Biomedical Engineering Reference
In-Depth Information
>>
% F consists of the magnitude 10 kN times this unit vector
>>
¼
F
10*unit_vector
¼
F
5.6569 -7.0711 4.2426
>>
% Or, more directly
>>
¼
F
10*(d/norm(d))
¼
F
5.6569 -7.0711 4.2426
>>
% (b) First write the vector r_xz that points from the origin
>>
% to the intersection of F and the xz plane:
>>
r_xz
¼
[12 0 9]
r_xz
¼
12 0 9
>>
% The dot product is given by the sum of all the term by term
>>
% multiplications of elements of vectors F and r_xz
>>
¼
% F_dot_r_xz
sum(F.*r_xz)
>>
% or simply, dot(F,r_xz)
>>
¼
F_dot_r_xz
dot(F,r_xz)
¼
F_dot_r_xz
106.0660
>>
% (c) Cross F with a vector that points from the origin to
>>
% any point along the line of action of vector F.
>>
% The cross product is given by the cross function
>>
¼
r_xz_cross_F
cross(r_xz,F)
¼
r_xz_cross_F
63.6396 0 -84.8528
>>
% Note that the cross product is not commutative
>>
þ
% resulting in different
- signs.
>>
cross(F,r_xz)
ans
¼
-63.6396 0 84.8528
EXAMPLE PROBLEM 4.2
Pointers are sometimes used in biomechanics labs to measure the location of a point in space.
The pointer in Figure 4.6 consists of a rod equipped with two reflective markers, A and B. The
locations of the two reflective markers are provided by a camera-based motion capture system.
Given marker locations A
(669, 191, 120) mm, determine the
location of the pointer tip, T, if marker B is a fixed distance, D, of 127 mm from the pointer tip.
¼
(629,
35, 190) mm and B
¼
Solution
Given marker locations
A
¼
(629, -35, 190) mm
B
¼
(669, 191, 120) mm
Continued
