ECE 470: Homework 7
Due Tuesday, December 1
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 7
1
Give an expression for the interaction matrix of two points p1 and p2 that satisfies
u 1
v 1
u 2
v 2
T
= L
in which cfw_u1 , v1 and cfw_u2
ECE 470: Homework 4
Solutions
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 4
1
Given a wrist center oc , nd the inverse position kinematics.
Given oc = [xc
yc
zc ]T ,
d1
d3
d2
zc
= xc .
yc
2
Given a wrist center oc , nd the inverse position kinemati
ECE 470: Homework 5
Due Tuesday, October 27
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 5
1
Consider a camera with focal length = 1. Suppose the optical axis of the camera is aligned with the
world x-axis, the camera x-axis is paral
ECE 470: Homework 2
Solutions
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 2
1
The frames for each link must be chosen with respect to the DH convention,
DH1 : xi+1 perpendicular to zi ,
DH2 : xi+1 intersects zi .
There is some choice in assignment of
ECE 470: Homework 3
Due Tuesday, September 29
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 3
1
Show that eS is in SO(3) if and only if S is in so(3). The following may be useful:
1. Jacobis formula: det(eM ) = etr(M ) ,
2. eM eM = eM
ECE 470: Homework 1
Solutions
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 1
1
A free vector is dened by the subtraction of two points in a given coordinate system, e.g., v = p1 p2 .
1 (a)
T
Using the fact that v1 v2 = v1 v2 , show that the dot produc
ECE 470: Homework 4
Due Thursday, October 8
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 4
1
Given a wrist center oc , nd the inverse position kinematics of Figure 1.
Figure 1: Three-linke rectangular manipulator.
2
Given a wrist cen
ECE 470: Homework 2
Due Thursday, September 17
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 2
Consider the the following manipulators, and derive the forward kinematic equations using DH convention.
Use of Robotica.m or symbolic Matl
ECE 470: Homework 1
Due Tuesday, September 8
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 1
1
A free vector is dened by the subtraction of two points in a given coordinate system, e.g., v = p1 p2 .
1 (a)
T
Using the fact that v1 v2 =
ECE 470: Homework 7
Due Tuesday, December 1
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 7
1
Give an expression for the interaction matrix of two points p1 and p2 that satisfies
u 1
v 1
u 2
v 2
T
= L
in which cfw_u1 , v1 and cfw_u2
ECE 470: Homework 3
Due Tuesday, September 29
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 3
1
Show that eS is in SO(3) if and only if S is in so(3). The following may be useful:
1. Jacobis formula: det(eM ) = etr(M ) ,
0
0
2. eM eM
ECE 470: Homework 6
Solutions
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 6
1
Suppose that q is a solution to = J q for m < n.
Show that q + (I J + J)b is also a solution to = J q for any b Rn .
Show that b = 0 gives the solution that minimizes the
ECE 470: Homework 6
Due Thursday, November 12
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 6
1
Suppose that q is a solution to = J q for m < n.
Show that q + (I J + J)b is also a solution to = J q for any b Rn .
Show that b = 0 giv
ECE 470: Homework 5
Due Tuesday, October 27
in class @12:30pm
Seth Hutchinson
Luke A. Wendt
ECE 470 : Homework 5
1
Consider a camera with focal length = 1. Suppose the optical axis of the camera is aligned with the
world x-axis, the camera x-axis is paral