 4 HW
September 30, 2011
Chapter 4 HW Solution
Problem 4.7. Repeatability is aected by:
Steady-state error in joint servo controllers
Backlash in gears
Clearance in bearings
Noise in joint sensors
Thermal eects
Accuracy is aected by
ME 482/582
Chapter 4 HW
September 21, 2011
Chapter 4 HW Hints
Problem 4.7. Be sure you understand the dierence between repeatability and accuracy.
Problem 4.8. If you add an additional joint and x the last link, the remainder of the mechanism behaves like
ME 482/582
Chapter 3 HW
September 19, 2011
Chapter 3 HW Solution
Problem 3.1. Use the link frame assignments shown in text Figure 3.7, with the corresponding link parameters
in Figure 3.8, and substitute into equation (3.6). Although we could use 3 3 T ma
ME 482/582
Chapter 3 HW
September 9, 2011
Chapter 3 HW Hints
Problem 3.1. This is the same planar robot thats used for the Programming Exercises, so you can make use of this
work for your programs also. The link frame assignments are shown in Figure 3.7,
ME 482/582
Chapter 2 HW
September 7, 2011
ME 482/582 Chapter 2 HW Solution
2.1 These are both rotations relative to the reference frame, so we premultiply :
c
R = RX ()RZ ()I = cs
ss
s
cc
sc
0
s
c
(1)
The I (identity) matrix in (1) represents the original
ME 482/582
Chapter 7 HW
December 2, 2011
Chapter 7 HW Solution
Problem 7.2. This is a straightforward application of
tting a cubic polynomial to a rest-to-rest motion. Using
the following boundary conditions:
i = 5 ,
f = 80 ,
i = 0,
f = 0
(1)
we get the